At comment 60 in this thread about self-described atheistic materialists who want portray themselves as being moral yet having no basis by which to be moral in any objective sense, Seversky says in response:
“However, it is a choice between able to be good in a way that actually means something and actually matters,…” to whom? That’s always the unspoken part of such a claim. Meaning only exists in the mind of the beholder and something or some one only matters to some one. Believers fell better if they believe that their lives have meaning and matter, which means they need a Creator to whom they matter.
Notice that, according to Seversky, meaning is an entirely subective pheonomena. IOW, in Seversky’s worldview, being good an entirely subjective narrative. It only exists in a person’s mind. There is no means by which anyone can be “good” in a way that is objectively valid and objectively meaningful (meaning, it is good to the mind that is the ground of existence, or god).
In the very next paragraph of his response, Seversky attempts to portray an atheist’s happiness as somehow more real than a theist’s happiness, as if the quality or value of ones experience of happiness would be increased if it referred to something objectively real. He uses a quote from Karl Marx to attempt to get his point across:
The abolition of religion as the illusory happiness of the people is the demand for their real happiness. To call on them to give up their illusions about their condition is to call on them to give up a condition that requires illusions. The criticism of religion is, therefore, in embryo, the criticism of that vale of tears of which religion is the halo.
So, after I make the point that being good would have more validity and meaning if it referred to an objectively real commodity, Seversky shoots that down by insisting that being “good” can only be a subjective narrative. Yet, he seems to think that happiness – which which would obviously also be a subjective state of mind in his worldview – can be of a higher quality if it was generated by a correspondence to objective reality (giving up illusions, as Marx said).
In that thread’s OP I said:
This is the tragic nature of the good, moral atheist; they want their good acts to be somehow more real or better than an act a religious fanatic considers and feels is good, but alas, under the logical ramifications of atheistic materialism, their good acts would be the factual, physico-chemical equivalents of Jihadis who felt they were doing good by driving planes into buildings. There is no source distinction between any act anyone does.
Seversky seems to agree with this about morality, but is apparently holding on to the idea that happiness is somehow different; that the happiness generated by physico-chemical processes under an atheist/materialist narrative is somehow of better quality than the happiness experienced by theists, as if the happenstance correspondence of one set of chemically-produced beliefs to physical reality would necessarily mean a concomitant better quality of happiness. Seversky is apparently asserting that the quality of ones mental state of happiness is proportional to how closely ones beliefs happen to comport with physical reality. Seversky is free to try and support this assertion, but we all know he cannot. All this can possibly be is part of Seversky’s anti-theistic narrative; there’s no reason (that I know of) to believe that a theist’s happiness is somehow of less quality than an atheist’s. Nor is there any reason to believe that theism confers any evolutionary disadvantage.
Under atheistic materialism, there are no bonus points after you die for believing things that happen to be true, or that happen to correspond to factual reality. Seversky’s only recourse then, in countering what he refers to as my “Pascal’s Wager” style argument, is that atheistic materialism somehow bestows a happiness quality advantage during life. Perhaps he might extend that argument to include some other ways that atheistic materialism produces some real-world experiential advantage. I’d like to see him or any other atheistic materialist try to make that argument either through logic or some kind of scientific evidence. It is nothing more than a materialist myth.
The theme here is that for atheistic/materialists it appears to be important to their mythic narrative that atheistic/materialism conveys upon them some sort of meaningful experiential advantage over theists; that somehow, in some real sense, atheism is superior to theism and that it somehow demonstrates some sort of individual superiority (at least in the sense of setting aside “illusions” – which is a recurring theme.). The problem is that the nature of their worldview logically precludes that from even possibly being the case; they cannot deliberately understand and accept true things because their consciousness, sense of free will and responsibility are illusions generated by uncaring matter.
Note how the illusion of self, self-determination and free will that refers to itself as “Seversky” claims that illusions such as he can “set aside” false, illusory beliefs and reap some kind of factual benefit. This is an enormous metaphysical myth – that somehow something that is itself an illusion can set aside illusions and see and understand “the truth”, and that such a recognition will be somehow substantively rewarded in some way that escapes other illusions of self that refer to themselves as theists, as if some illusions of self are better than other illusions of self, and as if such a difference substantively matters.
If atheistic materialism is true, then we all have the beliefs we have and act the way we act because such things are caused by physico-chemical forces that have no regard for the truth-value of such thoughts and beliefs. Additionally, there is no “I” that has supernatural power over what these materials and forces happen to generate. It’s not like we would have the power to stop a physical process from producing a false belief because that belief is false; our idea that it is false would also be a sensation produced by the same blind physico-chemical forces that produced the false belief in the first place. Those forces equally produce true and false beliefs and thoughts (wrt factual reality) and also generate our ideas that such thoughts are true and false. If factually true beliefs happen to coexist with a higher-quality experience of happiness, how on Earth would one evidence such a claim, or be confident that the view of the evidence and logic wasn’t actually false?
It’s far more likely (under Seversky’s worldview) that false beliefs confer some sort of experiential advantage because, if atheistic materialism is true, that is what nature has actually selected for – the supposedly false belief that god and/or a supernatural world exists. Also, Seversky seems to think that it is important to have true beliefs rather than false ones; but why? Surely he realizes there is no factual basis for the claim that holding a true beliefs confers a better quality of experiential happiness. Why bother defending the idea that if a programmed biological automaton happens to think things in correspondence with reality that this also happens to correspond with a better quality of (ultimately) illusory happiness? So what if it does? If Seversky’s worldview is true, our levels of happiness are entirely caused by forces beyond our illusory sense of control and self-determination. In fact, individual happiness itself is an illusory experience of an illusory self; yet Seversky claims the sense of happiness of one illusion of selfhood is less illusory than that experienced by another illusion of selfhood.
What the take-home point here is that Seversky and others, even though they assert themselves atheistic materialists, still argue and act as if they and others have some supernatural power to deliberately discern true beliefs from false and deliberately overpower the physico-chemical processes of the brain to force them to correspond to true beliefs; that true beliefs somehow magically confer a better quality of experiential happiness; that true beliefs are somehow magically necessary or important when it comes to life and the human species. It is just as likely that false beliefs are necessary both to long-term survival and for higher quality experience of happiness, and that atheistic materialism is an evolutionary dead-end that cannot compete with religious faith when it comes to factually thriving in the real world because it corresponds to physical reality.
The idea that “truth” can be deliberately obtained, forced onto physico-chemical processes, and that it confers upon illusory “selves” a higher quality happiness or evolutionary advantage is an enormous materialist fantasy. For them, truth is the equivalent of a magical commodity capable of overriding, transforming and guiding physico-chemical processes, and they have utter faith in its ability confer both immediate and long-term benefits to them and humanity. One wonders if materialists ever thought that, in an actual materialist world, perhaps an illusion of self working under the illusion of self-will with chemically-caused thoughts might actually require false beliefs in order to function successfully and thrive in the factual world, and that is why such beliefs are so widespread and so pervasive historically?
Well, no. Because whether they admit it or not, whether they realize it or not, they still think truth is in itself some sort of transcendental, supernatural commodity that fundamentally matters and necessarily affects our lives in a positive way if we can deliberately ascertain it and live by it.
Your title begins “Atheists Believe …”.
The first line of actual content seems to say that this is based on a single comment.
The post surely looks like a sweeping generalization.
Neil,
I’ve engaged in several discussions with many atheists that have expressed the same view that believing the truth (supposedly, the truth about an atheistic, materialist existence) confers some sort of advantage or bonus. In fact, virtually every atheist I’ve ever engaged has expressed this sentiment. Indeed, the condescension and ridicule atheists often heap upon theists implies this very idea.
And, no it’s not a sweeping generalization; many atheists do in fact believe there is some sort of benefit in such “truthful” beliefs, else why argue and advocate as if others should also adopt these beliefs?
So Seversky is saying his chemical reactions are better than my chemical reactions. How do we test that in the absence of any objective standard?
William J Murray,
Indeed, even if we grant the materialist an emergent “I”, his position still fails to make sense, since, such an “I” finds itself surrounded by brain chemicals — NOT by thoughts, meaning and logic. IOWs the emergent “I” has no direct access the faculty of thought. The emergent “I” must first manipulate brain chemistry in order to produce thought.
Even if we grant the materialist an emergent “I”, with the power of manipulating brain chemistry in order to produce thoughts, his position still fails to make sense, since, in this concept the manipulation of chemistry precedes thought. No one can manipulate brain chemistry in order to produce coherent thoughts, without planning and thinking.
Atheists have always believed in magic such as abiogenesis, Darwinian evolution, and the laughable notion that the big bang came into existence on its very own accord…out of nothing.
Check out a recent article posted at EvolutionNews.org regarding how atheists are – yet again – appealing to magic to explain the Cambrian Explosion. Here’s a snippet:
“Absence of evidence is not evidence of absence, some scientists like to say.” That’s fine. But if you want to make a case for a long fuse leading up to the explosive appearance of 18 or more animal phyla, sooner or later you need to show evidence. Three hoped-for classes of evidence have now been called into question by evolutionists themselves: the molecular clock, Ediacaran fossil connections, and now trace fossils. After 157 years of fossil hunting since Darwin, the reality of the explosion remains the best supported conclusion from the available evidence.”
Here’s the link:
http://www.evolutionnews.org/2.....03167.html
WJM,
Surely you accept that true beliefs are important in some cases?
For example, knowing whether or not the barista gave you the correct change; whether you are standing 10 feet or 1 inch from the edge of the Grand Canyon, and so on?
daveS @6,
“True beliefs”, in the context of the OP, are metaphysical beliefs; such as atheism and theism.
In short, WJM’s point is that, assuming that atheism is true, there are no bonus points for holding the correct belief (atheism).
Thanks, Origenes.
I think it’s odd for an atheist to claim those of his persuasion are happier. They strike me, more often than not, as miserable. I once heard one honestly state in a public debate that he was jealous of the happiness and contentment his Christian sister demonstrated.
This article reports a much higher suicide rate among atheists:
The tendency toward isolation mentioned above reminds me of Proverbs 18:1
What is there in atheism to possibly be happy about? The idea that there is no purpose and meaning in life is depressing.
https://www.youtube.com/watch?v=lL0041GDsqE
How can a fully evolved brain be a reliable truth detector in the first place? Its only interest is survival.
I really think atheists who deny free will and personhood should be listed as a irrational cult. The fact that they can’t see the incoherence of their world view is amazing. It is essentially allowing yourself to believe you do not exist. As Ravi Zacharias addressed one such inquirer, “Who, shall I say then, is asking the question?”
Didn’t you used to believe this garbage WJM. I think it is fortunate that even though my fascination with science started from boyhood, I was never infected with this irrationality. I just can not comprehend how any rational mind gets fooled into believing this materialistic crap. Can’t they see that by denying free will, and essentially denying personhood, they saw off the only limb they have to stand on? Perhaps you can comment on how it is possible to live and function on the other side, because I have to admit I just don’t get it.
I am really at a loss to understand how anyone can believe this garbage.
daveS said:
Under the premise of atheistic materialism, what does it matter what the content of my beliefs are in those situations, daveS? Under atheistic materialism, the content of my beliefs are effects, the illusory sensations of an illusory self. They are not in command or control of the behavior of my body, nor need they even be consistent from one moment to the next. As long as my body acts in a fashion that perpetuates its survival, what difference does it make what delusional world I experience mentally? Who knows what my body might be or what it might actually be doing while I imagine I am a sentient human being acting in a deliberate fashion?
JDH @11 said
Unfortunately, believed it and lived as if it was true, much to my regret.
WJM,
Really? Did you believe this when you were an atheist?
That’s not what I believe, for the record.
As to
And he is sadly mistaken in his belief that atheism makes you happier:
Of related note, increased belief in the reality of the afterlife has been shown to have positive mental benefits:
as to:
Indeed, if atheistic materialism were true it would result in catastrophic epistemological failure:
as to:
Indeed, Atheists can not possibly consistently live as if atheism were actually true, therefore atheism must be a delusion.
as to:
And indeed ‘the Truth’ does matter very much, but it is ‘the Truth’ that most atheists I’ve debated on UD are trying their best to run away from, i.e. ‘the Truth’ of Christianity in particular:
Verse, video, and music:
What do you believe DaveS?
Andre and WJM,
First please allow me to correct/clarify my post #14.
When I stated that “That’s not what I believe”, I meant that I actually do believe that my beliefs are in control of the behavior of my body. I didn’t mean to imply anything about what I think holds under “atheistic materialism”.
In my question to WJM, I was essentially asking whether he would have agreed with the quoted passage while he was still an atheist. (I know, it seems unlikely, but I want to be sure).
And that should also answer your question, Andre. Whether materialism is “true” or not, I don’t know. But I am convinced that it is important that certain of my beliefs are true, for example when I am standing near the edge of a cliff, because if I am wrong, it could be fatal.
How do you know they are true DaveS? What is your objective standard?
DS, I second Andre and ask you to SHOW how your evolutionary materialistic scientism does not undermine the responsibly and rationally free reasoning self through self referential incoherence. (Cf here on in context for a 101. Note also the past several weeks of discussion here at UD and the consistent evasiveness of advocates of such evolutionary materialistic scientism.) KF
Andre,
I don’t know for certain that they are true of course (I could be hallucinating, or a trickster god could be fooling me, etc), but I think theists also have this problem.
If we are talking about my beliefs regarding how far I am away from the cliff edge, ultimately my objective standard is a measuring tape. Even if I don’t have one on hand, I have many years of experience measuring things and can distinguish between 10 feet and 1 inch.
KF,
Well, I’m not an evolutionary materialistic scientism-ist, and I didn’t sign up to defend that view here.
I do think that truth is important to atheists in at least some cases, and that’s what I prefer to focus on.
daveS,
If you’re not an atheistic materialist, then the argument here doesn’t apply to you.
Please try and understand that these arguments are about the logical entailments of the premise of an actual atheistic, materialist universe as if we lived in that universe, and the entailments of what many atheists assert, and about how people who self-identify as such do not live as if their beliefs are true.
Perhaps you are agnostic. However, if you hold that the experienced content of your beliefs can hold some kind of top-down power over the physical processes of your body, then you are necessarily saying that such physical processes do not cause the content of your beliefs, because those would be contradictory claims about reality.
If physical processes cause the content of beliefs, and those beliefs exist as some kind of caused physical arrangement in the brain, then to say that beliefs are in control of some bodily processes and decisions is a semantic dodge that tries to position some physical states as being “something else” than a caused physical state. If beliefs are caused and are physical states, they will produce whatever actions they cause due to the nature of their physical arrangements and interactions, not according to whatever the caused consciousness experiences those beliefs as “meaning”.
Atheistic materialists cannot have it both ways; either their beliefs, their ideas about what is true, and their behavior are all physical conditions caused by matter interacting according to physical constants and chance, or there exists some form of non-physical commodity which allows for some sort of independent judgement and control.
But, more on point of this OP, under A/M truth is a physically caused sensation in the experience of a physically caused consciousness, and those physical causes are not themselves necessarily wired to actually correlate to actual facts or truths, nor do those consciousnesses have any independent capacity to evaluate those truths nor do they have an capacity to coerce their physical processes to accept those “truths” as such.
However, atheistic materialists such as seversky seem to think that we (if atheistic materialism is true) have some sort of capacity to independently ascertain true beliefs, willfully force them into our physiology, and then those true beliefs will magically generate a superior form of happiness upon our physically programmed selves.
daveS said:
Of course truth is important to self-described atheistic materialists. That’s not the point; the point is, if we actually lived in an atheistic materialist world, why should it be important to them? Under A/M, it would be an illusory concept programmed by physical interactions to be held in the illusory mind of an illusory self.
Whatever that illusory self experiences that illusory concept as “meaning” has no bearing whatsoever on what the physical state of a physical body physically causes next. Under A/M, the sensation of deliberately choosing actions is an illusory sensation caused by the physiological state of the body. There is no autonomous, uncaused, top-down control over anything under A/M philosophy.
So, why is the idea of “truth” important to them? It’s just another programmed sensation that may or may not bear any relationship to either any facts or to what they might do next.
I dispensed with caring about the idea of “truth” when I was an atheistic materialist. To this day, I still don’t worry about whether or not my beliefs are factually true. That’s actually what opened the door for me to become a theist – realizing that in an actual A/M world, having true beliefs couldn’t possibly matter, per se, one bit, so there was no intrinsic benefit or value in holding the belief that I lived in an atheistic, materialist world, even if i did.
WJM,
Yes, obviously. I am an atheist and I am undecided about the materialism/non-materialism issue, just to be clear. I can, like anyone else, at least try to view things from a materialist point of view.
A/M’s believe that truth is a “physically caused sensation”? Hmm. Are you saying that under A/M, the truth of the proposition “2 + 3 = 5” is a physically caused sensation? And that if there were no consciousnesses in the universe, this proposition would fail to be true (per A/M’s of course)?
You also refer to this “brain in a vat” problem that A/M’s have, where their experiences could be uncorrelated with reality. Isn’t that also a problem for non-materialists? I’m guessing you experienced typing on a computer or other device around 6:31 AM MDT. How do you know that it’s objectively true that’s what was happening? As you say, your body could could have been engaged in some completely different activity and the typing was just a delusion.
Edit: I typed this before I saw your post #23; I have to go now, but will read it later today.
WJM,
Before I go, I did notice this from #23:
It’s a bit jarring to read this, but I want to understand exactly what is meant here.
Do you worry about whether the statements you have made pertaining to A/M in this thread are factually true?
daveS said:
I’m saying that under A/M, the experience that “something is true” cannot be anything other than a physically caused sensation. Logically, speaking, under that premise, what else could it be? Numbers and math are all physically caused conceptual experiences. What else could they be? If interacting matter causes you to bark like a dog and drool, and think you’ve correctly answered the 2 + 3 question, that is what you will do.
I’m saying that unless humans have some uncaused capacity to (1) evaluate the truth value of the concept as per the meaning and not the physical state which produces the meaning, and (2) install the true concept upon their physiology thus overriding erroneous physiological states, the idea of identifying truth and deliberately adopting true statements and values is absurd.
Look at it this way. Computers do not evaluate concepts; they physically react mechanically to inputted physical states. Period. If the programming (which is actually a set of physical states in memory) dictates that a computer answers “6” to the question of “what does 2 + 3 equal?”, that is what the computer will answer. If humans are programmed thoughts and responses which are caused by physical states, then we may answer “6” and be convinced it is a true answer, and unless our physical programming happens to change for whatever reason, that is what we will say and believe.
I don’t worry about what is objectively true, but in that I’m probably different than most theists here. My argument here is not that we are not brains in vats, and it is not that theism is true, and it is not that materialism is false.
My argument here is that even if atheistic materialism is true, there’s no intrinsic reason why one should believe it is true, because in an A/M world believing what is true would grant you no brownie points nor does it necessarily offer any experiential benefit. Contrary to Seversky’s absurd “better quality of happiness” view, it’s not going to necessarily make you any happier.
Also, my argument is that the premise of an A/M world and the logical entailments thereof directly conflicts with our actual experience. We act every second of every waking day as if we have a supernatural capacity to affect our physiological states in a top-down, uncaused manner and deliberately ascertain the truth value of concepts and coerce them into our physiologies. We act as if truth matters greatly, as if being good matters greatly, and as if we have the free will to independently guide our thoughts and behaviors.
We act as if we have the moral right to intervene in the affairs of others in certain circumstances, as if some things are universally wrong whether regardless of what society or culture says. We act as if we have the obligation to protect the rights and liberties of the weak and innocent. Why? Under A/M, no such inherent rights or obligations exists – they are just sensations caused by the happenstance interactions of matter.
There’s a difference between arguing that something is factually true or false, and arguing that it just doesn’t make any sense to believe a thing is true. It doesn’t make any sense to believe that the world is atheistic/materialistic in nature. There’s just no way to rationally justify it.
daveS said:
I’m not worried about whether or not the world is factually an A/M world.
My argument is rational in nature. You are as capable as I (unless you’re a biological automaton) in evaluating the logical inferences and conclusions contained in my statements. It’s not a matter of whether or not my statements about A/M are “factual”, it’s about whether or not my extrapolation of the A/M premises into inferences and conclusions is logically valid.
WJM,
I don’t have a lot to say in response, but I still have a few questions.
But is the brain like a computer, assuming A/M? And incidentally, is there some canonical list of A/M premises that we can refer to which has been vetted by A/Ms?
Surely there some instances where you do worry about objective truth? “If I step forward 1 foot, I will fall off this cliff”, for example. From your point of view, it’s very important to accurately assess the truth value of such statements, no?
Well, is it important to you that it be factually true that your argument is valid (and sound)?
I just don’t see how you you can avoid worrying about objective truth at some level.
Truth Will Set You Free,
Materialist believe in all those magical explosions with creative powers behind them without intelligent mind behind them or an intelligent cause.
One of the most puzzling ones I personally found for them is the source of energy behind the expansion and the acceleration of the universe. They know its there but they will not accept any possibilities of a transcendent, powerful and creative mind…
William J Murray
Further, if atheistic materialism is true, then we would be incapable of lying, because “lying” (the fabrication and dissemination of information known to be false with the intent of causing someone else to accept that information as true) would be an impossible contradiction of the same physico-chemical forces.
If I were to turn back the odometer on my car from 200,000 miles to 20,000 miles and offer to sell it to seversky as “only driven 20,000 miles” and seversky reads the odometer and belives the falsehood as if it were true, the physico-chemical forces that have no regard for the truth-value (or falsehood value) operating in seversky cause him to believe the mileage is 20,000 while those identical physico-chemical forces operating in me have produced the exact opposite effect, a falsehood I know to be false (the mileage is actually 200,000).
If atheistic materialism is true, the exact same physico-chemical forces operating me to produce a true belief (the mileage is actually 200,000) cannot simultaneously operate in me to conceive the lie and in seversky to produce the opposite false belief (the mileage is 20,000).
But we all know I can rollback an odometer and lie to seversky who will believe the lie. The true belief I have and the false believe seversky acquired from me, about the exact same odometer, can not both have been produced by physico-chemical forces. Moreover, I can tell a different lie to someone more discerning about wear and tear on a vehicle, or not lie at all, entirely at my discretion regardless of physico-chemical forces. I can even experience ecstatic happiness at unloading my high-milage vehicle on serversky for a low-mileage price, and seversky can likewise experience ecstatic happiness at having found such a great deal.
And for those about to argue “but seversky is under a different set of physico-chemical forces, a set that now includes a false odometer reading”. Yes. But I was able to overcome and subvert the physico-chemical forces operating in me to produce a false odometer reading; I was able to exert “free will” over my physico-chemical forces to manipulate the physico-chemical forces operating in seversky (his desire for a low-mileage used car). The same physico-chemical forces operate in both of us, but I overrode mine with the same free will seversky has to go back through the maintenance records and review the mileage on each work order. I.e., seversky’s beliefs are not constrained by his physico-chemical forces either, though those forces (physics, chemistry, quantum mechanics, etc.) are identical in both of us. And I could alter the maintenance records as well, and seversky can freely either believe the records or suspect them and reject the offer as “too good to be true”.
And if that were correct, there wouldn’t be any fraud. Bernie Maddoff could not have succeeded to defraud billions from his clients. And seversky would always know the true condition of anything he purchases.
But there is fraud; convincing, persuasive, believable fraud because lies can be told by atheists and believed as truth by other atheists because physico-chemical forces are irrelevant to truth, falsehood or atheistic materialism.
One of the problems I have with the atheist interlocutors who visit this site is that they are all heartless and soulless. Now just watch. Someone (some atheist) is going to become offended. But why? Isn’t that how we would rationally describe a human being on an atheistic worldview? To their credit there are a few atheists– a very few– who do not come across like they are heartless and soulless. Unfortunately, they are the hypocrites, because they are not acting consistently with their world view.
daveS:
It would be like a computer in that it was processing physical states into other physical states. What else could it be doing, under A/M?
You’re the one apparently taking up the argument for A/M; if you have a rational objection to any of the premises here or how they are presented, you are free to explain your objection. Or is what you are saying here is that you haven’t really examined your own position, haven’t really looked into the premises and what they mean, and really have no idea how to present any rebuttal, and so are looking to us to help you make your case?
Since it doesn’t appear you have examined your philosophical worldview to any great degree, instead of debating what it appears you are ill-equipped to debate, how about we set aside such arguments, turn to casual discussion and you answer a question: Why are you an atheist?
WJM,
Certainly under A/M our brains would be purely physical, and if that’s all you’re saying, I would agree. But I don’t know, for example, if this “processing” is deterministic or not, as the operation of my computer is. The computations my computer carries out can be simulated by a Turing machine, but I don’t know whether the same applies to my brain. For all I know, this “processing” the brain carries out could be fundamentally different than any processes that take place in a computer.
No, that’s not what I’m saying.
And it was a serious question—wouldn’t it be convenient if such a list existed? So that if someone stated “under A/M, X“, one could check whether this followed from the accepted premises?
Simply put, I don’t find the evidence and logical arguments for the existence of god to be very compelling. The proposition “there is no god” also appears to me to be consistent with what I observe in the world. Therefore I doubt that there are any gods (I’m a weak atheist, to be clear).
DaveS
The evidence for the first mover is very good. Had you said there is evidence but you don’t accept it I would applaud you but in the end you are just another dishonest atheist that are not willing to grapple with the truth.
Grow a pair, and no I don’t care if your feelings are hurt. Dishonesty to oneself about the facts of a matter is the worst kind of deception there can be.
Andre,
Please notice I didn’t say the evidence for the first mover isn’t good.
Rather I simply stated that I don’t find the evidence for god (and the first mover as god) very compelling. I could be wrong on that, obviously.
My feelings aren’t hurt in the least, FTR. But it might be more productive if we don’t assume our “opponents” are being dishonest so frequently.
WJM:
This is something that I’ve been wrestling with recently. Taking a look at Wikipedia’s description of a phenotype:
Wouldn’t religion be (something like) a phenotype? And isn’t it clear that the religion “phenotype” has a much stronger presence in the human population than the non-religious “phenotype?”
Why argue against what has likely been selected for survival as though it had not been selected for survival, or as though what was selected for should not ultimately trump any ideas about truth (itself ultimately explicable only in terms of survival and what survival formed in us via evolution). Even if you believe (based on a mechanism likely constructed more for survival than truth) that religion is not best for survival, if you trust evolutionary processes, why not simply wait for religion to be selected against as it must ultimately be, given ongoing natural selection?
More that merely believing in the magical, I am convinced more everyday that atheists actually believe in god. That is, they believe in something eternal that has the stupendous power and ultimate capability of producing all that exists, including self-aware, conscious humans that marvel at their own apparent design. They just don’t like giving this something the “god” label. They’d much prefer to think of it as some sort of vague, mind-numbingly serendipitous quantum foam or the like. But isn’t this a distinction without any real difference? If the issue isn’t about god’s eternal nature and creative power, but more about whether he is a personal being, then why not admit you believe in an impersonal god? At least that would be a rational step forward from merely assigning god-like attributes to blind chance.
daveS said:
What difference does that make? Are all your beliefs based on what you consider to be compelling evidence?
How so?
WJM,
For beliefs of the form “X exists”, generally so. I can’t think of any exceptions offhand. How do you decide whether to adopt “X exists” as a belief, assuming you don’t currently know whether it’s true?
Well, I don’t know of any inconsistencies between this proposition and my observations. For example, I’m not aware of a god blatantly intervening in the world, as some people say happens.
Wow Jesus Christ was God intervening blatantly with enough written about it by many witnesses. The evidence is compelling and yet DaveS is just not aware. Like I said DaveS you are not being honest.
Andre @39,
With respect to daveS, I have to say, even though I think there is a bias at play and that for some reason he doesn’t really want to conclude that God exists, he is one of the only atheists on this site who I consistently believe is trying to be somewhat open-minded and is interested in understanding what the theists are saying. I will plainly state that I think he’s giving himself some kind of excuse to not follow the logic and evidence where it most reasonably and naturally leads, but the very fact that he is open to the possibility that his defenses against certain theistic arguments may not really work and that he asks questions and tries to understand the theistic arguments rather than just twisting them or sticking his head in the sand is, in my opinion, worthy of some commendation.
daveS:
Okay. Since your beliefs about what exists are based on “compelling evidence”, what constitutes “compelling evidence”?
A few follow-up questions:
1. How have you determined that what you experience/observe is what your would expect to experience/observe if there is no god?
2. What would such “blatant interventions” look like?
3. How do you know that what you experience every day is not an ongoing “blatant intervention” by god in order to establish and maintain an orderly, continuous, cause-and-effect habitable universe with necessary material behaviors (physical laws) to house an intelligent physical species with free will?
3. How would you know that what was doing the “intervening” was god?
4. What about gods that are not postulated to blatantly intervene in the world? How would you experience be inconsistent with that kind of god?
You ask:
If it seems like the belief will benefit me, I adopt it as I do all my beliefs – on a provisional basis.
HeKS,
Thanks.
WJM,
Well, that depends, and such a determination would be a judgement call. A couple of examples:
1) There has been some internet discussion recently concerning the existence of thylacines on the Australian continent. I would consider things such as a live specimen, high-quality video, or a carcass (among other things) to be compelling evidence for the existence of these animals. Unfortunately, there doesn’t seem to be any, and I doubt they actually exist.
2) For the existence of God, miracles, signs, and wonders would count as compelling evidence, in my view (I think we’ve actually discussed this before). Now there is an issue of connecting these events to God, I concede, but the bible says God has caused them in the past, so if I observed one in the present day, it would occur to me that they were the work of God.
In a recent discussion with KF, I suggested the use of cryptographic-type puzzles. Suppose a being, claiming to be God, offered to demonstrate his/her powers to me. I would give them a large semiprime number (product of two primes), and ask them to write down the factorization, within a set time limit, say 10 minutes. Now this factorization would be designed to be infeasible for a human to carry out in 10 minutes. It’s easy to generate such puzzles which would take years to solve, even with many computers working in parallel.
Again, although this wouldn’t conclusively “prove” this being was God, I would be convinced that they have superhuman powers if they were able to solve the puzzle.
Miracles, signs, wonders, solving infeasible factorization problems, levitating the Pentagon all would capture my attention. Of course less dramatic interventions would also count, but I would need to know the details before I sign on.
That would be difficult, admittedly. I think I could conclude whoever was intervening had godlike powers, anyway. But who would I think the most likely candidate would be? Probably God.
Well, they might be harder to “detect”, so to speak. I suppose any god could choose to keep a very low profile, in which case I might not find out about Him/Her.
Acknowledged. We do apparently differ in this respect. I try to keep costs/benefits out of the process.
daveS, you answered before I was finished editing my questions @41. My fault – I didn’t expect you to answer so quickly. Could you possibly revisit them? At least the ones that are significantly changed.
daveS said:
If you are walking down the street in one direction, and suddenly people in front of you start running the other way (towards you/past you) yelling “There’s a bomb! Run!” .. will you wait for compelling evidence of a bomb, or provisionally believe that there is a bomb and run the other way in consideration of what would be the most beneficial for you if the proposition is true?
daves @38
It seems to me that you are making a mistake with respect to God’s existence that I find to be very widespread among atheists. You are approaching the proposition of God’s existence from the wrong end. What I mean by this is that you are approaching the question of God’s existence as though God is just another thing that may or may not exist in the world, like Bigfoot, or fairies, or the Loch Ness Monster. You are essentially taking the existence of the world as a given and then asking whether or not there is any evidence that God exists in the world in addition to everything else. While this could be seen as an appropriate approach for many of the gods of polytheism, it is not appropriate with respect to the God of monotheism, who, as we have discussed previously, is a Necessary Being who lies at the root of the world and who is needed to account for how the world that we seem to perceive could even exist and actually be as we perceive it. Of course, that’s not to say that there cannot be scientific and empirical evidence pointing to God’s existence, because there is, at it has been a topic of discussion here lately, but this kind of evidence acts as a confirmation of realities that can already be established by reason.
When you get right down to it, it is more rational to doubt the reality of the world we seem to perceive than to doubt the reality of the existence of a being like God.
WJM,
Sure, I think #1 and #3 are the ones that have been added:
Well, when I talk to my religious friends about how they know that God exists, they often mention that they sense His presence, or that they have experienced some sort of “intervention” (for example an angel catching them when they fell out of a chair) and so on. I have never observed any of these things, so in that way, my observations are consistent with there being no God.
That could be the case, I suppose, but Jesus is said to have healed the sick, turned water into wine, fed the multitude, etc, and people (myself included) apparently find these events more obviously “supernatural” than the orderly continuity that we observe in the universe. Whether any intervention is required to maintain this continuity, I don’t know, but if I see someone turn water into wine (under controlled conditions), I know something’s up.
WJM,
Depending on circumstances, the fact that these people are yelling about a bomb could be compelling evidence on its own (for example, if I knew the people and felt they were trustworthy).
But I would likely turn around and run in any case, even if I was 99.9% certain there was not a bomb. I certainly would not “choose to believe” there is a bomb because of the great risk bombs generally pose.
daveS, I would be interested in your response to HeKS post. I have tried, and just cannot get why God is necessary and why reality would be absurd without God. I tend to be more pragmatic than philosophical. I have never had a need of God to make sense of the world. Like you I see no evidence of one existing. But I guess the main point is I just don’t get the argument based on reason and logic as to why God must exist. Do you?
HeKS,
An excerpt:
And I think it’s fair to say that a primary aim of this blog is to disseminate such scientific and empirical evidence. I personally would find that kind of evidence much more convincing than the rather abstract arguments involving necessary beings. I’m guessing many others do as well. I don’t think I’ve ever heard the term “necessary being” in a church service. When people tell me why they became theists, it’s generally due to them having some sort of transcendental experience, the testimony in the gospels, bible prophecy, “Evidence that Demands a Verdict”, and so forth.
Pindi,
Tbh, HeKS and others would be better at elaborating on this vast field than me.
I have to run now, but maybe I will try and respond to your post tomorrow.
I can say now that my main issue with these abstract arguments is whether they refer to things that actually exist. For example, it’s not clear to me that there really are “necessary beings” (and I’m not alone in that worry).
Ok, thanks DaveS, talk later.
daveS,
You can have questions or doubts about necessary beings (though I think you have less doubt about them than you might think), but my ultimate point here is that if you want to deal with this subject honestly then you need to take the proposition of God’s existence on its own terms, in the sense that you have to try to think about the proposition as it is actually put forward by those who defend it, which is something that bears no resemblance to the proposed existence of some random contingent being in the world (I gave examples like Bigfoot, fairies and Loch Ness Monster).
So when considering the evidence for God’s existence, you have to accept that the evidence on offer extends beyond (i.e. is not limited to) the sort of empirical evidence that might be offered for the possible existence of some contingent being existing within the world. There is empirical and scientific evidence of that sort, which has been discussed in a few recent threads, but the evidence also includes the logical entailments of an atheist/materialist world (on the assumption that such a world even could exist) and the logical arguments for the existence of a necessary being that matches the characteristics attributed to God. You must understand that all of these things are included in the evidence for God’s existence, and so when you say that you don’t find the evidence for God’s existence compelling, you are either ignoring the argument for God as necessary being and the fact that atheistic materialism leaves one without any foundation for rationality (i.e. pretending these arguments don’t form part of the evidence), or else you are saying that you are not convinced by all this evidence even though you don’t seem to have any counter-arguments against God as necessary being or the lack of grounding for rationality on atheistic materialism.
In other words, saying, “I’m not convinced cause I don’t see miracles”[1], simply is not enough to make atheism a rationally defensible position.
I’m a little tired right now, so I don’t know if I’m really getting the point across clearly here, but I guess the way I’d try to illustrate it is that you’re standing in a particular place, looking forward and trying to see evidence for God’s existence on the road in front of you in the form of overt miracles, and yet you’re ignoring the fact that if you looked behind you you’d see you’re standing on the edge of a world hanging out over nothing with no rational explanation for how you could have gotten there if not by the will of God. So if you really want to deal with this issue honestly, you have to look both ways.
———
[1] You may also recall our previous discussion where I pointed out that if Christianity is true, you actually should not, in our time, be expecting to see overt public miracles of the sort performed by Jesus and his apostles.
DaveS,
Suppose that you and 29 other people wake-up in a building, very much like Château de Versailles, situated on an otherwise barren deserted planet. The 30 of you are the only living beings on this planet. Let’s suppose further that all of you suffer from amnesia and have no idea how you got there and who you are.
At some point a discussion ensues among the 30 members of the displaced group about the existence of the designer(s) of the building and its intricate features. Some argue that the existence of a designer is ‘necessary’ for the building to exist. Others are not convinced by this ‘abstract’ argument, demand empirical evidence and rightly point out that nowhere on the planet designers have been spotted.
What would be your position?
daveS,
It appears to me by your answers that your atheism is entirely framed by a certain conceptualization of a Christian god – you refer to the Bible, gospels, miraculous events, and as HeKS points out, an embodied, contingent being kind of entity as god. (I’m not saying that is an accurate reflection of the Christian god, I’m saying that is a conception of that god a lot of people have). So, a lot of your ideas about “compelling evidence” for a god is based on that particular concept of god.
Although the two concepts employ the same term – “god” – that concept and the one being argued largely by people here are two entirely different concepts. The kind of god you are an atheist in relation to is really not much more than a superhuman entity. You yourself admit that the “compelling evidence” you cite would not even necessarily indicate that the being providing such evidence would in fact be god. Indeed, given your conceptualization of god, I would also probably be an agnostic or a weak atheist.
But, that is not at all what is being argued here, and until you can set aside that particular framing (at least for discussions here), you simply won’t be able to understand what the arguments here are actually about. Your “atheism” is so off-base to what is being argued here that, to use Pauli’s phrase, “it’s not even wrong”. It’s inapplicable. We’re not talking about afairyism or ayetiism or asuperhumanbeingism.
IMO, you and others here are the most superficial (no disrespect intended) kinds of atheists in that you haven’t really considered any but one very particular, narrowly-constructed concept of god, and you haven’t (apparently) examined very thoroughly the broader logical ramifications of atheism. It seems to me that your “atheism” is more of a “Well, I don’t see any compelling evidence for the Loch Ness Monster, so you can call me an alochnessmonsterist” kind of atheism. IOW, it’s just one more proposed being that you have no reason to agree exists, because being an alochnessmonsterist doesn’t commit your worldview to any further logical consequences as a result of your lack of belief that the loch ness monster exists.
In other words, you think everything else in your worldview and how you understand your existence can stay the same whether or not you believe in god. That’s true with regards to the kind of god you are conceptualizing; it’s not true wrt the kind of god being argued here.
The loch ness monster is not proposed as a necessary being, a fundamental ground for both morality and free will, the validity of mathematics and logic, the cause of the fine-tuning of the universe, the acausal root of cause and effect, etc., where the lack of such a fundamental entity has extreme, inescapable logical consequences for the very nature and meaning of our existence.
Until you can understand, engage in and respond to those arguments, not only are we not in the same ballpark, we’re not even playing the same game. This is why the big league atheist/materialist philosophers agree that without god there is no basis to believe we are rational, volitional creatures. This is why they call our consciousness, free will and sense of morality “illusionary” – because without the kind of god actually being argued here as the fundamental root of such things, those things can only be the projected, illusory experiential effects of interacting matter processing from one physical state to the next. And if that is true, it has very deep, very profound, very troubling implications for our very existence, which those big-league atheistic philosophers agree would be the case.
This is why Dawkins, Sagan and Harris are considered lightweight atheistic philosophers – they, like you, talk about the same kind of god you talk about, as if things like invisible spaghetti monsters or dragons in the garage are conceptually comparable to the essence of classical theistic arguments.
as to:
“This is why Dawkins, Sagan and Harris are considered lightweight atheistic philosophers”
And let’s not forget to include Krauss in that list:
Origenes (and others),
First, I’ll have to answer these various posts in somewhat random order, as I get time. Hopefully I can respond to them all today,
If the amnesia is mild enough so that I recall what buildings are and how they come to be on Earth (they are manufactured by humans), then I would agree that the existence of a designer/manufacturer is necessary for their existence.
If I somehow forgot completely what buildings are, I don’t know. Perhaps I would still be able to make a design inference, but it might take longer. If I don’t even understand the concept of “building”, I might be too impaired to make a judgement.
I don’t consider this situation/argument to be especially abstract, since it involves no “necessary beings” in the sense HeKS and others are discussing, we have lots of physical evidence, etc. I do think that if one of our space probes sends back pictures of an alien “city”, there’s a good chance we could identify it as designed or manufactured.
HeKS,
I do agree that it’s important to deal with the actual arguments put forth by theists on this matter.
And I acknowledge that god (by most theists’ accounts) is very much unlike Bigfoot, et al.
But I think you can appreciate how one could be skeptical about arguments where terms such as “necessary being”, “maximally great being”, “great-making properties”, and so on are thrown around, when it’s not clear whether these terms actually refer to anything real. While they might be interesting to ponder, they raise a lot of questions as well.
If I were a Christian, I think I would take the position reverse to yours: I would base my faith primarily on things like evidence from the bible, perhaps my own experience of miracles (overt or not), scientific evidence, and regard the Cosmological Argument, etc., as secondary.
WJM,
A partial answer to #54:
It is true that I’m primarily interested in the Christian God or something very similar, but I don’t think of Him as an embodied, contingent being. I understand that at least most Christians regard Him as a necessary being [Edit: I think, anyway. I’m assuming that here]. And yes, I’m not that keen to discuss entities such as a non-personal god, for example.
And I strongly disagree that I’m focusing on a mere “superhumanbeing”. Not at all. I have in mind a very mainstream, Christain-centric admittedly, conception of who God is.
WJM,
I don’t have anything more to say about #54 presently, because I believe it is based partly on a false premise—that I am thinking of God as a mere “superhumanbeing”.
But I will ask, is the God you believe in a personal God?
And if so, do others worship the same God as you?
DaveS @56,
Thank you for your answer. To be clear, in my example (see #53) there is little reason to suppose that the scenario is situated on Earth. But, if I understand you correctly, then this is not your assumption.
I suggest you err on this assessment. The structure of the argument is exactly the same. A logically necessary being is a being whose non-existence is a logical impossibility. Given the Château de Versailles, a designer is a necessary being. In the same sense that, given the universe, the First Cause is a necessary being.
I take it that by “lots of physical evidence” you are referring to Château de Versailles. However, the amount of physical evidence has never been a problem for First Cause arguments—the entire universe can be offered as physical evidence.
Let’s hope that common sense will indeed prevail.
Origines,
Thanks. And yes, I meant that on Earth, buildings are designed and manufactured, and reasoning by analogy, the same would likely be true on this other planet.
Well, I’m currently located inside a building, and while I would agree that given that it exists, it’s “necessary” in some sense that there was a designer, that designer was a person or persons, and these persons are generally regarded as contingent beings. Are we talking about the same thing? From wikipedia:
Well, wrt designers, it’s “obvious” to me that the Château de Versailles was deliberately designed and built (by humans). The entire universe (aside from buildings etc)? That’s less obvious to me.
DaveS @61,
Strictly spoken you are correct of course. Surely, the designer of this building is him/herself in need of an explanation. When I said “the structure of the argument is exactly the same”, I meant to say that in a narrow context — if we only consider the designer and the building —, the logic is very similar. Every possible world must necessarily have a First Cause, every possible Château de Versailles must necessarily have a designer; otherwise these things don’t come into existence.
Again, you are correct. Logic informs us about several exotic properties of the First Cause, and the same properties do not apply for the designer of any Château de Versailles.
Or unknown alien(?) designers, as in the example (see #53) we are discussing.
The (entire) universe is in need of an explanation — just like the displaced Château de Versailles. Assuming that an infinite regress is incoherent, there must necessarily be a First Cause.
Origenes,
A very brief response:
Although I think the first cause argument is a reasonable one to make, it’s not at all clear to me that the premises on which it rests are true. Specifically, that the universe itself is in need of an explanation and that an infinite regress is incoherent.
DaveS @63,
I don’t understand why you doubt that the universe is in need of an explanation. Don’t we give up on rationality if we allow for universes to pop into existence from nothing?
An ‘infinite regress’ and an ‘uncaused cause’ are both concepts that are offered as an explanation for the existence of the universe. Based on previous discussions, you seem to prefer an infinite regress over an uncaused cause. Is that a fair assessment of your position?
DS,
first, the universe, U exists, in a sequence of states s1, s2 . . . sn, sn+1 etc. We may and do freely ask why, expecting to find a sensible answer.
In particular, the observed cosmos credibly had a beginning and the cosmos is clearly highly contingent.
These both point to the reasonableness of a cause, ontologically antecedent to and sustaining of such a universe.
In this context, something — a world — from utter non-being is an obvious non starter, as were there utter nothing such would forever obtain.
Nor, given fine tuning, is blind chance and/or mechanical necessity a plausible answer.
This already makes design a serious candidate, indeed the most serious.
Now, on infinite past attaining to the present, the same issues obtain as previous discussions indicate.
These are so whether or no you may prefer otherwise.
Specifically, we have stage-wise causally linked succession of states.
Such a chain is inherently incapable of actually traversing and completing an endless span of states in stepwise succession. There is no good reason to hold that such has happened, and there is every good reason to infer that such has not happened, that there was in fact a finitely remote initial condition of the observed cosmos that is not explained on prior chain of succession.
That is, there was a beginning and a cause, even through a speculation about a prior multiverse or quantum foam etc.
Infinite regress is simply not a good explanation, though it is the only alternative to a beginning, which entails an ontologically prior cause.
I simply note that if there were such a succession, at some pointw, it had to have been endlessly remote from the sequence since a useful beginning point, say 13.85 BYA, set as s0, then s1, . . . sn, now.
That is, we see (with ellipses of endlessness indicated by FOUR dots):
. . . . w+2, w+1, w, w-1, w-2 . . . . k, k-1, . . . s0, s1, s2 . . . sn + –>
There is a finite, causally successive stepwise span from s0 to now, no problem.
But to get to s0 from w we have to count down across a span that is endlessly extensive. We might as well say:
w –> 0, w+1 –>1, etc, . . . . | s0 –> OMEGA, i.e. the order type of the natural numbers as spanned from w.
Mathematically, i.e. logically on structure and quantity, we may say that the endlessness of succession can be assigned an order type omega, but that is utterly different from being able to actually stepwise span it and traverse it. No, we see where it would go, and say, okay that endless span has a quantity, omega. We have delivered a logical result on the set as a whole per its logical structure, we have not actually spanned it in causally connected finite stage successve steps.
Whereas, by contrast we could say:
s0 –> bang
s1 –> inflationary period
s2 –> first stars
s3 –> forming “second generation” stars and associated structures such as galaxies, clouds with high metallicity, etc
s4 –> Formation of sol in Milky Way, and associated planets
. . .
sn –> now
(Where we could assign some k as finitely remote actual beginning; what we can warrant per logic of successive cumulative finite stage steps.)
KF
PS: The challenge of endless traverse can be seen by postulating two tapes punched at an even finite interval, say 0.1 inch, starting left and endlessly going right. One pink, P and the other blue B. Advance P by some arbitrarily large but finite k steps, such that k+1, k+2, . . . . are now in 1:1 match with B at 0, 1, 2 . . . . where both are still endless to the right. The import is, endlessness is definable on terms of such a k, k+1 etc having no effect on the continuation to the right and continued 1:1 match of P and B. As a direct implication, at any finite stage k, there is still an endless succession k+1, k+2 etc still to go, proposed finite stage stepwise spanning of endlessness is futile.
Origenes,
I do think the “from nothing” part could be a problem. Whether there has to be an explanation for the universe, and whether we have to give up on rationality if there is none, I don’t know.
I don’t really have a preference. I find them about equally difficult to comprehend.
KF,
I think much of what you sketch out is plausible (I don’t see how anyone could have a problem with your form of the PSR, for example).
But I must point out once more that this does not hold:
Just as there are infinitely many integers, each finitely distant from 0, the past could be infinite without any particular instants in time being infinitely remote from the present. In other words, when I posit an infinite past, I’m not committed to having any omegas on my time axis.
The late Cornell university astronomer Carl Sagan was well aware of this historical conflict between naturalism and theism, or as he described it, between science and religion. In his book Broca’s Brain, in a chapter titled, “A Sunday Sermon,” Sagan appears to vacillate about the relationship of science and religion. At times he seems to be sounding a conciliatory note, but then, at other times, he’s confrontational. For example, he writes, “A universe that is infinitely old and a God who is infinitely old are, I think, equally deep mysteries.” However, a few pages earlier he praises a book by Cornell universities’ founder and president, Andrew Dickson White, entitled A History of the Warfare of Science with Theology in Christendom. Despite Sagan’s enthusiastic endorsement, White’s book has almost universally been discredited by historians of science as being more an anti-religious propaganda piece rather than a work of serious scholarship. Most historians of science reject the so-called warfare thesis put forth in White’s book as a myth. The relationship between science and the Christian faith is much more complicated and nuanced than White implies. Sagan, however, appears to uncritically swallow White’s thesis hook-line-and-sinker.
As a Christian-theist, who has thought long and deeply about the basic assumptions underlying my world view, I don’t think Sagan, along with other likeminded naturalist’s, really understand the fundamental differences between the two world views. They are not really equal. For example, the naturalistic worldview that Sagan seemed to prefer, requires an infinite regress of causes. However, is such an infinite regress something that is scientifically provable? Is it even possible?
Sagan thought it was at least possible. He thought it was possible we lived in an oscillating universe that has gone through an infinite number of cycles, each cycle beginning with a new Big Bang which then ultimately collapses on itself. However that idea has since been discredited. It is now known that the universe is expanding too quickly to ever collapse back on itself. So, we do not live in an oscillating universe.
However, Sagan also thought that mathematics was on his side. He writes,
The famous German mathematician David Hilbert would have disagreed. He wrote,
“The infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought… The role that remains for the infinite to play is solely that of an idea.”
So, according to Hilbert an infinite sequence of real causes does not exist. Of course other mathematicians would disagree. But the fact that mathematicians disagree about the existence of actual infinities cast doubt on the idea that the theological arguments would have been easily undermined. Indeed one could just as well argue that it would have had little effect over the status quo. It certainly doesn’t provide the knockout argument that Sagan thought it would.
daveS,
As usual, every time you make this statement you clearly seem to be failing to take into account the arrow of time. Yes, it is true that any particular integer is finite steps away from zero, whether you’re going in the positive or negative direction, but as I took great pains to try to explain to you in that other thread, this is irrelevant when the task you’re faced with traveling towards zero from some abstract concept of either positive or negative infinity. When traveling away from zero and toward “infinity” in either direction you are only ever dealing with a potential infinite. When you are traveling toward zero and from “infinity” then you are suddenly talking about an actual or completed infinite that is traversed through a series of finite steps, and that is what is impossible. As long as you allow yourself the cheat of imagining moving backwards through time toward infinity then you are never going to appreciate the logical incoherence of an infinite past or infinite regress of events.
HeKS,
But we’re not traveling toward zero from “infinity”, abstract concept or not. Keep in mind that there is no starting point in this exercise. It’s a beginningless process, in WLC’s vocabulary.
It is true that the number of seconds, say, elapsed in this process up to the present is a completed infinity, but if you simply assert that this is impossible, you’re begging the question.
Have you read any of the literature on this subject, by the way?
daveS,
That is precisely my point. I’m using a shorthand here where I went into a good amount of detail in the other thread to explain exactly what I was saying the problem was with this way of looking at things, but I don’t really feel like repeating myself in such detail here. A beginningless process is one that is never begun, that it is impossible to begin, but which is claimed to at some point be finished.
A step-wise traversal of the infinite is something that, on its face, is nonsensical, and I explained the problem in some detail in the other thread (as did some others in different ways). The notion is prima facie incoherent and as such the burden of proof lies on those who would seek to claim that the traversal of an infinite temporal past can be made coherent as a concrete and truly existent reality (as opposed to just an abstract mathematical concept).
Not mathematical. As I’ve admitted on this site several times, math is a weak area for me (though it’s one I eventually hope to shore up). I’ve read some philosophical articles on the subject and read attempts by people to defend the possibility of an infinite past, watched lectures and presentations in which people tried to defend it, and have seen people put forward such arguments in debate, and I’ve found them universally unconvincing to the point that they didn’t really seem to make any progress towards making the concept coherent. They largely seemed to fall into the trap of confusing potential and completed infinities, or resorted to abstract infinities, or tried to argue that certain other things constituted completed infinities that actually didn’t.
Didn’t you actually cite one such attempt in the other thread? And I think even you admitted that it didn’t really work (unless it was someone else in that thread).
By the way, I just want to clarify that when I said in #71…
… I meant precisely what I said. In other words, I’m not saying “I’m not convinced” in the way that atheists on this site typically throw that statement around with respect to the evidence for God’s existence. I’m not saying that I’ve decided some amount of evidence for an infinite past is just not sufficient to convince me it’s true. There really is no evidence for that. All the evidence points the other way. What we’re talking about here is arguments, and even there I’m not saying that the arguments for an infinite past have simply failed to convince me that an infinite past is true. Rather, I’m saying that the arguments have utterly failed to convince me that the concept or proposition of an infinite past is even logically coherent. The more I think about it, the more clear it is to me that it is logically incoherent, and no argument I’ve heard on the other side has caused me to move even a hair’s breadth in the other direction.
HeKS,
It seems you are making somewhat different arguments than KF is, so I should clarify my position.
I claim that the arguments which assert that an infinite past entails the existence of instants in time infinitely remote from the present, are erroneous and therefore don’t succeed in demonstrating that an infinite past is impossible. This type of argument is what got the original thread started.
I also don’t believe that an infinite past raises any purely logical or mathematical difficulties. I don’t know if you agree with this, but I haven’t seen any specific logical or mathematical problems raised. You can say that beginningless processes are incoherent, but can you pinpoint any particular contradictions, for example? JAD brought up the infinitely old oscillating universe cosmology, which was apparently considered quite viable at one time (and actually survives, I believe, but is on life support), and I don’t see anything obviously incoherent about the idea.
Now I don’t claim to make a positive case that beginningless processes can or do actually exist in this universe. I’m just saying that I don’t think you can knock them down via logic or mathematics alone.
Yes, I do remember reading a paper which supposedly supported my position, but which I didn’t think succeeded. There were actually several I ran across, on both sides of the argument, which I felt were quite weak.
Edit: Just saw this:
The first sentence sounds totally reasonable to me. I’m not trying to make a positive case for an infinite past, but rather to show that alleged disproofs of an infinite past don’t work.
Regarding the second sentence, if in the future you can demonstrate that it’s incoherent, I would be eager to see that.
DaveS @66,
Needless to say that I’m no cosmologist, but it seems obvious to me that, without intervention, the universe is heading for “heat death”. In my understanding of the second law of thermodynamics there can be no other outcome. Stars will die and planets will loose their internal heat. Therefore an eternal universe—a universe that just is—doesn’t make sense.
It follows that the universe is in need of an explanation. This conclusion seems so inescapable to me that I don’t understand how people can seriously hold another view.
You are in good company though. For instance, during the famous Coplestone vs Russell debate, the latter argued against Coplestone’s first cause argument by saying ” … the universe is just there, and that’s all.” N.B. this debate took place in 1948, before the acceptance of the Big Bang.
DS, pardon but I think you are making a contradiction in terms. If there were an infinite past, then there HAS to have been an infinitely remote point of time, some past stage w that is endlessly remote from now in a way that a transfinite succession of steps therefrom has led to now. Otherwise, you are trying to assign a finitely remote value and properties to the proposed infinite past. I agree, any actually reachable point in the past will be finitely remote on the premise of successive causal stages of finite character, but that is my point. Namely, this includes a beginning at some k. My underlying point, is that a proper understanding of a set of transfinite cardinality constructed on a stepwise ordinal succession requires that there be a recognition of an ellipsis of endlessness which cannot be completed by some finite stage stepwise cumulative process. That is what the Math is telling us, and it is what the P vs B thought exercise underscores. I agree, if there were ever utter non-being such would forever obtain, so if a world now is, something always was, but that something has to be of character that is radically different from an infinite stepwise cumulative succession of causal stages going back to an infinite past material or quasi-material physical cosmos. What fills this bill will be a necessary being integral to the framework for this or any world to exist, and with adequate causal capability to serve as world-root. God in some form is one serious viable candidate [unless it can be shown that such a God is impossible as a square circle is impossible], an infinite past material world that is stepwise causally cumulative is not. KF
PS: There are not infinitely many integers, each finitely distant in steps from 0; there are endlessly many in principle possible steps but any reachable value of an integer, z, will be finitely remote for reasons tied to the P/B example as was again given. To get to the order type of the set of natural numbers from 0, we are forced to reckon with the ellipsis of endlessness. That ellipsis is an implicit recognition that we cannot actually complete the endlessness cumulatively in steps of finite stage, and the only meaningful sense of “distance” is number of steps of count from 0, on {} –>0, {0} –> 1, {0,1} –> 2 etc ENDLESSLY. What we do is to impose a logical in principle and deliver the order type of that endless succession as a new quantity logically accessed, OMEGA, the first transfinite ordinal. So, we never actually show that all z in N are finite, but instead all that we can reach in stepwise iterative definition will be finite, and there is no natural limit to the process, so endlessness has to be incorporated into the definition of N; that is N is non algorithmic as an algorithm must be finite. No algorithm can be constructed to actually complete N, i.e. there are not infinitely many finite cumulative steps from 0. Saying there are infinitely many finite numbers in N is in my considered view a poor and even contradictory expression. That is why we had that exchange at the beginning of the year on this exact subject.
HeKS:
Very well put.
This is what I tried to capture in the sequence:
. . . . w+2, w+1, w, w-1, w-2 . . . . k, k-1, . . . s0, s1, s2 . . . sn + –>
It is not just that one may regress in thought about the past from sn [now] to s0 [bang] and even k [some finitely remote antecedent to s0], these being finitely remote. Nor is it that there is some transfinite onward succession but that if there were an actually completed endless past then there must have been some w that is transfinitely remote in steps from sn and which is causally contributory to sn, now.
It matters not that at such a w there is an onward endless regress given by the leading 4-dot ellipsis. The problem is that there is such an ellipsis from w to k. That ellipsis would have to be completed in finite, cumulative causal stages to get to w, and we know logically [cf the P/B tape thought exercise] that such cannot be traversed in steps.
That is, there was no actualised physically, causally connected w that then spans a transfinite cumulative stepwise process to k, from which sn can be reached in finite stage steps.
That is, we are only justified to propose some k as a finitely remote beginning.
Which calls for a causally adequate, finitely remote world root. A begin-NER to account for a credible begin-NING.
Where some aspect of that root must be necessary being, with all that entails.
KF
DS, I fully endorse HeKS’ argument and have just said that it expresses aptly in words the logic in the sequence I have used in one form or another since the beginning of the year. I am trying to lay out in a causally connected finite stage sequence, what is implied by claiming an actually completed transfinite past of successive cumulative finite causal stages to now. (I of course point out that a cumulative succession of infinitesimals is not relevant; Zeno is not part of the problem.) As cause is past to present, present to future . . . connected to entropy as time’s arrow . . . to go from w to k requires actual traversal and completion of a transfinite stepwise process. But such is inherently non algorithmic and impossible of completion. We are only justified in going back to some finitely remote k, an actual finitely remote beginning point. And I am not committed to k being s0, the bang. Where, this is a good reason to disbelieve notions of an actually completed infinite past of successive cumulative finite stages to reach now. Note, the distinction from, it is possible to in effect construct the negative integers branch of the surreals . . . which is not done in actually completed infinite accumulations of finite steps and which includes generous use of ellipses of endlessness which are inherently non algorithmic due to being endless. KF
PS: Oscillatory sequences run into many difficulties not least accumulated entropy and no serious bounce mechanism, multiplied by a density issue that points to endless expansion. Where if anything the rate is seen as speeding up as of last I checked. IIRC 100 bounces is the proposed upper limit, i.e. endless oscillation is non-viable.
daveS said:
Why?
Yet, the content of your responses, such as your examples of “compelling evidence”, seem to indicate that is exactly what you are talking about. Further, the nature and wording of your questions:
… indicates the same … you ask, “who” god is? If god is the ground of existence, god is not, in any meaningful sense of the term, a “who”.
I think that you believe you are not thinking about god in that manner, but you continue to ask question that indicate you are thinking about god in that manner. I suspect you still do not comprehend what “ground of existence” means, nor comprehend much of anything I have personally said about my views about god, because you ask the following questions:
How can what is the very ground of my existence not be both personal and universal? What can you possibly mean by that term wrt what I have already said? Are you asking if god is some sort of personality I can interact with?
And then this:
We obviously do not all “worship” the same concept of god. I’m not sure what you mean by “worship”. If you mean “a feeling of reverence and and adoration”, all we can have those feelings towards are our concepts of god. I think some concepts of god are more rationally consistent and more practically useful than others.
It is these kinds of questions that make me wonder how much you’ve thought about any of this.
For example, I love my wife with all my heart, but all I know of her is my concept of her based on my experience of her. That is all I can rationally say that I actually love. I can’t read her mind or experience her state of actual being; I assume/believe (act and think as if true) that my concept of her is a fairly close approximation of who/what she really is, but it is still necessarily my concept of her that I love.
My concept of god is a god that doesn’t require nor asks for worship. The god I conceptualize doesn’t even care if you’re an atheist or not. I’m not saying recognition, gratitude and worship of god are not useful and productive behaviors or states – I think they are. But I don’t think god demands or requests such behaviors or states. That’s entirely up to us.
But, I’ll leave the abstract arguments to others who have already presented them quite well. I’d like to return to the issue of how you form your beliefs. You said:
So, you are saying here that one form of “compelling evidence” is the testimony of people you know and trust. If people you know and trust tell you that they have experienced god, would you then believe in god?
WJM, I suggest a God who is capable of design, communication/language, is inherently good (including loving) setting basis for moral government, etc., will be personal in a significant sense that makes oour hag=ving imago dei in relevant senses a meaningful claim. That is volitional, decision-making, moral in character, intelligent and communicative in language, and more. KF
Origenes,
I think you are right about the “heat death” part, at least according to the current evidence.
But even if the universe is not eternal, does it require an explanation? I don’t know.
DS, while time pressure is on just now, a quick thought. The issues pivot on there being a world, which raises issues of roots of being. Non-being has no causal capacity so if ever there were utter nothing, such would forever obtain. This means — strange as it may at first sound — if a world is, something always was, something at causal root. Where, that points to necessary being that is integral to the framework for a world and which is material to the cause of contingent beings such as we observe and exemplify. Necessary beings will be things like abstracta or minds, both of which can constrain reality (think about mathematical constraints to the point where it seems magical, almost). The cosmos does not so much require an explanation as it requires a causal root; which is of explanatory character also. Time up for now. KF
PS: Entropy is time’s arrow and is keyed to random molecular level behaviour and trends that imposes.
KF,
I’m sorry, KF, but these are just non-starters for me. I think it’s very difficult to have exchange on this issue when we have such a fundamental disagreement right out of the gate.
It does raise an issue which I think is interesting, however: Can one who is some flavor of finitist (mathematically) perhaps still accept the idea of an infinite past (so an “infinity” in the world)?
Presumably you agree that the actual remote history of the universe is independent of your (and my) mind, and also our limitations, including the fact that we can’t finish counting infinite sets “in time”. Maybe there are or could be completed infinities in the universe, but we can’t comprehend them?
WJM,
Mainly lack of interest. With work and my other activities, discussing non-personal gods is fairly low on my list of priorities. Almost all my theist friends are Christians who do believe in a personal god, and part of my purpose here is to understand their point of view better.
Well, Christian friends and pastors I know use the word “who” in connection with God all the time. What can I say?
I’m literally asking if god is a person you can interact with (where “person” does not mean “human being”). Here’s a random link I found explaining further.
Do you assert that it is factually true that the god (or concept of god) that you are referring to exists? Or is it a belief you have adopted because it benefits you?
I would consider the word of people I believe are trustworthy to be compelling evidence, but there are many other sources of evidence that I would weigh as well. As it happens, many people I generally trust have witnessed to me, but at this point, after pondering the evidence I have, I’m still an atheist.
Why can’t we stipulate that even if nobody can offer a strong proof that an infinite regress of natural causes is impossible (or possible), such a regress is not scientifically provable and must be accepted on faith?
The kind faith I am talking about is the exact kind of faith that is described in Hebrews 11:3.
“By faith we understand that the universe was created by the word of God, so that what is seen was not made out of things that are visible.”
Of course if the materialist/ naturalist reject God he has to believe:
”By faith we understand that the universe is the result of an infinite regress of natural causes.”
If an infinite regress of natural causes is neither self-evidently true nor subject to proof, then it MUST be accepted by faith.
In other words, to accept an atheistic world view one must do so by faith. That’s not exactly the way atheists present themselves, is it?
DS:
Pausing for a moment, I give a fuller cite of my PS:
In short, I point out specifically where I disagree with the claim of an infinite number of finite integers, where distance from 0 is in effect number of +1steps to reach a given one. All naturals that we may so reach, z, will be finite but as the P/BB thought exercise shows, beyond any finite k from 0, there is still onward endlessness. This is the first principles logic of the scheme of counting numbers.
The notion of infinitely many finite counting numbers is self contradictory, as to get to any such number in finite steps implies just the opposite of infinite. The onward values go to endlessness, which cannot be exhausted. We stipulate that the endlessness is a quantity in its own right, and assign it as being the first transfinite ordinal.
That is, we have imposed a logical step that introduces a new class, one that depends crucially on our inability to complete a stepwise +1 succession of all natural numbers. Where, for any z that is finite, the preceding numbers up to z – 1 will also necessarily be finite.
So, we have to reckon with endlessness in its own right and have no right to stipulate that every z in N will be finite and bounded by a number of steps from 0 that is finite.
Every z we can reach will be so bounded but the endlessness is material.
KF
KF,
Obviously you’re free to do mathematics however you like. But does all this tell you anything about the physical universe, for example whether it can “contain” completed infinities?
DS, mathematics is the logic of structure and quantity, it is not completely arbitrary. This then reflects constraints on reality insofar as reality will be coherent and quantitative as well as structured. In this case, if there were an actually infinite number of causal successive cumulative stages to reach the present, some such stage, w for argument, would have to be infinitely removed from the present in steps. Counting up to the present from w as an effort then brings to bear the challenge of traversing an endless span in successive finite steps. By the logic involved, such cannot be done that way. In Math we indicate the trend in some way and then use an ellipsis to complete it. That cannot be done physically, one would have to actually traverse the span step by successive finite stage step. Which then fails. KF
KF,
So even God could not create a universe which contained a complete infinity?
daveS:
Then I will leave your education about Christian views in more capable hands.
I appreciate your time.
DS:
Strictly speaking, nothing really requires an explanation. Any need for explanations usually originates internally in the form of curiosity. Is there a particular reason your curiosity appears to wane when faced with possible explanations for the universe?
I think Origenes makes a good point with regard to heat death. If the universe has existed an infinite amount of time, it is still the case that within some finite amount of time something would have needed to have intervened in order to drastically lower the entropy. Perhaps you are not curious as to what has the capability to do that, but I am.
daveS,
Even if we were to allow for the sake of argument that a completed infinity were possible, the idea that an infinite set could be contained within the confines of a finite space seems to be logically incoherent. And God cannot what it is logically impossible to do. When theists attribute the quality of “omnipotence” to God, they do not mean that God can just do absolutely anything that you can represent in words.
DaveS @80,
There are two kinds of people: those who demand understanding and those who do not.
For me, “demanding understanding” often serves as a guide. For instance, I discard the possibility that the truth does not exist, solely on the ground that this concept would not allow me to arrive at an ‘understandable truth’. On the same ground I discard the possibility that things (like a horse or the universe) pop into existence without an explanation.
IOWs during my search for an ‘understandable truth’ such ideas are of no use. I weigh them and quickly move on after I conclude that they won’t get me where I want to go.
as to:
“So even God could not create a universe which contained a complete infinity?”
is this:
Of related note to the ‘newfound infinity’ of Christ’s resurrection from the dead is the unbridgeable Zero/Infinity conflict between GR and QM and Christ’s credible reconciliation of GR and QM:
Verse:
PS: BTW, DS, I have not asserted or implied w is an absolute beginning. As noted, beyond w is a leading ellipsis of endlessness. All I have said is that w is such that it is itself remote to infinite degree from 0 taken as the big bang for concreteness. That is, I am using the fact that beyond any particular time there must be an onward endless prior past if there were an actually infinite, beginning-less past of the physical world in some form. Just, w is also similarly endlessly remote from s0, on the requirement of an actually infinite past for the sake of argument. The problem is the onward stepwise causal progression from w to s0. And that leaves the issue of traversal of endlessness in steps on the table. The issue is real and cannot be evaded.
DS, an endless stepwise, finite stage cumulative causally tied process cannot be completed from an initial point. WE CAN HAVE A POTENTIAL BUT NOT A COMPLETED INFINITE OF THIS TYPE. The naturals are of this type as formation from {] –> 0, {0} –> 1, {0,1} –> 2 etc shows. KF
HeKS,
Well, if all the components of the completed infinite were physical objects existing simultaneously, then I do expect it would require an infinite amount of space*, but is that a problem for God?
Unless you consider Zeno’s paradox-type cases, where a physical object of finite size could consist of infinitely many components. Probably not possible given the laws of physics in our world, but perhaps logically possible? I don’t know.
Pinehas,
It’s not that my curiousity wanes, it’s just that I think that’s a very difficult question, and I don’t know how to tackle it.
I’ve described exactly that issue previously in these threads, pointing out that God could periodically intervene to “reset” things, enabling the universe to persist over infinite intervals.
WJM,
Thanks for the discussion.
KF,
I think I understand what you are saying, but does it entail that God cannot create a universe containing a completed infinity?
“I think I understand what you are saying, but does it entail that God cannot create a universe containing [square circles]?”
DS, God cannot make a square circle; a form of words impossible of being. He cannot lie and be true to his nature, so he cannot lie on an issue of being inherently good as to character. God cannot both be and not be. God, as a serious candidate necessary being is either impossible or actual; but cannot be both. And more. If something is impossible of being, then it is impossible. The P/B thought exercise shows why a stepwise, cumulative, finite stage endless succession cannot be traversed to completion. We can point out its nature and ellipsis of endlessness, and assign order type omega by way of quantification, but that’s it. We can have an endless succession that is potentially infinite but no such stepwise finite stage process will complete step by step to actual infinite values. Endlessness is at the heart of such a process. KF
KF,
So I gather your answer to my question in #88 is that yes, God cannot create complete infinities because that is logically impossible.
This does surprise me a little. It doesn’t seem as obviously logically impossible to me as creating a square circle. I think quite a few eminent Christian thinkers in the past have actually believed the universe to be infinite, so the impossibility wasn’t obvious to them either.
For my part, I didn’t know there was any obvious problem with God creating an infinite collection of things all at once, rather than one (or maybe finitely many) at a time, as if counting through N.
DS, no causally connected, finite step successive cumulative process can run to an actual infinity. When we see a logical entity the set of naturals, we see a stepwise successive process and its unlimited extension, thus a potential infinity. We never complete the process to actual infinity but can recognise a new order of quantity, the transfinite ordinal omega. And that is what is relevant to a proposed infinite past. I suggest, further that there will be no all at once lumped countable infinities in the material, physical world. (Infinite sets readily appear in abstracta.) KF
PS: Impossibilities can be obvious or not obvious, as obviousness does not control logical [in-]coherence.
KF,
Yes, “we” could not even in principle create an infinite number of origami cranes, for example, even if we had unlimited time, material, energy, etc. I didn’t know (and still don’t know) why God could not create them all at once (N.B. not in a finite step, successive cumulative process).
DS, we live in a finite world, ~ 10^80 atoms etc. That is not consistent with an infinite collection of material entities. As if that were relevant to the proposed infinite temporal past, which is a stepwise finite stage causally connected cumulative effect process. This may in principle go on endlessly, but it cannot actually attain to an infinite number of such stages/steps. And so we see the potentially infinite, unlimited future. Going to the past the need to traverse an infinite span from w to now, points to the severe problem of an infinite past physical world. KF
KF,
Yes, but I’m talking about what is possible for God, and not constraining myself to the conditions present in our actual universe.
My question is, could God have created a universe with infinite space/volume (all at once!), and then created an infinite number of origami cranes within it, again all at once?
If I understand you and others here, you are saying that is logically impossible, but I don’t see how you know that.
DS, irrelevant to the focal issue. Which is a claim about an infinite temporal past. That’s why I have not spoken to it (and no I have not spoken to such). Such a world would have radically different physics [start with cosmology], to begin with. Math and logic would be fundamentally the same. KF
kairosfocus @ 107: Well said!
KF,
Ok, fair enough then.
daveS: could God have created a universe with infinite space/volume (all at once!), and then created an infinite number of origami cranes within it, again all at once?
If I may chime in for funzies, who the hell knows. I, for one, don’t or can’t “believe it”, since the idea of an infinite number of objects is meaningless to me. (And you too.) Bottom line, it’s not possible for there to be an infinite number of objects within the universe we live in. Beyond that, we’re talking about a completely unknowable reality (“God”, “Ground of All Being”, or whatever you want to call it) beyond all human reason. Speculation about it is a complete waste of time. Better to get on with loving neighbor as self and walking humbly in the knowledge of your limitations.
What was God doing before the creation of the world? According to St. Augustine, “He was creating hell for people who asked questions like that.”
Of course, he partially meant it as a joke. I think his point was there are inane and stupid questions that aren’t worth answering because as any honest person should know they are not really answerable.
Honest questions deserve honest answers. Dishonest, disingenuous “gotcha” questions don’t.
mike1962 & john_a_designer,
I actually agree. I really doubt that I could ever answer them with any confidence. But sometimes I see these utterly mind-boggling questions answered readily here, and I’m left thinking, “What?? How could you possibly know that?”.
DS, that a stepwise, finite stage cumulative process cannot accumulate to spanning a transfinite range is not equivalent to a speculative cosmos that would have to have a drastically different physics than is warranted for our own. Similarly, there are key metaphysical concepts or constructs that are well warranted but seem incredible to us. Like, as simple analogy, being able to stand at one point on Earth and be due north of London, Kingston Jamaica and Tokyo. Sometimes it is inadequate or false concepts we have that blind us to things that are actually well founded. One such is something like the significance of impossible vs possible and necessary vs contingent beings. KF
KF,
In this case, I wasn’t referring to your argument about finite stage cumulative processes. Note that at least one poster in this thread does seem to believe that it is logically impossible for God to create a complete infinity (see #100).
The problem seems to be that while we cannot accept infinities, we cannot escape them. An infinite regress of cause and effect is rejected for various reasons. But the only alternative is to propose an Uncaused First Cause, however contradictory that might sound. Unfortunately that doesn’t really help. If, as we agree, you cannot get something from nothing and if an Uncaused First Cause was not the effect of a preceding cause by definition, then that Uncaused First Cause must always have existed. In other words, we are back to an infinity.
Here is an interesting article which I think has some relevance to the present discussion.
http://plato.stanford.edu/entries/leibniz-modal/
For example:
It may seem so but my post was to point out the fact that some (most) Atheists seem to think that because they can string up a bunch of words to form a seemingly coherent statement and then ask if God can do X concerning it else Y proves something.
As to “complete infinity”, I have no idea what you’re trying to describe.
Vy,
Sorry, if I misread your intent, I withdraw that part of my post.
And I meant, in that series of posts above, “actual infinity” rather than “complete infinity”.
One other point: in the OP WJM wrote
As far as I remember, I never implied that accepting an atheist/materialist (A/M) account of the world would be likely to make anyone happier. Quite the reverse. Living in a purposeless universe, filled with dangers and forces that could snuff us out in an instant, is a bleak prospect. The reason I quoted Marx is because he recognized, as many of us do, that religion offers a powerfully appealing alternative to that bleak prospect. That’s why I think anyone who thinks religions are going to disappear any time soon are deluding themselves. As I see it, there is nothing wrong with living in a way that makes one feel good, as long a it causes no harm to others. But just because something makes you feel good doesn’t necessarily make it true.
No problem 🙂
Absolutely agree but you do realize that several Atheists would argue that Atheism makes them feel good?
I remember quite a few saying being free from the “shackles of faith” is exceedingly liberating.
Seversky, an uncaused first cause is not a self-contradiction. Once there is a world, there is a necessary — and thus uncaused — being in its framework. (For simple instance try to conceive of a world before two-ness existed, or where it ceases to exist, including facets such as the contrast of distinct things such as A and ~A) Second, so long as we are responsibly and rationally free enough to be able to genuinely argue via ground-consequent (instead of merely go gigo-limited computing via cause-effect chains), we are self-moved, ensouled first causes. The perceived contradiction arises because of prior conceptions that make a necessary being, first cause of the cosmos seem absurd. When, we would be better advised to consider the comparative difficulties challenge as regards roots of the world. KF
Seversky,
“The problem seems to be that while we cannot accept infinities, we cannot escape them. An infinite regress of cause and effect is rejected for various reasons. But the only alternative is to propose an Uncaused First Cause, however contradictory that might sound. Unfortunately that doesn’t really help. If, as we agree, you cannot get something from nothing and if an Uncaused First Cause was not the effect of a preceding cause by definition, then that Uncaused First Cause must always have existed. In other words, we are back to an infinity.”
It seems you are conflating the problem of a physical space-time infinity with a non-physical one, as though they are the same.
infinite regresses are absurd in the physical sense, because of our inability to traverse an actual physical space-time infinite.
A uncaused First Cause is not contradictory in that sense, because it is not a physical space-time infinite. Such a first cause transcends space-time.
William Lane Craig is famous for popularizing the Kalam cosmological argument. (Anything that begins to exist has a cause/ the universe began to exist/ therefore it had a cause.) However, I prefer another argument he has used in some of his debates– a reworked version of one of Leibniz’ arguments. It goes like this:
Read more: http://www.reasonablefaith.org.....z4LtiUs6Su
While I like this version I think we could improve it by revising the argument slightly as follows.
My reason for the alteration is that many non-theists don’t really understand what we mean by “God”. For example they tend to confuse God with gods.
The advantage of Leibniz argument is that it is pre-Big Bang. In other words, it works even if we don’t know whether or not the universe had a beginning.
For causality to exist, one needs Time to sort out what happened first and what caused what.
It’s believed that space-time came into existence at the very beginning of the big bang. Thus, causality began with the big bang.
-Q
KF, HeKS, and anyone else interested: Here’s another paper on the “infinite past” issue, which I just ran across, which looks very clear and accessible:
“Methuselah’s Diary and the Finitude of the Past” by Ben Waters.
-Q
Causes can and do exist concurrently. There are some good arguments for God’s existence that use this fact.
john_a_designer,
Please explain, John. An example, even theoretical would also be helpful.
Thanks,
-Q
Creationism: the philosophy which divides reality in 2 fundamental categories of creator and creation. The categories are linked by the mechanism of creation, which is choosing. To choose means to make a possibility, which is in the future, the present or not to make it the present.
Creator
– all what is in this category chooses
– the existence of all what is in this category is a matter of opinion
– an opinion is formed by choosing it
– for example, love, hate, God the holy spirit, the human soul
Creation
– all what is in this category is chosen
– the existence of all what is in this category is a matter of fact
– a fact is obtained by evidence of a creation forcing to produce a 1 to 1 corresponding model of it
– for example planets, organisms, mathematics, fantasyfigures
So when you apply this scheme, it means for instance that love chooses, it may be the motivation for the decision for people to marry. But the existence of love is a matter of opinion, one cannot model love 1 to 1. One cannot state as fact that married people love each other.
It means a planet, like the planet Venus, was chosen to be. It means there was the possibility of a planet Venus, and then this possibility was made the present. Maybe it was 1 decision, maybe it were many decisions. The decisions could have turned out another way, in which case there wouldn’t be any planet Venus. One can model the planet Venus 1 to 1 in a book, in the form of words pictures and mathematics, and then one would have all the facts about the planet Venus.
What is in fantasy is just as well a matter of fact, as what is out in the universe. When fantasizing about superman, then really and in fact one has an image of superman in mind. The fantasyfigure Superman is just as well a creation, as are the other creations in the natural world.
Querius @ 127,
In his work Aquinas (like other medieval thinkers) made the distinction between sequences of causes which are essentially ordered vs. those which are accidentally ordered. He gave the illustration of a stone being moved by a stick which in turn is being moved by a hand as an example of an essentially ordered sequence.
A modern example would be of a golf ball being given its momentum by a golf club, which in turn is given its momentum by the arms and hands of the golfer who is intentionally trying drive the golf ball towards a particular goal. Notice that even though the golf ball is designed to fly aerodynamically through the air it has no power in and of itself to do so. It is given that power through an instrumentally connected series of causes. The same thing could be said of a golf club which is used as the intermediary cause. Notice that momentum is given to the golf ball in the instantaneous moment that the golfer hits the ball with his gold club. In other words, the sequence of causes is virtually concurrent at a single moment.
William Lane Craig explains it this way:
Read more: http://www.reasonablefaith.org.....z4M1gWIU9z
JAD, a similar case is a fire sustained by heat, oxidiser, fuel and an undisturbed oxidation chain reaction which must be simultaneously present for a fire to begin or be sustained. KF
DS, I am not arguing the Tristan Shandy case or anything like it. The issue I raise is that if an infinite past of days for convenience has passed to date, then some w must exist in which the world was, where w is in a causally ordered sequence that accumulates to the present and w is infinitely distant in days already past from the big bang, then onward our time. That is what I showed in the sequence (where 4-dot ellipses are of transfinite scale) at 65 above:
. . . . w+2, w+1, w, w-1, w-2 . . . . k, k-1, . . . s0, s1, s2 . . . sn + –>
The problem is not that w is a beginning, it is a start point for a count down:
w, w-1, w-2 . . . . k, k-1, . . . s0, s1, s2 . . . sn
But, this can be put in one to one correspondence from w with:
w, w-1, w-2 . . . .
0, 1,2, . . . .
This means the endlessness applies and the P/B example shows that the process of count down from w will never complete to reach s0, the big bang.
For at any w – k, k finite, due to endlessness we may put this in correspondence:
w -k, w- (k+i), w-(k+2) . . . .
k, k+1, k+2, . . . .
0, 1,2 . . . .
and see that each is equally endless, that is the stepwise cumulative causal succession of days will never exhaust an endless onward process.
We are warranted to conclude per best reasonable explanation, that to have arrived at today, there was no endless past.
That is, the temporal domain had a beginning that is finitely remote.
And as non being has no causal powers, if there were ever utter non being that would forever obtain, and there would not be a world.
There is a world, so we are warranted to hold that there was a past with a beginning, and that this implies necessary being at the root of the world.
NB sufficient to cause a world in which we exist as responsibly free and rational creatures, and in which there are strong signs of design in the cosmos and in biological life.
KF
KF,
Yes, understood. I just felt the “beginningless Tristam Shandy” argument was intriguing, although it really is incompatible with the tack you are taking.
I have to again say that once you assert the existence of this time coordinate ω infinitely remote from the Big Bang (or the present, or whatever), I’m out.
I am starting out with the assumption that all time coordinates are real numbers, and there is no real number ω infinitely distant from the time coordinate of the Big Bang. In fact, any two time coordinates in the model I am using are separated by a finite number of days.
You are certainly free to consider more exotic models of an infinite past with non-real or infinite time coordinates, but then you are talking about something different from what I have in mind.
KF,
One correction: On rereading your #131, I guess your ω and other elements in the sequence are labels for events rather than time coordinates. In that case I’m saying that my assumption that all time coordinates are real implies that for every pair of events a and b in the sequence, the difference in their time coordinates t(a) – t(b) is finite.
DS, I actually mean w, I forgot that this might suggest omega. I suggest that two distinct real numbers that we specify will be at finite remove the one from the other, as we may only specify finite reals, which will be interwoven with finite integers and indeed finite rationals composed from ratios of integers. This is different from, we have a finite step -wise cumulative causal sequence said to be of transfinite span, i.e. past-infinite. This will require that some stage we may tag w (per the above sequence) will be at transfinite remove from sn or s0. Or else, “infinite past” is self contradictory and meaningless. This, injects an endless span into the reckoning, by meaning of infinite in such an ordinal — highly material issue — stepwise successive, cumulative, causal context. And yes, I am highlighting the significance of the ellipsis of endlessness in stipulating the integers in succession per say the von Neumann construction, with omega as order type of the set of naturals (where we interweave the rationals and reals to get a continuum), and so forth. The problem then is not, that w is a beginning point, it is not as we can see. Instead, it is that an endless span would have to be traversed in finite stage cumulative, causally connected successive steps. The P/B thought exercise shows why that necessarily fails. We are warranted to hold that the past is finite and bounded at a definite beginning. KF
KF,
Thanks, I wrongly interpreted your notation.
I (and I think just about everyone else) disagree with this.
When we propose that the past was/is infinite, we simply mean that it was/is not finite, meaning that it’s not the case, for example, that every event in the universe has occurred within the last 13.8 billion years, say.
So let me try this: Consider the proposition “for every positive integer n we can compute, the universe already existed n seconds ago”. Now suppose this proposition is true. Under that assumption, is the past finite?
Correction to #135:
DS, either infinite means what it says or it becomes a synonym for finite. If time (the context of cumulative causal processes) is infinitely old, there must be a stage that is transfinitely remote; on pain of meaninglessness. Hence, implications of w. It is easiest to see this using finite, stepwise stages that cumulatively lead to now. Such are patently ordinal and can be tagged with the integers successively. I simply assigned the big bang event as a convenient zero. Beyond that for infinite past stages, some specific actually once existing then present and now infinitely past stage — w for convenience — must be transfinitely . . . endlessly . . . remote (hence w), but your admission just now is in effect there are no such stages. In short, we see the way infinite and finite are being inadvertently conflated as though they both mean actually finite. KF
PS: As you know, I argue that every countable we can reach will be finite but the set of naturals continues endlessly beyond any such count. Any two specific counting numbers we can reach or state will be finitely separate, but that just means two finites will be finitely different. The infinitude does not lie here, it has escaped. Which is where transfinite scale of the set of naturals comes in as an essential part of the meaning. Symbolised ever so misleadingly simplistically, as an ellipsis of endlessness.
KF,
I’m requesting a direct yes/no answer to this question:
DS, I have already given enough for you and others to see why proposing an infinite past runs into a serious issue of incoherence. We are instead well warranted to see that the past credibly was finite in duration, and the cosmos therefore had a beginning, per relevant logic. Not just things like evidence pointing to a beginning 13.8 BYA, with no actual evidence of a quasi-physical spacio-temporal world beyond that; never mind my for argument projections. The evidence is, the cosmos had a beginning. The logic of structure and quantity says much the same. This is warranted, and it is further warranted that that beginning did not come from utter non-being, as nothing has no causal capacity. Multiply by our being credibly responsibly and rationally free just to have a reasonable discussion. Mix in evidence of fine tuning of cosmos and design of C-chemistry, aqueous medium life that the fine tuned cosmos sets up. All this puts on the table as the only serious candidate a world-root that sounds a whole lot like the inherently good creator God, a necessary and maximally great being worthy of loyalty and the reasonable service of responsibly doing the good in accord with our evident nature. KF
PS: The observed universe evidently existed 13.8 BYA, expressible in seconds, and any number n of s from 0 to that equivalent [~ 2.86 * 10^17 s] will indicate the big bang as a zero point n back relative to it. As for beyond this time, that is another story.
pps: Note, the timeline of the cosmos is inherently causal and sequenced stage by stage, much as human generations are. This imposes the finite stage, stepwise, sequenced cumulative causal pattern that I have addressed above. It is that pattern that in turn raises the challenge of bridging endlessness in finite stage steps, which is what any proposed infinite past directly implies. Cf 65 above etc.
PPPS: I should note again on my logic that if the past was infinite, it must imply that at some time point w for convenience (the then present) there was a time infinitely remote from today, which has derived in cumulative, finite stage causal steps and processes fro0m w. Otherwise, it means nothing when we say there was an infinite past.
KF,
This does answer my question from #135 (from my perspective) considering that I assume from the start that all time coordinates are finite, regardless of where we set the origin. And that answer is “yes”.
To review, even if it is true that for any natural number n that we can compute, the universe already existed n seconds/years/whatever unit ago, the past is finite.
In fact, even if it is impossible to form a false statement of the form:
the past is finite.
Doesn’t that strike you as odd?
Each of the statements in the following “potentially infinite” series could be true:
yet the past is finite!
DS, insofar as we set specific time coordinates — presumably as real values interwoven with the span of counting numbers — they will be finite. That does nothing to the problem of traversing endlessness from some point/stage w in finite cumulative steps to reach the present. The issue comes to, does endlessness or infinity mean just that? If not the term is meaningless. Playing with oh we can only specify finite particular values does nothing to that. Endlessness is endlessness, A is A, and A is not ~A. Where it is also A X-OR ~A. Yes, we are back to core logic. KF
It’s not literally meaningless—our own universe apparently does not satisfy each statement “The universe existed n billion years ago”, for every natural number we can compute.
In any case, that’s how the term “infinite past” is used, and if our discussion is a mere argument about definitions, it’s not so interesting.
the past is finite.
It would seem so, given that “past” is related to cause/effect.
Doesn’t that strike you as odd?
Ultimately, everything is “odd.” That’s because existence as we know it ultimately makes no sense. But it’s a problem with human reason, not with existence. Obviously, existence is what it is, even though we have no rational access to it beyond the fish-bowel universe we occupy physically.
It’s fun to ponder these things, but ultimate reality is beyond the reach of human reason. (Not necessarily beyond consciousness, however. That’s a different subject.) One of the things that separates us from other animals is that we can perceive the limitations of our own thinking processes. That’s kind of fun to realize, isn’t it?
DS, again and again, you have dodged the central issue: if our past is infinite in our space-time domain, given the causal connexion, there was at some present moment w a stage that is causally antecedent to now, that was at infinite remove from today’s present. Where, the future arrives stage by stage in a causal succession. That leads to the implication of traversing an endless succession to sn — now — in finite stage steps. Which is demonstrably impossible per the P/B thought exercise. What you have consistently done is to argue on how finite value times can be specified and will be finitely separate, indicating that any past time given will be only finitely removed. This equivocates and runs into meaninglessness by self contradiction. You will recall our earlier exchange where I highlighted that the naturals are defined in such a way that endlessness beyond any value we can name or specifically state, is a material part of its being infinite, and that this un-traversible endlessness property is what gives rise to its transfinite order type omega. That is where there seems to be a hole in how we have often thought and talked, and I am standing on the point that infinite is not a synonym for finite. Nor is it coherent to claim that there is an infinite number of FINITE counting numbers at +1 steps removed in succession from 0. Instead, there is an endless extension of +1 steps that cannot be exhausted stepwise (which is in effect how we define a finite span) such that the endlessness is material to properly understanding the naturals. The reality comes first and our frames of thought must conform to it in the end. KF
mike1962,
I do agree with much of what you say, especially “ultimate reality is beyond the reach of human reason”.
On the other hand, what kicked off these threads was the claim that it can be proved, using human reason, that the past is finite. I remain skeptical of this.
KF,
I haven’t dodged it; I have repeatedly stated that I believe this is false.
Note that I haven’t denied the possibility that such a stage at infinite remove from the present could exist. I simply state that its existence does not follow under the definition of “infinite past” that apparently everyone else (including me) uses.
I’m going to go out on a limb and grant the (very real) possibility that the universe had always existed. That still does not mean it need not have an extrinsic explanation for its existence, for the universe is but the collection of material things, and material things are contingent, and contingent things require something else to ground their existence.
KF,
I maintain that daveS’ problem is precisely what I indicated in that original Craig and Durston thread and earlier in this thread. DaveS is fooling himself into thinking that an infinite past is a coherent concept and he keeps talking about how every specific number is finitely removed from zero or any other number because he keeps envisioning an infinite past as a step-by-step voyage from the present into the past, thereby converting an actually infinite past into only a potential infinite, like we would have with the future. He is converting a claimed beginningless sequence into a (potentially) endless sequence, but endlessness and beginninglessness are not the same or even comparable.
If you picture an infinite past by saying something like, “If I go back a billion years the universe is there, and if I go back a hundred billion years the universe is still there, and if I go back a trillion years the universe is still there…”, and so on, then you are reversing time’s arrow and fooling your mind into viewing time like the negative integers on a timeline, where you count 0, -1, -2, -3, and you could go on forever. That is simply not properly representative of an infinite past. It is coming at the issue of an infinite past from the wrong end … literally. If the past is infinite, we got to this moment by arriving at it, step-by-step, from the infinite “end” (for lack of a better term). In the Craig and Durston thread I tried to illustrate this idea with a man supposedly completing an infinite climb down a ladder to step on to the ground. As I said there, the problem is not with accounting for how he could get to the ground from any particular rung of the ladder, it’s how he could get onto any rung of the ladder at all in order to be making his descent. If we picture this scenario and envision the man already in the midst of his climb down the ladder, with one end of that ladder touching the earth, then we have already bypassed everything about the scenario that needs to be explained. The problem with arriving at the present moment from an infinite past is precisely the same problem as trying to count down to zero from ‘positive infinity’. It’s not that it would take you way too long to do it, even if you lived forever. The problem is that you could never start!
From what I understand of what you’ve been saying, KF, I agree with you that it is meaningless to talk about an infinite past while denying that there is any day, second, whatever, that is infinitely removed from the present. Granted, the idea of any particular number being infinitely removed from zero (or any other number) in any direction seems obviously absurd, but that’s precisely the point, and shows that the idea of an infinite temporal past is also obviously absurd. The only thing that seems to allow someone to affirm the possibility of an infinite past while denying the possibility of some day that was infinitely far from the present is this conceptual error of converting an actual infinite past into a potential infinite past by picturing the infinite period as extending from the present towards the past rather than from the past and arriving at the present.
It seems quite telling to me that of all the people I’ve personally seen try to argue for an infinite past, every one of them has either described it in a way that shows implicitly or explicitly that they are approaching it from the wrong end and thereby illegitimately converting it to a potential infinite or else that have actually affirmed that it might be possible for some specific past day to actually be infinitely removed from the present (which, if true, would still make it impossible to ever reach the present).
If daveS could adjust his thinking on this and his method of conceptualizing it then I think he would pretty immediately see that the past cannot possibly be infinite.
DS, Sorry but there it goes again. Kindly explain to us an infinite past of the world that does not include past times or stages that were once present but are now infinitely distant in the past; bearing in mind the specific, causal and cumulative nature of the development of the world across time. KF
HeKS,
I’m glad you posted on this, HeKS, because I don’t believe I answered some of these points directly before.
Let me lay out some of my suppositions about this proposed infinite past.
The totality of past events forms an actual infinite set, which exists independently of whether I think about it or not. In particular, when I describe a certain collection of past events and associate them with counting numbers 1, 2, 3, …, in no way does this convert the infinite past into a “potential infinity”. Say one of these events was the Battle of Gettysburg. Certainly my “counting” this event does not cause it to spring into existence—it’s already in the set. Just like the rest of the past events (say before some fixed time, for example last Thursday). We are not in the situation where we have finite sets which can be extended arbitrarily (which is how some think of the set {1, 2, 3, …}).
First, I am paying very close attention to the arrow of time—this was a major issue in the last thread.
Second, there literally is only one end to an infinite past, so I can’t go to the “other end” and look at the situation from that point of view.
Third, this is the definition of “infinite past” that “everyone” uses—namely, that an unbounded past is infinite.
Yes, and if you can find a mathematical or logical proof that shows that beginningless processes are impossible, I would like to see it!
I will stress again that I don’t believe it’s possible to “convert” this actual infinite set to a potentially infinite one—how could that even happen? I have no influence on these past events, AFAIK.
I think I have looked at this problem in every way that you suggest—however, no disproof of the possibility has been demonstrated.
But again, if it were so obviously impossible for an infinite past to exist, wouldn’t there be a paper somewhere in the literature that shows this? Some pretty smart people have tried (for example WLC), but none to my knowledge have succeeded.
KF,
Well, I did try to use several simple illustrations in the previous thread, essentially stating that the valid time coordinates for the past are the negative real numbers (assuming t = 0 is the present). It didn’t seem to help. [Edit: I also referred to the eternal cyclic cosmology models, which are still out there. Can you prove these are impossible without resorting to empirical arguments?]
But is that my job? I don’t think so. You are the one making the argument that an infinite past is impossible, so presumably you have the burden of showing than under this hypothesis, points infinitely removed from the present must exist.
daveS,
When I say that you are “converting” the past from an actual infinite to a potential infinite, I obviously don’t mean that you are actually affecting the reality of the past. I mean you are converting it conceptually in your mind. By making this conceptual conversion you suddenly make an infinite past seem like a coherent concept that is ultimately indistinguishable from the potential infinite of the future. That is, by counting backwards in time and supposing you will never reach an “end” to your counting you recast an infinite past as endless and ignore the show-stopping problems associated with a past that would actually have to be beginningless, not endless. By starting at the present and working backwards you can make actual progress moving from one event or day to the next as you move backwards in time, which you can extrapolate indefinitely, and you thereby convince yourself that it could work precisely the same way moving forwards in time from an infinite past. This ignores that the only reason you can make any progress in traversing the days or events backwards in time is because you have a definite starting point. But if you were to try to turn it around and make the progress from the infinite “end” you would be lacking any starting point from which to make any progress at all. This means that the two scenarios are not interchangeable. That you can envision counting backwards in time indefinitely in no way implies that progress could be made moving forwards in time from an infinite past. The notion comes across as little more than word salad.
Also, you seem to be getting caught up in how you “and everyone else” would define an infinite past. That is simply not the issue. Of course you would define an infinite past as one that extends backwards in time to infinity, or something along those lines. That does nothing but describe what is intended to be understood by the phrase “infinite past”. That, however, has absolutely no relevance to the issue we’re discussing here, which is not what kind of concept we intend to encapsulate in the phrase “infinite past”, but what would actually have to happen and be true – how time and events and causal chains would have to unfold – for an infinite past to actually exist. It’s when we start considering those things that it quickly becomes clear that an actually existing infinite past is simply nonsensical.
Also, I disagree with you on where the burden of proof lies here. The notion of an infinite past creates problems and states-of-affairs that, at least on their face (and I think much deeper than that), seem unworkable. We have already explained those problems in some depth and have therefore made at least a prima facie case for the impossibility of an infinite past. The burden of proof is therefore transferred to you to establish that the concept of an actually existing infinite past is workable after all, and not as utterly absurd as it appears on its face and as we’ve argued. A burden of proof is not some kind of absolute commodity that belongs to only one side of a debate or discussion. Any claim entails a relative burden of proof … even a denial of another claim that has raised arguments or evidence in its favor. KF and I have asserted that an actually existing infinite temporal past is impossible and we have offered several arguments and illustrations showing why we think that to be the case. You, in turn, have denied that these arguments prove our case, but without actually answering them or showing how they are mistaken or how an infinite past could be workable after all, and so you have not (as yet) shouldered your own burden of proof in asserting the possibility of an infinite past or in denying the sufficiency of our arguments against one.
There is also a further issue here, which is that we must ask what is the most reasonable or most likely answer to this question about the possibility of an infinite past. Our position with respect to God’s existence is that, based on the current state of human knowledge and the application of logic and rationality to the world around us, belief in God’s existence is the most reasonable and rational position. This does not require that we prove God’s existence, or the impossibility of an infinite past, or anything else with 100% certainty. If you simply assert that we can’t rule out certain things or establish the truth of God’s existence with 100% certainty, that really has no bearing on the validity of our position. If you want to say that one can deny the certainty of God’s existence by simply citing the possibility that reality does not conform to rationality or logic, well, OK, fine … nobody has said otherwise. Of course, that’s not only a far cry from the typical atheist claim that there is no evidence for God’s existence and that belief in God is irrational, but it’s actually precisely the opposite of that claim.
HeKS,
PS to my #152:
I absolutely agree that endlessness and beginninglessness are not the same. KF and I went around and around on this in the previous threads, and I am painfully aware of the difference, so I deny that I am converting one to the other.
In fact, this very “conversion” is the basis for some of the more obviously fallacious disproofs of an infinite past, which go like:
HeKS,
I can only respond to part of your post at the moment, but will read the rest later.
Well, I am pointing out KF and I are using different definitions, which is creating some issues. In fact, reviewing #138 and #139, I’m still not sure we’ve come to terms.
What do you think is the appropriate definition for “infinite past”? Do you think my definition (essentially that an unbounded past is infinite) is a bad one?
daves: On the other hand, what kicked off these threads was the claim that it can be proved, using human reason, that the past is finite.
I don’t think anything ultimately can be proved with regards to these questions. Because “proving” is an act of reason. Which we know is limited. (And what in us can “see” that reason is limited, and still be judging our own reason? You know your reason it limited. “You” can “see” that. Ponder that.) One thing, though, “finite past” as a term should be dispensed with for the more fundamental question of infinite cause/effect. It’s the same, using different words. And more clear, I think.
All I can say is that ultimate reality, whatever it is, is nothing that can be apprehended with reason. Your own consciousness cannot be apprehended that way. It’s no use. But at least we can see why. So why do we beat ourselves up trying? Fun? Well, maybe a little. Maybe koan? Maybe to wake up those who are ready? The adventures of consciousness, however, can be a lot more fun. After the koan of cause/effect is dispensed with.
Probably a simpler thing to grapple with is the conscious distinction of color. Red? Green? What the hell are those? “Conscious experience?” When your consciousness is in a state of “experiencing green” (to give it a label) what is really going on? And what relation does it have with “time?” I.e, cause/effect. Green? Red? Blue? Time? Huh?
O Reality, what is thy name?
Some of us love gazing at our navels. Oh yes we do. Donchyoo?
P.S. consciousness is primary.
daveS @155,
While that argument is technically incorrect, the conclusion in (2) is accurate apart from the the word “therefore”.
The primary problem with the argument is the very essential difference between the processes described in (1) and (2), which is that in (1) it is clear that progress can be made counting towards infinity (in the sense that the necessary sequence is defined and one can clearly proceed through the sequence and check counted items off a list, even if they are never actually getting any “closer” to infinity). In (2), on the other hand, it seems equally clear that no progress of any kind could be made proceeding towards zero (the present) from infinity.
Number (1) in that argument corresponds to counting upwards from zero to infinity, while (2) corresponds to counting down from infinity to zero. They are different, and they present different challenges, with (2) in a sense being “infinitely” more difficult than (1), because in (2) you can simply never get started, but in both cases you will never finish.
Suppose that X promises you $100, as soon as he gets it from Y, who promised X $100, as soon he gets it from Z, who promised Y … and so forth. Now, if this chain is without an end, all promises are perfectly empty and X will never hand you the money. In fact no money exchanges hands. There will never be $100 that passes through the chain.
Origenes @159,
Exactly. Because there is no first person to start progress through the chain.
The problem I’ve been talking about with respect to how daveS is looking at this scenario is that it’s kind of like starting with the proposition that you have actually been handed $100 (i.e. the present), which you got from Jim, who said he got it from Bob, who said he got it from Zeke, etc., and being told that this chain extends on into infinity and concluding that this just might really be possible because, after all, you’re holding $100 in your hand (i.e. you’re in the now). In reality, what you should conclude is that if the chain of persons prior to you was truly infinite, you would not now have $100, and neither would anyone else, and so clearly there was a first person who started passing on the $100 bill.
I really think the biggest stumbling block on this issue is the ability of people to imagine some arbitrarily large number of days ago as the present with some indefinite period of time already elapsed and think, “Well, days would be passing, so eventually we’d get to the present even if the past was infinite”. But no, the problem is in imagining the countdown of days as already being in progress and that right there is completely incoherent in precisely the same way that it would be incoherent if someone told you they were counting down from infinity and had arrived at some particular arbitrarily large number. Whatever that number would be, the question would be, “How did you get to that number?” It simply doesn’t make any sense, because if you were to ask someone to count down from infinity and to say out loud the very first number in their countdown you could wait for an infinite amount of time and you would never hear the person say a number.
DS:
If you can’t get from here to the “other end” how could you possibly get from the “other end” to here?
HeKS,
I’ll try to get to the rest of your earlier post tonight, but responding to #158:
Well, I agree that the processes are radically different. Counting down from 0 is easy to comprehend, and it’s clear, under the suppositions that I make, that you will never finish.
However, at least to me, it’s not clear that progress upward toward 0 is impossible (see the infinite cyclic cosmologies for models of this—where’s the problem). I do admit and understand that it’s a very bizarre scenario, but how can you prove it’s impossible mathematically/logically?
I will again stress that this discussion arose out of an alleged mathematical proof, so that’s what I’m most interested in seeing.
daveS @162,
I’m not sure how you think that cyclic cosmological models have anything to do with the problem. Philosophically we can be just as sure they are wrong for precisely the same reason we can be sure a non-cyclical cosmological model can’t be past eternal, and it’s for the same reasons we’ve been discussing. Empirically, we know entropy would carry through the cycles and so they could not extend back infinitely into past.
Further, noting that God could intervene to reduce or reset entropy presents two problems. 1) It doesn’t make the extension of the scenario into the infinite past any more coherent from a logical standpoint, and 2) It still requires God to exist, which seems to kind of defeat the point of your defense of the possibility of an infinite past.
Finally, as far as I’m aware, cyclical models are not remotely in favor anymore, except perhaps by those who are desperate to escape a beginning to our universe because of the theistic implications, which is precisely what motivated the creation and popularity of those models in the first place.
Well, as I’ve said, I’m pretty much worse than useless when it comes to any remotely complex math, and I simply don’t have the symbolic vocabulary to follow arguments that are framed purely in mathematical formulas. So I really can’t help you here.
HeKS,
I disagree with this. Let me state again what my question boils down to: Are there are sound deductive arguments proving that the past (actually a mutually agreed upon mathematical model of the past, presumably) is finite. I’m not trying to convince anyone that an infinite past is workable or not absurd. The question is whether such an argument exists.
As I’ve stated before, I do believe that the most reasonable explanation for the known evidence is that the past is finite (not that my opinion means much here). All I’m asking is whether the alleged proofs made by WLC etc. are sound.
Origenes,
If I understand this scenario, I do agree. No money ever changes hands, so person X never gets anything.
HeKS,
It’s just an example of a proposed beginningless process that doesn’t seem obviously absurd to me. It clearly doesn’t prove anything.
Do we? There are people working on these models in the present day, and the models supposedly don’t violate laws of thermodynamics.
I agree that it doesn’t make the proposal any “more logical”, but I’m not convinced there are any logical problems to begin with.
Regarding 2), to me, this infinite past question has approximately nothing to do with the existence of God. As I stated elsewhere (maybe above in this thread), no matter what the actual history of the universe is, I doubt I could comprehend it.
And to stress once more, my goal is to understand whether there are any sound deductive arguments for a finite past.
Pinehas,
I think the difficulty with that question is that if you do try and state it precisely, you have to deal with the fact that there is no “other end”. You’re always, throughout an eternal past, at a finite distance from 0, moving forward.
First off, thanks John for the clarification.
While events might be ordered in a causal relationship, it seems that time is required to effect them, even non-constant time . . . unless quantum time is a set of temporal locations without mathematical continuity.
There’s also a distinct possibility of the existence of more than one time dimension—in which one can travel at one rate in one and a different rate in the other: dx, dy, dz, dt1, dt2 . . .
Second, considering simultaneity, inertial frames, and causality, together with delayed choice quantum erasure, one can construct a simple thought experiment that places causality far in the future from a quantum event, which is the reverse from normal experience.
-Q
The above would mean the existence of potential causality, which is present in QM. Hmmm.
-Q
daveS @166,
I’m finding this a little confusing.
First of all, surely you know that it is trivially easy to offer at least valid deductive arguments for the finitude of the past. In fact, we have been providing some throughout the last few discussion in non-syllogistic form. More formally we could say:
1) If the past is infinite then infinity has been traversed in a series of finite steps to arrive at the present
2) It is impossible to traverse infinity in a series of finite steps
3) Therefore, the past is not infinite
OR
1) If the past is infinite then the number of past days/events constitutes an actually infinite set existing in the world
2) It is impossible for an actually infinite set to exist in the world
3) Therefore, the past is not infinite
OR
1) If the past is infinite then it was made so by successively adding moments that were once ‘the present’ to the number of past moments, one at a time
2) It is impossible to create an infinity by the successive addition of finite amounts of any quantity
3) Therefore, the past is not infinite
Now, you’re saying you want to know if there are any sound deductive arguments for the finitude of the past. This depends on the premises being true, or, more realistically (given epistemological constraints), being more plausibly true than false. But that these kinds of premises are true is precisely what we’ve been arguing all this time.
So you’ve already been given implicit, non-syllogistic deductive arguments (and now explicit syllogistic ones) for the finitude of the past along with arguments, illustrations and explanations supporting the truth of the premises, showing the arguments to be sound, or at the very least seemingly so.
In the absence of any counter-argument from you, we have reasonably discharged our burden of proof. If you wish to assert that these arguments are not sound after all then you need to show for each argument that either one or more of the premises are more plausibly false than true or that the argument itself is invalid. In other words, given the prima facie case we’ve made, if you wish to assert that the arguments are not sound then that entails a burden of proof on your part. If, on the hand, you simply want to throw your hands up and claim to be unconvinced then that entails no particular burden of proof, but that does not make for a very productive discussion and it raises serious questions about how open you are to reasonable truths on these issues if you don’t consider your request for a sound deductive argument to have been met after we have offered valid deductive arguments with premises that are more plausibly true than false and for which you apparently have no counter-argument other than to say you’re not sure the premises are true because maybe reality is just really weird. I mean, perhaps it is. And perhaps dead 1st Century Jewish religious figures are spontaneously resurrected to life after a few days through purely naturalistic chance events. That would be really weird, but maybe the the universe just is really weird.
DS,
The actual case I made in 65 above (and earlier) does not pivot on a beginning or on a count backwards from now, or Tristan Shandy discussions, etc. But instead on the meaning of having an actual infinite past of the world. As you must have known in the onward discussion:
This, you have never satisfactorily addressed or answered. I continue:
In your responses you have tried to suggest that between any two specific real values (which are interwoven with the counting numbers) there is a finite span. Where also, implicitly, there is no defined final real.
But the issue is not on reals, it is on discrete, stepwise successive stages. For first instance, accumulation of infinitesimal stages is irrelevant. What is needed is to address the ordinal succession that builds the natural numbers {} –> 0, {0} –> 1, {0,1} –> 2 etc. This is inherently unlimited and cannot be completed. At any finite k, we go k+1, k+2 etc and put k –> 0, k+1 –> 1, k+2 –> 2 etc endlessly onward. For Tristan Shandy fans, the same obtains for: k –> 0, k+1 –> 1,000, k+2 –> 2,000 etc. or the like. The point WLC highlighted is that endlessness is endlessness, finite step size is irrelevant to the property. But, if Shandy takes 365 days to write up one day in his life, the CAUSAL logic of succession is that every year he has added 364 unrecorded days while recording just one. His writing deficit piles up endlessly even if he lives endlessly. He cannot ever complete his biography at that rate. Whatever else one may say about Craig’s argument, this is patently the most credible conclusion.
Attempted spanning of endlessness in successive, cumulative steps is futile.
Where also, the relevant distance metric is one of succession or counting onwards between two ordinals p and q say. That is, the relevant distance between states p and q is the count 0, 1, 2 etc that matches the span from p to q, which BTW is obviously the same in both directions. (This is how addition and subtraction of wholes works.)
Now, we introduce the property, endlessness. That is, when such a count becomes endless it is of order type omega and cannot be spanned in steps. We take the logical step of assigning this degree of endlessness a quantitative label. There is no finite number t such that t + 1 = omega.
Likewise, a count up from zero to any finite k will be such that k, k+1, k+2 etc can be placed in 1:1 correspondence with 0,1,2 etc and will never terminate, i.e. beyond any specific finite k in the succession from 0, endlessness still obtains.
Thus, if one finds that between any two specific numbers p and q, there is a finite span, all one is showing is that both are finite and are bounded by some b that is at least equal to the larger. One has not addressed the onward endlessness.
This is where infinite past arguments break down.
For, beyond w in the causal chain of succession above, there is a span of endlessness to k. This is NOT a span between two finitely separate values. The count-step metric applied to w and k fails.
Instead, once an infinite past is claimed, it either means that there can be no stepwise spanning from w to k, or else “infinite” is being equivocated. That is it has been implicitly converted to mean finite spans only, when the issue of a beginningless infinite past is that there was a point w that was once the present but is now endlessly remote from us. Not large but finite, infinitely remote. Where also, causal succession is stepwise and unidirectional.
The span w to k cannot be bridged in successive steps, by counting or by cause-effect stages and processes.
We have no warrant for implying w in short.
The future beyond sn may be potentially endless, but we are warranted to hold that the past beyond s0 was finite, where s0 is finitely remote from some k, which we may call the point of beginning or creation.
“En arche . . .”
Thus begins Genesis in Septuagintal translation, and thus begins John.
Profoundly, wisely, and warrentedly.
This is where we are, therefore; on many grounds . . . at the foundation of Western Civilisation as we have known it:
And again:
After 2000 years, we are back here, where our civilisation as we have known it — Christendom — begins.
KF
PS: entropy, time’s arrow, is the bane of oscillatory cosmologies. And, the evidence is that the density and expansion of our world are not oscillatory. Indeed, expansion seems to be speeding up if anything.
Given an infinite past, there can only be a potential causal chain — akin to ‘unfulfilled promises’. An actualized causal chain needs grounding: a person who is not waiting on promised money but who actually has money.
A causal chain with an infinite past is a non-starter.
Origenes,
Yes … literally 🙂
HeKS,
As much as I enjoyed your ‘man climbing down the ladder scenario’ — by now, family and friends are familiar with it 🙂 —, my unaesthetic ‘$100 bill scenario’ might be more accessible to some.
HeKS,
First, I agree you make a reasonable point. Second, I actually have responded to the premises in the above three arguments you make above (in the old thread(s)). Specifically, I have criticized premise 2 in each.
But let me explain how I have tried to approach this question in an attempt to respond to your points.
First, since we are debating the finitude of what I take to be a set, I have insisted that we immediately fix a mathematical model for the “past” which we agree on. For example, in your ladder illustration, I take the set of integers less than or equal to zero {0, -1, -2, …} (along with some elementary math) as an appropriate model for the relevant instants in time. I think everyone agreed this was suitable (at least at first). Now I’m not saying this “proves” anything, but if we all agree on the model, and on elementary mathematics, then we have some basis for discussion, and no one can complain about the implications which follow from analysis of this model.
If we can’t come to agreement on the model or on the basic mathematics, then I don’t think we really can proceed very far in a mathematical discussion of the problem.
Of course, then we try to explain to each other why our own models are more plausible than our “opponent’s”. And in some cases, why our own philosophy of mathematics is best. I, for example, have tried to argue why “infinite numbers” should not be, or at least need not be in our model of past time.
So yes, I believe you are right that plausibility enters the picture, and that I have some burden.
Now ideally, two people discussing this issue would agree on the model and on some philosophical mathematical issues, and I think then there would then be no room for disagreement on whether to accept a particular argument as sound or not. Not that this means they have necessarily arrived at the truth, mind you, but rather once each accepts a certain list of “rules”, then there can be no disagreement on soundness.
Origines,
I’m not sure what a “potential causal chain” is, tbh. And I’m somewhat reluctant to address anything having to do with causation because I will immediately get in over my head, but consider this, if you don’t mind entertaining a ridiculously counterfactual scenario:
Person X1 just handed you $100. She tells you that she received that $100 yesterday from X2, and that X2 received the $100 from X3 the day before, and so forth throughout an eternal past.
That’s similar to the infinite past scenario that I have in mind, and I’m not aware of any mathematical or logical problems with it; now if you bring in grounding, require an explanation for this sequence, a “start” of some sort, etc., then there likely will be issues, I agree.
KF,
As I stated in #82, and taking some direction from HeKS in #170, we have been unable to agree on what the term “infinite past” even means. I have decided to take the pragmatic approach and try to follow common usage (which I think you can verify to your satisfaction)
So, what should we do?
DaveS,
The fact that $100 is handed to me proves that this causal chain had a beginning. Put another way: someone brought the money. It is exactly this beginning — or “start” or “ground” — that an eternal past fails to ground. An eternal sequence implies that each member of the causal chain will deny being the beginner. Each member will point to a previous person.
NO MEMBER BROUGHT THE MONEY, SO THERE ISN’T ANY.
Money does not enter the chain from nothing / by magic. So, given an eternal sequence, there is no “start” — there is no money — and therefore no $100 that passes through the sequence.
It runs into the same logical issue: it cannot ground a start and is therefore a non-starter.
Origenes,
Agreed. It is simple but effective.
Origenes,
Well, as I said, if you bring in premises concerning grounding and so forth, you can likely carry out the proof.
But I am talking about arguments which can be faithfully represented in terms of mathematics, and some have been offered by KF and others. How do we represent causation or grounding in terms of the mathematics of the set {0, -1, -2, …} (or whatever model you choose)?
Such arguments have been offered. For example:
Of course I don’t accept this argument because I don’t believe premise 1) is true. Or, put another way, we don’t agree on our model to begin with.
DS, it is patent that an infinite past means that there were times (which were then present but have since become past . . . leading to an intervening duration or succession of stages up to sn, now) — I used w as an example — which have led up to today (I used sn) such that the difference in times is infinite, endlessly beyond any finite value of past time. Or else, infinite is being redefined to mean finite and becomes meaningless. In particular, there cannot be an infinite number of distinct whole counting numbers in +1 steps from 0. What happens is there is endless potential succession so beyond any finite value k however large there is an onward endless succession that cannot be traversed in finite stage steps. KF
PS: Merriam Webster, meaning 4a: 4 a : extending beyond, lying beyond, or being greater than any preassigned finite value however large .
KF,
I go by how the people actually making these arguments use the term “infinite past”, and with I think one exception, they mean infinite in the sense of unbounded.
Referring to the dictionary definition, I also think that’s consistent with what I’m saying.
Assuming an “infinite past” (my understanding):
The universe is older than the preassigned value 14 billion years
The universe is older than the preassigned value 100 billion years
The universe is older than the preassigned value n billion years, where you can replace n by any natural number that we can compute.
DS, unbounded here means endlessly beyond any finite value no matter how large. This is exactly what I have consistently spoken. Note Merriam Webster 4a just now. If there was an infinite past, given that time marches as a succession of present moments, then there was some past time w, some past stage w, that is such that it is endlessly beyond any past time k that is finite, no matter how far back k is. Which is exactly where the problems lie as from w in succession the finite stage steps cannot span endlessness, [add:] so you have no basis of going in successive steps to k from w. W would exist if there were an infinite past. [: end-add] Where also time is forward marching at all times. When I began this comment is now past, and in a moment when I submit this time of composing will be past. KF
KF,
Remember our lengthy discussion of:
1. (There exists a time t)(For all natural numbers n)(t > n)
versus
2. (For all natural numbers n)(There exists a time t)(t > n)?
I believe that’s relevant here.
So, given that we can’t agree on this point, what should we do? Any suggestions from the gallery are welcome 🙂
HeKS,
I think it would be reasonable for you to ask at this point exactly what arguments am I concerned with. I have given one example in #180 and have stated that I am only talking about “mathematical or logical” arguments (maybe just “mathematical” would be more accurate), but it’s probably not clear what this really means. If I think of a way to clarify it further, I’ll post it, but it’s possible I might have to just say that I will recognize them when I see them, and decide on a case-by-case basis.
DS, the pivotal matter is that there is an inextricable causal and cumulative succession across time, in stages that we can view in terms of finite steps. This means, states, transitions and successors, so it is not just numbers and logic, though the logic of temporal quantities in light of their successor relationships, is relevant. In that context, the claim that has been made from your side is that there is an infinite past. For that to be reasonably meaningful, it has to be so that there were once past stages or states that are endlessly removed from the present or finitely remote past in a sense that is countable in principle and which then would require traversal of the endless span intervening. That is, w makes sense and k and sn make sense, which then lead to the inability to span the endless separation from w to k much less sn in finite stage successive steps. No matter how far removed k is from sn, so long as that span is finite. KF
PS: There is no guarantee of an endless future, and the above shows that proposed endless past is deeply problematic given the causal structure of time.
PPS: Just as a reminder from above and originally 65:
daveS,
I don’t have time right now to address previous comments, but I’m wondering what you would think of this argument for the finitude of the past, which just popped into my head.
1) The past consists of moments that were once the present
2) If the past is infinite, then for any given moment there were infinitely many moments that preceded it
3) If an infinite past entails that for any given moment there were infinitely many moments that preceded it, then an infinite past entails that any moment that was at one time the present was preceded by an infinite number of prior moments already constituting the past
4) If an infinite past entails that any moment that was once the present was necessarily preceded by an infinite number of moments already constituting the past then it entails the existence of infinitely many past moments that were never the present
Therefore:
5) Either premise 1 is false and the past does not consist of moments that were once the present, or the past is not infinite
6) Premise 1 is not false and the past does consist of moments that were once the present
Therefore:
7) The past is not infinite
Thoughts?
KF,
All I can say is that’s not the way the term “infinite past” is used (almost uniformly) in practice. I don’t really care to debate whether it’s a poor choice of wording or not, as long as I understand what it means when used by others.
HeKS,
This is indeed an argument that I consider “mathematical”; I can interpret it as statements about the set of nonpositive real numbers, in particular.
I accept premises 1 and 2, and possibly 3? Certainly I do accept that under an infinite past, “any moment* that was at one time the present was preceded by an infinite number of prior moments already constituting the past”, from the view of the moment marked with *.
I don’t agree with premise 4. In fact, I don’t agree that under my model of an infinite past, there were any moments that were never the present.
daveS @189,
I’m once again confused.
If you accept premises 1 and 2, premise 3 follows necessarily, so you can’t just “possibly” accept it in a questioning way.
Also, if premise 3 is true, as it must be if 1 and 2 are true, then premise 4 also follows necessarily, because from 1, 2 and 3 we see that ANY present moment would have to ALREADY be preceded by an infinite number of moments that ALREADY constituted the past. In other words, you could NEVER have a moment that was “the present” without ALREADY having an infinite number of moments preceding it called “the past”.
So if you want to deny 4 then it’s going to require more than simply saying that you don’t agree and saying that your model of an infinite past doesn’t include any moments that were never present. You’re going to have to explain how that could possibly work, because the whole point of my argument is to show that a model like the one you claim to hold is logically impossible, essentially by definition.
HeKS,
What I meant was, if I understood premise 3, I accepted it, but I must not understand #3 after all. Let me walk through my thought process, starting from the beginning.
I’m representing time coordinates with the set {…, t(-2), t(-1), t(0)}.
#1: The past consists of moments that were once the present.
So the past from the point of view of the present, t(0), is {…, t(-3), t(-2), t(-1)}. And yes, all these moments were each themselves once the present.
#2: 2) If the past is infinite, then for any given moment there were infinitely many moments that preceded it.
Yes. The past from the point of t(k), which is {…, t(k – 3), t(k – 2), t(k – 1)} is is an (actual) infinite set for any integer k = 0 or less.
#3: If an infinite past entails that for any given moment there were infinitely many moments that preceded it, then an infinite past entails that any moment that was at one time the present was preceded by an infinite number of prior moments already constituting the past.
Do you mean “already constituting the past” from the point of view of the “any moment” in bolded italic?
Let me use t(k) to represent this particular moment which was at one time the present.
The past from this point of view is {…, t(k – 3), t(k – 2), t(k – 1)} (just like above).
t(k) was therefore preceded by an infinite number of prior moments already constituting the past from the point of view of t(k) (or later).
Is that consistent of what you are saying?
Edit: Responding to:
This is correct and is consistent with my model. But I deny that means there exist moments that were never the present, which is what I take premise 4 to say.
daveS,
As far as I can tell you have correctly understood the premises.
That said, let me clarify for you the logic that informs premise 4.
Here it is again:
Now, to (try to) clarify …
In an infinite past, in order for any moment to be identified as “the present”, it must already be preceded by an infinite number of prior moments.
This means that the existence of a prior infinite set of moments is a precondition for the existence of any moment that could be identified as “the present”. To deny this is to deny the reality of an infinite past.
This means that in a cosmos (i.e. all physical reality) with an infinite past, the existence of some infinite set of moments called “the past” is logically prior to the possible existence of any moment called “the present”, because you could not ever have any moment called “the present” that is not already preceded by an infinite number of moments. This is a necessary entailment of an infinite past.
This, in turn, is precisely opposite to the order of logical priority we assign to “the present” and “the past” in any model where “the past” is said to consist of moments that were at one time “the present” (i.e. premise 1).
In any model where “the past” is said to consist of moments that were at one time “the present”, “the present” has logical priority, and we might also say ontological priority, as any moment must first exist as the present prior to it becoming the past. Such a model works to describe a cosmos with a finite past. But it does not work to describe a cosmos with an infinite past because in such a cosmos an infinite number of moments would have to already exist before any moment could be “the present”, so no moment in that infinite set of moments could ever have been “the present” because that set had to already exist in order for any moment to be “the present” in a cosmos with an infinite past.
HeKS,
Getting into “logical priority”, this is less mathematical, so it likely is outside the class of arguments that I am considering, but I will give it a shot.
I can think of a couple points:
1) The correct formulation is that any moment t could be the present only after all (infinitely many) moments prior to t already have already been the present and now are past. And this always holds in my model, for any t, so there is no violation of this logical priority principle. There is no instance where a moment becomes present before (or even at the same time as) all moments in its past have been the present.
2) It never is the case that fewer than infinitely many “past” moments exist. That is, any moment must be of the form t(k), and at that moment, {…, t(k – 3), t(k – 2), t(k – 1)} already are in the past, hence it’s legal for t(k) to be the present.
DS, Infinite has a meaning, and infinite past has a meaning. I put it to you that an infinite past quasi-physical world must properly refer to a past of our world in some form endlessly beyond any given finite past stage or date, say k, however remote itself. That is, beginning-less and extending into the past without any limit or bound. Which directly implies that there will be some w that is endlessly remote onward from k. For simple instance I met in electronics class many many years ago now, this is why a strict mathematical sinusoidal oscillation is physically impossible as it would extend from infinite past to infinite future. KF
PS: You will note that I have emphatically spoken to causally successive stepwise cumulative transitions from past to present and onward, as this avoids the confusion of the infinitude of a continuum. Reals, anyway, are interwoven with the integers, so that is of no real consequence save as a rabbit trail. The issue is, an infinite past will have stages or states or steps of finite scale, that were once the present but now are in the past beyond any finite value, however large.
PPS: Note Durston, http://p2c.com/sites/default/f.....v.%203.pdf
daveS,
I can’t figure out how what you’re saying makes any sense.
Consider the scenario in a finite cosmos.
We begin with a first moment, “the present”, and no past. That first moment is then replaced by a new moment. Now that new, second moment is “the present” and the first moment has become the first member of “the past”. This continues on and on and “the past” grows as each present moment becomes a past moment, with us finally reaching about 13.7 billion years worth of past moments in our universe. This works. Under this model it makes perfect sense how every past moment could have at one time been a present moment.
This, however, is not the case in a cosmos with an infinite past. In such a cosmos there is no first moment and so it is impossible for all past moments to have first been present moments. Instead, you’re faced with a scenario where for any given moment to be the present, there must first have been an infinite number of moments already existing. Again, I’m worse than useless in trying to present this stuff in any kind of standard mathematical formulation, but it seems we would present this as saying that in order for some moment, t(k), to be “the present” in a model where all past moments were once present moments then we would require not only that the infinite set of {…, t(k-3), t(k-2), t(k-1)} must already exist, but that t(k-1) was previously the present. However, in order for t(k-1) to have previously been the present, we would need the infinite set of {…t((t(k-1))-3), t((t(k-1))-2), t((t(k-1))-1)} to exist and for t((t(k-1)-1) to have previously been the present (I think there’s an unnecessary layer of parentheses in there but I was trying to visually isolate the ‘t(k-1)’), and so on to infinity.
In reality, I think trying to present this in a formula is only making it more confusing coming from someone who doesn’t have the background to present the argument this way, and as KF has said numerous time, the ellipses hides all of the logical problems with the scenario.
The point is that it is logically impossible for the existence of “the past” to either precede or be concurrent with the existence of “the present” and yet for all past moments to have once been present moments. But if the past is infinite then it is logically necessary that an infinite number of moments must already have existed before any moment could be “the present”. In a cosmos with an infinite past, there cannot be a present moment unless there is already an infinite number of prior moments. So we are faced with two propositions or claims: 1) in order for any moment to be “the present” it must first be preceded by an infinite number of “past” moments, and 2) every past moment was once “the present”. These propositions cannot both be true. If you think that they can be then you’re going to have to explain how that could be without appealing to an argument that conceptually recasts the past as a potential infinite by relying on a perspective that moves backwards through time, thereby hiding the logical impossibilities within conceptual ellipses.
Also, KF, if you have any comments on my argument in #187 I’d be interested in your thoughts.
DaveS,
It seems to me that you are saying: a $100 bill has exchanged hands an infinitely many times and today X hands it to me. No logical problem.
However, what’s been skipped over here is how any moment becomes the present (how the $100 bill comes into existence).
Given an infinite past, a moment can only become present (getting an actual $100 bill) when it is preceded by a moment which was the present (had an actual $100 bill to give).
However, if every moment must point for the grounding of its existence to another (previous) moment, then there is no grounding at all.
Similarly, given an endless line, if everyone points to the person on his left for the $100 bill then there is no $100 bill at all.
If Y carries Z and Y is carried by X and X is carried by W … and so forth. And this goes without an end, but no one is standing on the ground, then no “carrying force” is going upwards through the chain. IOWs there can be no carrying at all.
F/N: The challenge then is to get from w to k in finite, successive, cumulative steps one after the other. This runs into the problem of attempted traversal of endlessness in such steps. A potential infinity can be created that way but it cannot be traversed that way. Precisely because at any finite stage onward from w, say v, there will always be an onward endless succession that can be put in 1:1 correspondence with the counting numbers from 0. Thus, we cannot traverse endlessness in such steps. This shows that if we are at a finite remove from s0, there can only have been finitely more prior past stages, say to k. KF
HeKs, I only say, interesting, cf Durston as linked. KF
PS: Note, I argue that any specific integer reachable from 0 by counting or the like will be finite, the endlessnesses beyond any such in positive and negative directions are a crucial part of the set’s meaning.
Origenes,
Once again, exactly. That is how I’m reading daveS’ response to my argument as well and it simply doesn’t make any sense to me.
In a cosmos with a finite past, the existence of the past relies on the prior existence of the present. In a cosmos with an an infinite past, the existence of the present depends in infinite regress on the prior existence of the past, which means it is logically impossible for every member of the set of infinite past moments to have previously been a present moment. There must be an infinite number of “past” moments that were always past but never present.
(Note that my argument in #187 doesn’t even deny the possible existence of an actual infinity in the world, even though I do think this is impossible)
HeKS,
Yes, no problem there.
I really don’t see the logical problem here; granted an infinite past seems much stranger than a finite one. But I will read on.
Yes, agreed.
Yes, true. Every one of t(k – 1), t(k – 2), t(k – 3), and so on, must have each been previously present.
I think I understand what you are saying. If so, I might phrase it like this:
and so on.
Referring to the last sentence, according to my hypotheses and model, there always have already existed an infinite number of moments, one present, and infinitely many in the past (each of which were once present).
Now I think your argument shows that such an infinite past can never have a “starting point”, because there is a chicken-egg problem: You can’t have a present moment without that moment’s past already existing, and you can’t have all these past moments existing unless they were present at some time.
But under my hypothesis, I don’t think there are any violations of this logical priority principle; you can’t point to any particular instant t(k) that occurs before or at the same time as a moment in its past.
So I think my strongest response would be to ask for you to exhibit a violation of logical priority.
I’m just not convinced that this potential infinity issue is even relevant here. I take it we are both assuming that given an infinite past, it is indeed an actual infinity, and nothing can change that. And I am very aware of potentially “hiding” the strange nature of an infinite past when referring to these infinite sets in reverse temoporal order, although I’m not convinced there are any logical impossibilities here.
If you consider quantum erasure, you will have a different perspective on causality, remembering that causality is tightly bound with time.
I suspect that there are no physical infinities.
-Q
Origenes,
I don’t think your $100 bill problem creates any mathematical problems; certainly if you bring premises into the problem pertaining to grounding, everything that exists having an explanation, etc., surely you can prove this example is impossible.
HeKS,
Indeed. And I get the impression that DaveS is unable to incorporate this causal relationship (this dependency) in the mathematics.
I agree. There is no “first present”. Similarly, there is no first step on the ladder, no first $100 bill and no one standing on the ground.
Origenes,
True. The “purely mathematical” arguments I’m concerned with really don’t have anything to do with causation, IMHO. For example, my post #180.
DS, stepwise, finite stage cumulative causation is critical to the issue. KF
It’s interesting that so much of ID and theistic argument centers around trying to explain concepts that seem (at least to me) to be absurdly obvious, or around making cases that really make themselves once one understands the concepts and terms.
DaveS and HeKS,
I think I can see where the problem with your discussion lies. Possibly the following helps you to refocus a bit. The following is (very) non technical, there are much more precise definitions than those given here.
First a definition for infinity:
(1) Infinity is an entity greater than every (natural) number
We’re leaving aside the question, whether such an entity can really exist in the real world.
Now a really non mathematical definition for sets:
(2) A set is a mental bag, where we can put (hypothetical) items into.
(3) an infinitite countable set (ICS) is a mental bag that contains all natural numbers (or an equivalent).
An ICS has the following properties:
(3a) An ICS does NOT contain infinity!
(3b) An ICS cannot be counted to the end!
In the act of counting an ICS eventually leaves behind any natural number, and so it approaches infinity as a limit (without ever reaching infinity itself)
(4) an actual infinite set (AIS) contains more than an ICS, it contains infinity itself. Such sets are frowned upon, because they are really weird, to the point where everyone questions whether they have any connection to reality.
Now when you both speak about the eternal past, you use your own mental bags labelled “eternal past”.
DaveS’s bag labelled “infinite past” contains an ICS of past moments but not infinity.
HeKS’s bag labelled “infinite past” contains infinity in addition to what DaveS has in his bag, so he sees an AIS.
With this in mind we can rephrase your discussion as follows:
HeKS: When I look into my bag labelled “infinite past” I see some really weird stuff that shouldn’t be true in the real world.
DaveS: I’m looking into my bag labelled “infinite past” and I don’t see anything like what you describe.
More helpful would be to discuss the question, whether an infinite past contains/ must contain actual infinity (=an actual infinite amount of past moments) or not. DaveS clearly thinks, it doesn’t, while HeKS think it does. When this question is clarified, everything else should follow easily.
One pointer:
Just because we can enumerate an ICS of past moments, doesn’t tell us in itself, whether an eternal past contains an ACTUAL infinite amount of past moments. Those two are not the same. An ICS is not/doesn’t contain actual infinity.
I think (3b) above tells HeKS that the infinite past must be an AIS.
I think the fact that you can enumerate past moments like natural numbers tells DaveS, that the infinite past is an ICS.
Hope that helps a bit
The following simple equation captures the problem:
No matter how many times a $100 bill is promised (see post #159), if no one actually has a $100 bill, then “$100 bill” equals an empty set.
If Z is claimed to be carried by Y and Y is claimed to be carried by X and X is claimed to be carried by W … and so forth. And this goes on without an end, but no one is standing on the ground, then no “carrying force” is going upwards through the chain and all claims are connected to what is a perfectly empty set.
HGP,
First, as say the surreal numbers show, there is no one “infinity,” so it is better to say that the infinite is endlessly greater than any specific, arbitrarily large but finite counting number we may identify in succession from 0.
This captures that there is a specific metric process of succession from zero that reaches specific values, say v, and the onward endless succession beyond any such value:
{} –>0
{0} –> 1
{0,1} –> 2
. . .
{0,1,2, . . . [v-1]} –> v
{0,1,2 . . . v} –> v+1
etc.
[without limit, i.e. endlessly]
Notice, I am emphasising the endlessness of succession as a key property of this set or construction. Endlessness is not a member as such, but it is a defining characteristic. It is specifically the basis for the claim that the set of counting numbers from zero is transfinite, having order type omega. That is, we see the endlessness and recognise this to be a type of quantity amenable to logical and structural analysis, thus a mathematical quantity. We denote it with a label, omega, and proceed to have other transfinites in succession therefrom. Resorting to the surreals (in effect capturing individual numbers in successive branched vice-grips like jaws of a locking plier starting from {|} and generally using {L|R}), we see all sorts of numbers great and small in a strange tree-like array, of infinitesimal and transfinite character as well as those which are finite.
A countable set then is one that may be put in 1:1 correspondence with this counting in +1-step succession finite stages (“counting numbers”) set; up to some limit [its scale], or else endlessly. If the latter, the set is also transfinite or infinite in scale. (I actually prefer transfinite. [other transfinites are such that they cannot be so matched, the continuum is a classic example. Just to make sure we are on the same page.)
The further point then is, if there were an infinite actual past, then unless “infinite” is meaningless (e.g. a de facto synonym for large but finite . . . as in, every particular value of remote time or stage of the past of the world we inhabit was FINITELY remote from us . . . ), there were specific stages or states of the world, say w, in the deep past. Where, any w is such that it was once the present but is now — by reason of the hypothesis, for argument — ENDLESSLY remote beyond any specific past time or stage, say k. Where, further, s0 is say the big bang (finitely successive to k) and sn is now, with more to follow through causally successive connexion.
Where, as well onward states follow immediate predecessors causally as a finitely removed onward stage, even as there is causal succession as one steps down the finitely separated rungs of a ladder one after the other. (Rungs of course need not be exactly evenly spaced.)
Thus, as has been presented from 65 above and so forth (with the four dot ellipsis representing endless succession not finite succession). Note also, there is no claim that w is a beginning state, just the opposite.
Clipping again:
In short, there is no warrant for proposing an infinite past as this poses the challenge of spanning the endless in stepwise, finite stage, causally cumulative succession from w to k or whatever way one may otherwise express this.
We are warranted instead to suggest that some k, finitely remote from now, is instead the beginning of the world as we know it.
To this, we add that it is axiomatic for good reason to see that non-being [“what rocks dream of,” per Ari] has no causal powers. So, were there ever utter noting, such would forever obtain. As a world now is, then, there was something at the beginning as a world root that has adequate causal powers for a world such as we experience to come from that root.
This raises the issue of being, impossible vs possible and of the latter, contingent vs necessary. A fire is a classic illustration of a contingent possible being, and the form of words “square circle” shows impossibility of being, as core characteristics for each half stand in mutual contradiction. Necessary beings are such that no world may exist without them, they are framework to a world, i.e. they lack dependence on external enabling on/off factors, are such that once a world is they must be there at its root (the only place they can be), and have neither beginning nor end. To see such, try to imagine a world in which two-ness (including the contrast A vs ~A) did not exist.
The point is, if the world we inhabit credibly had a begining, it had a causal root that is of adequate existential and causal character to account for it. This, involving, necessary being as an integral part of that root.
Where, a serious candidate necessary being (silly parodies such as flying spaghetti monster or any composite entity etc need not apply) will either be impossible or else possible — existing in at least one possible world — which then entails existing in any possible world.
Yes, we are in unfamiliar and even strange grounds, but this is because we are addressing hard questions beyond what we are wont to do in this day and age, and face questions of being, cause, succession, infinite and more.
For instance, unless we are capable of responsible, rational freedom, we are not fit to be able to discuss rationally; including these matters. This means that the root of the world must be adequate to ground rationally free and morally governed beings such as we are. Where gigo-limited, necessarily blindly mechanically interacting computational substrates [think, Pentium chip recall . . . ] cannot account adequately for this.
There is only one serious candidate, after centuries of debates: the inherently good creator God, a necessary and maximally great being, worthy of loyalty and the reasonable service of doing the good in accord with our evident nature.
If you doubt, simply propose and discuss a serious alternative that does not run into insuperable comparative difficulties. Such as, the self referential incoherence of implying that responsible, rational freedom reduces to blindly mechanical computation or conditioning etc. and/or the nihilistic chaos that moral government reduces to might and/or manipulation make ‘right,’ ‘truth,’ ‘value,’ ‘meaning,’ ‘duty,’ ‘justice’ etc.
Big issues are on the table.
KF
kairosfocus @209
Thank you for filling in the technical details I left out of my post.
I very much think, that an eternal past is impossible (just like HeKS). But I think the discussion between HeKS and DaveS suffers from concentrating on side points while leaving out the main point: Does an (hypothetical) eternal past contain any moments removed from the present by an infinite amount of time? If yes, what you says follows immediately and I very much agree with your take. DaveS OTOH seems to think, that an eternal past doesn’t contain moments removed from the present by an infinite amount of time. Therefore he doesn’t see all those problems that everyone is talking about.
My proposition was to concentrate on this issue. After this problem is resolved, everything else should easily fall into place according to what you just wrote.
[QUOTE]There is only one serious candidate, after centuries of debates: the inherently good creator God, a necessary and maximally great being, worthy of loyalty and the reasonable service of doing the good in accord with our evident nature.[/QUOTE]
Generally, I agree with you on this.
HGP,
the problem is, that is what I put on the table from the beginning, way back [this actually follows from several discussions across the course of this year], but this is being side-lined consistently. What does it mean to have an infinite actual past given the characteristics of the world we live in, of causal step by step succession of finite stages?
Unless it is meaningless, a claimed infinite past must include stages like w in the above. Which then INHERENTLY poses the issue of stepwise spanning of an endless succession from w to k. Where k beyond s0 the big bang is there to account for multiverse hypotheses, oscillatory universes and the like. DS is using claims that all counting numbers are finite and the set infinite in cardinality, to imply that it is enough to point to there being finite predecessors to any particular time.
(This led to considerable discussions earlier, including ordinary vs transfinite induction, the nature of sets and the structure of quantities, ending up with his suggesting the surreals, which seem to be the best framework for discussion, the transfinite hyper reals on my view are one of the branches of the surreals locked away within ellipses of endlessness; I suggested that we catapult back and forth to the infinitesimals near zero and up to the transfinite hyper reals by the trick of numerators falling towards 0 or increasing without limit. My conclusion — and I accept this is “heretical” — is that endlessness is a key characteristic of the counting numbers and is where the infinite cardinality comes from. So, ordinary induction is that any successor we can reach will have the chaining property once we have an initial established case. I find it an absurdity to claim that one has used induction or the like to show that there are infinitely many distinct, +1 step removed successive counting numbers from 0 where all are finite in value. By definition, the finite is bounded by a succession of steps from 0 that will terminate at a definite, non endless, stage. So the property of succession is not compatible with such values being both finite in scale and infinite in number. Instead, I suggest there is an inherent endlessness so that any number we can reach by counting is finite but inherently there is no bound to onward succession and this property is the source of the infinite character. Hence emphasis on endlessly beyond any particular value reachable by successive +1 steps from 0 or extensions thereof. )
My point to him is this in effect reduces the infinite claim to a finite claim.
HeKS has pointed out that the approach from now in successive recession through the past invites the conceptual confusion that a potential infinite [which is actually finite at any stage of succession but unbounded pointing to what is boundless].
Latterly, he has asked, where’s the beef, using a $100 bill, to suggest unless it comes from somewhere, it cannot be passed in succession.
Substitute for this, existence to see his point.
Given causal succession, any stage of the cosmos . . . contingent . . . has to receive its existence form a prior one sufficient to account for it. But this cannot come from thin air (oops, air is SOME-thing, let’s go back to Ari: a rock’s never-never dream world . . . ) or be smuggled in as endlessly passed. Every stage is contingent and contingent entities are not causally self explanatory. So, where’s the beef?
De hamburger bun is empty, in short.
KF
PS: use the usual limited html tags with angle brackets.
OOPS: Denominators falling or rising.
(I decided to go back and fill in thoughts then paragraphed.)
BTW, going back to a connexion to the OP’s focus, unless there are moral and logical truths that we may freely reason about and come to so warrant that we credibly know, all discussion is futile. This leads to needing a root cause adequate to account for a world with morally governed beings in it such as we must be just to discuss. This then makes nonsense of schemes of thought that reduce moral thought to illusion or social or personal conditioning or whatnot. Which then points onward to the issue of a world-root adequate to issue and pass on the beef, the $100 bill, of moral government. That is what puts ethical theism and comparative difficulties analysis firmly on the table. So, it all connects. KF
Origines, yup, where’s de beef? Somebody got to start the beef for it to be passed on! A contingent chain is not self explanatory, per root of existence. Nor is the never never world of a rock’s dreams — a genuine non-being, a true nothing — enough to get the chain started. And, resemblance to printing money and where it can lead if money is created out of thin air without credible labour, goods and services to back it up, is not accidental. Thence, many a financial crisis and chaos. KF
hgp,
I think that HeKS and I are actually on the same page on this matter, based on HeKS’s comments above—he and I agree that no moments in the past in the model I’m using are infinitely far from the present. None of the arguments he’s making depend on the existence of such a moment, certainly.
And just to be clear, I consider the past to comprise an AIS as well.
DS, if there are no infinitely remote past moments or stages that were once the actual present of the world, then past time has been finite. KF
KF,
Right, well, I’ll let you harass HeKS about that one. 😛
DS, notice what you just wrote: “no moments in the past in the model I’m using are infinitely far from the present.” That is why I responded: if there are no infinitely remote past moments or stages that were once the actual present of the world, then past time has been finite. KF
KF,
Yes, I understood. But so far HeKS hasn’t objected to that particular feature of my model, so perhaps he agrees with me on this point? He can clarify, if he chooses so.
hgp and daveS,
Hey hgp. Nice to see you here (I’m assuming you’re the hgp I know from TT).
Regarding your comment about ICS vs. AIS, I can’t say that I’m any kind of expert in the finer points of this distinction, but it seems to me that an Infinite Countable Set in which all members are only finitely removed from zero and where the ICS is not an AIS but where the members could be counted forever without coming to an end is simply a potential infinite.
For example, let’s say I decided at 10am this morning that I wanted to sequentially count all the seconds that had passed since midnight last night (i.e. 10 hours earlier) up to whatever present moment I finished counting. In other words, I don’t just want to count the seconds from 12am to 10am, but from 12am to whatever time I finish counting by catching up to the present second.
If I were able to count at an average rate of 5 prior seconds per present second it would take me a couple hours to catch up to the present. However, if I were only able to count at a rate of 1 prior second per present second then it wouldn’t matter that the number of seconds between midnight last night and the present moment was and always would be finite. I could count forever at that constant pace and never reach the end, because I would always be 36,000 seconds (i.e. 10 hours of seconds) behind the outer limit of the set of seconds that had passed since the midnight I was counting from. This set would then serve as a potential infinite, but this obviously only works because the set is continuously being added to and I don’t have the capacity to catch up with its ever-increasing but always finite limit.
It seems pretty clear to me that daveS is not envisioning this kind of past, where past moments are constantly being added, with the number of those moments approaching infinity as a limit without ever forming an actual infinite set. He has always been talking about the past as an actually completed infinite set. And, indeed, he has since confirmed that this is what he means. So I think daveS is correct in saying that we are essentially on the same page with regards to what he is talking about.
Oh, and as a kind of side point, I also want to point out that I think the only way that an infinite past (whether actual or potential) can be viewed as an ICS, being placed in one-to-one correspondence with the negative integers, is by starting at the present and working backwards, which is precisely what I’ve been saying has been causing a problem all along. Events and causal chains in the universe did not unfold in reverse. As I’ve been saying across multiple threads, calling the past infinite and then starting at the present, counting backwards and saying, “just keep counting forever, it works, no problem” completely avoids all the logical problems with an actually infinite past because it conceptually converts what is claimed to be an actually infinite past into an only potentially infinite past for the purposes of discussion and argument. It creates the illusion that an infinite past can be forever traversed without having to arrive at the other “end” when the actual claim is that infinity was traversed one step at a time from the infinite “end” (for lack of a better term, obviously) in order to finally arrive at this end, the present. The problem is that there is no correspondence at all between these two scenarios. Though infinite can never be reached, one can make progress towards approaching infinity as a limit when one begins at a finite starting point and counts towards infinity. It is utterly impossible, however, to make any progress at all when trying to count from infinity down towards a finite limit.
daveS,
I think that the bolded statement is the one I’d be more comfortable affirming. My argument against an infinite past and the model you seem to be advocating does not rely on any moment being identified as infinitely far from zero or any other moment. That said, I’m not at all convinced that your model does not necessarily entail such a moment.
I’m somewhat torn on this issue. I agree with KF’s point to the extent that I understand it, which is that it seems meaningless to refer to the past as actually infinite while denying that any point in the past is infinitely far from the present. If all points in the past are only finitely removed from the present then it seems to be a contradiction in terms to refer to the past as infinite. At the same time, I also understand that it seems rather nonsensical to say that any two specific points in time in a sequence placed in one-to-one correspondence with, I guess, the negative integers, are infinitely far apart. Of course, to me, there’s a very simple way to explain why both of these contradictory views seem like they would have to be true in an infinite past while both also seeming absurd for their own reasons, and that is because actually infinite sets are merely abstract mathematical concepts that cannot exist in the real world.
HeKS,
I guess it’s not really necessary to resolve this issue unless it really becomes relevant to our arguments. One question to consider is, in your ladder illustration, do you regard the ladder as infinite? I certainly do, despite the fact that every rung is a finite distance from the bottom rung.
A couple of points on your response to hgp:
I think there are no mathematical problems, but certainly there could be other types of issues. My “mathematical model” is simply an ordered set which is easily defined, all in one fell swoop, and I don’t believe there is any “counting (backward) forever” involved. If I want to say something about the various moments in time, in an “orderly” fashion, it’s sometimes convenient to work with the moments in reverse order, but obviously that is not meant to have any implications about the actual traversal in the forward direction. People can (and have) been confused by the lack of symmetry (traversing the points in time order is totally different from traversing them backwards), but I don’t find it overwhelmingly difficult to keep things straight.
daves: I don’t believe premise 1) is true
Then if each time interval in the infinity is not an infinite differential from t[now] then what does it mean to say there is an infinite number of them relative to now?
w[now] – w[arbitrary-past-interval] = finite value
is not in the same domain as
w[now] – w[infinitely-past-interval] = infinite value
You cannot ever incrementally count up to the infinite-past-interval index. You have to take the “whole infinity” (whatever that means in the first place) else some finite value. And if you can’t count up to it, then how did the universe itself “count up to it?”
I think the whole “infinite time” thing suffers some the same defect that infinity does in the first place: it doesn’t represent anything real.
mike1962,
I don’t think I understand your questions. I can explain why I don’t accept premise 1 with HeKS’s ladder illustration, though. If you imagine an infinite ladder (with one end planted on the ground), it has infinitely many rungs and is infinitely long, but every rung is a finite distance from the ground.*
*Well, no rungs infinitely distant from the ground need exist, anyway.
DS (and all):
The first issue is,
In short, the empirical evidence in hand on the only actually observed cosmos points to a beginning at a singularity, c 14 BYA. Any proposed infinite extension in the past therefore has a huge challenge of empirical justification; never mind the popularity of talk on multiverse models and the like.
Going beyond, the nature of time as duration based on causally connected stepwise succession is also suggestive. For, were there an infinite past, that means not only that there is some hypothetical pile of a completed infinity of past stages that cumulatively have led to our present era (for which there is precisely zero observational evidence), but that we have to address the core meaning of infinity in the context of such duration.
That is, that the infinite is by general understanding that which endlessly exceeds any identifiable finite value, no matter how large. Typically, we use the interwoven nature of numbers based on counting numbers, and we talk of being endlessly beyond any finite counting number [one arrived at in succession from 0 by something like the von Neumannn construction or the like successive and cumulative process or extensions thereof such as the place value notation system and/or scientific notation, exponsntials, or log compression etc], no matter how large.
It is easy to see that any such large finite, k, will be exceeded by k+1, k+2 etc without onward bound. This is the basis for the conclusion that no finite stage, successive process or scheme built on such can successively span an endless succession comparable to the counting numbers from zero up.
Now, the significance of time as duration enters.
For, time is unidirectional, with a definite flow vector, and a cumulative causal succession from past to present and onwards as time flows on, turning the present of a few moments ago into more past. And so forth, as far as we can see potentially endlessly.
What does this mean for a hypothetical infinite past?
Plainly, that if the past was infinite, its duration must be infinite, such that there must be moments (say, w) in the stepwise cumulative, finite stage succession of stages building up to the present, that are remote in the past beyond any finite bound (say k), however large.
That is, with sn –> now, and s0 –> the big bang and with k beyond that and w yet beyond, with the three dot and four dot ellipses denoting finite and transfinite spans respectively, we are back to the sequence I laid out in 65 above. Thence, the challenges it poses:
In short, if the duration of the past is infinite, then it requires that there be moments w (note, not beginning moments or stages) that are ENDLESSLY remote in the past beyond any finite past bound k. Where w was once the present that then has to build up stepwise in finite successive stages to arrive at k then s0 then sn.
Going from k to sn is no problem that is finite. But the spanning of w to k by stepwise succession runs into the challenge of endlessness, Endlessness required for w to be infinitely remote in the past.
Which is patently impossible to span, as the down count from
w, w-1, w-2 etc . . . . k –>
can be put in 1:1 correspondence with the set of counting numbers from 0:
0,1,2 . . . .
That is, it must flow in that way and it would have to stepwise span endlessness, which is not possible. Only finite values of duration from w on could ever be spanned and it would never get to k.
So, something is deeply wrong.
Spanning endlessness in finite stage steps is impossible.
The definition of infinity I used accords with general usage and with what is generally meant and understood by speaking of an infinite past that has been completed, never mind assertions and constructions to the contrary.
The hypothesised onward allegedly completed endlessness from w further back is irrelevant.
Spanning from k to s0 and to sn is very possible.
The conclusion is there is no warrant to go beyond k and hypothesise some onward allegedly completed infinite duration up to and beyond w.
We see that we are fully warranted to conclude there was a finitely remote beginning to temporal order, and this traces back to some k, a terminus at a beginning.
Which calls for a begin-ner.
Which seems to be the real problem, determined refusal to acknowledge that the factual, empirical and logic of quantity and structure evidence alike point to a beginning of the temporal order we inhabit.
Where as nothing or non-being can have no causal powers, it cannot give rise to the sequence of cumulative, contingent stages that are stepwise causally connected to yield the present.
if there was a beginning, there had to hav ebeen a begin-ner sufficiently powerful to cause the sort of world we observe and experience, including our existence as responsibly and rationally free beings capable of genuine, reasoned discussion.
Which points strongly to something very much like the God of ethical theism.
But if one is committed to there not being such a God, then one can always determine to accept the difficulties or even patent absurdities of alternative schemes.
However, such comes at a stiff cost, as pointed out by a certain peasant teacher in C1 palestine in his home province, Galilee, in his most famous sermon:
It is time for us to ponder the worldview level alternatives and what happens if ever we make crooked falsity our yardstick for judging truth; as, then the real truth that accurately corresponds to reality cannot ever correspond with such falsity, and is liable to be rejected while one professes to be enlightened even though one is only in fact endarkened. Woe to those who put darkness for light and light for darkness, falsity for truth and truth for falsity, good for evil and evil for good.
March of folly, are we as a civilisation, folly patently headed to ruin.
Even as so many proclaim themselves ever so wise and brilliant. Only, such “wisdom” is only what we perceive through our own endarkened and confused eyes. Woe to those who live in Plato’s cave and imagine themselves free and enlightened. Deeper woe tot hose who willfully spin out shadow shows they know or should know are deceitful and foolish, leading to ruin.
Woe to those who willfully cause even just one of these little ones to stumble from the truth and the right tot he harm of his or her soul.
Woe to us, foolish and willful civilisation on a determined manipulated march of folly to ruin.
Let us have the common sense to stop, realise where we are headed and turn back. Just perhaps, it is not already too late. Maybe, we can avoid falling over a crumbling cliff.
And yes, this brings us full circle to the focus of the OP, truth and its special significance.
KF
HeKS, KF, anyone interested,
I found a philosophical dialog about the general issue of the infinite past, including more details on premise 1 that mike1962 referred to:
Here’s the section on google books. I can read all of the dialog there (pages 14–28), but I don’t know how google books works; hopefully all the pages will be visible to others here.
daves: If you imagine an infinite ladder (with one end planted on the ground), it has infinitely many rungs and is infinitely long, but every rung is a finite distance from the ground.*Well, no rungs infinitely distant from the ground need exist, anyway.
Sorry, I find nothing here that registers meaning to my mind. Firstly, infinity is not applicable to real objects. (Do you disagree with this?) Secondly, I (nor can anyone else) imagine a ladder with an infinite number of rungs.
I think if you are going to assert that time has an infinite number of intervals in the past, the burden is on you to first demonstrate this is at least a bare logically possibly within the real universe.
It seems to me that those who wish to believe that time has infinite intervals in the past think that infinity applies to real measurable things within our universe. This is puzzling to me.
daveS @221,
Well, the ladder was used to illustrate an idea, but what you have to remember is that I don’t consider the ladder of my illustration something that could possibly exist in the real world. Also, as I believe I said in the thread where I initially used the ladder illustration, I consider the infinite “end” of the ladder to be within the domain of infinity, which is entirely distinct and infinitely separated from any arbitrarily large finite domain. And that’s kind of the whole point here. Infinity is not simply a really large and/or continuous extension of some finite domain. That would be a potential infinite. The actually infinite and the finite exist in entirely distinct domains that cannot possibly be bridged through any number of finite intervals. So for the ladder in my illustration, while it is true that any two specific rungs that we can number would exist a finite distance from each other, we also have to realize that the infinite “end” of the ladder is something very different from the end that is standing on the ground, and the rungs in the infinite domain are wholly unlike the ones near the ground, and there is an infinite distance between the two domains that cannot be traversed. Starting from the ground, we could climb forever, moving towards infinity as a limit, and still never enter the infinite domain of the ladder. From within the infinite domain, we could not make progress climbing at all or transition into the finite domain where there remains only a finite number rungs between ourselves and the ground.
daveS @225,
Thanks, I’ll check it out when I get a chance.
HeKS,
I have to admit I’m not at all clear on what this “infinite domain” is. Or what this has to do with actual vs. potential infinity.
If we may continue to use the ladder illustration, my view is that the “neighborhoods” of each rung are (almost) identical. Consider any rung k in the ladder. It is “preceded” by an infinite number of rungs (those above it) and “succeeded” by a finite number (possibly 0) of rungs below it. There is really no essential difference between any rung near the bottom and rungs more distant.
Furthermore, the infinite number of rungs (moments in time) before rung k always comprise an actual infinite set, because they have already occurred. They are not mere “potential” events that might occur.
mike1962
Well, I don’t know if it is applicable or not. I guess that’s the ultimate question here.
Maybe not fully, but I don’t think that means the concept is totally off-limits. Many philosophers etc. have spent a lot of time and ink reasoning about the infinite.
I don’t know if I can do that. I can propose a simple model, and if it interests anyone, we can discuss it. Some might claim to be able to prove my model is logically impossible, which is itself of interest (to me).
I don’t know about that. I’m not one who “wishes” for an infinite past, but I haven’t ruled out the possibility that infinity does apply to real things in the universe.
Sorry, I find nothing here that registers meaning to my mind. Firstly, infinity is not applicable to real objects. (Do you disagree with this?)
Well, I don’t know if it is applicable or not. I guess that’s the ultimate question here.
An “infinite set” means that at no point, ever, is it actualized. If it’s ever actualized, it is by definition finite. Thus, infinity contradicts the Law of Identity, where A = A. It is a denial of identity.
Infinity is a metaphysical concept, by design. That’s what Cantor explicitly intended to convey. Something metaphysical cannot be physical, by definition.
(Cantor claimed God gave him a revelation about all of this, that God was the “infinity of infinities” and somehow all of this infinity voodoo was suppose to have some enlightened meaning to it with regards to God. Maybe so, but it is not applicable to the real world, and therefore not applicable to time.)
And yet here you are trying to apply infinity to the real world.
The primary blunder in all of this is that there is no such thing as a “set of all integers” or a “set of all real numbers.” These are mere words that never find an instantiation in this universe. And using … ellipses is nothing more or less than waving a magic wand and invoking mysticism.
Even in the world of quantum equations, the use of infinity in QED fields is a trick that referece to “potentialities” and nothing real, and the results have to be renormalized (another trick that even Feynman was dubious of) to have an sense. The way “infinity” is used in QED, it never refers to anything actual, and that’s an important thing to remember. It is used similar to how “imaginary” numbers are utilized with respect to phase. There is no magic or mystery at all in the way these symbolic tricks are employed, and why digital computers can handle the equations just fine.
I am open for correction.
What happened to the edit function?
mike1962,
I understand “infinite set” just to mean a set that can be put in 1-1 correspondence with a proper subset of itself. I don’t believe that this implies that no infinite set could ever be actualized.
aleph null + aleph null = aleph null
which means
A + A = A
Identity violation
If you’re willing to accept that, then what aren’t you willing to accept?
BTW, this paper should be of interest to any “students of infinities.”
https://arxiv.org/abs/1203.0494
If you can show me an instance of A != A, then I would agree that would be a violation of the law of identity.
I have no problem with Aleph null + Aleph null = Aleph null. It does not imply Aleph null != Aleph null.
daves,
In the real world, the only identity that holds up to the identity…
A + A = A
… is if A = 0
Which effectively means that in the real world alpha null is equivalent to zero or nothing.
not true Mike. In the real world, when i mix paint, green+green=green.
the fact is you are using your very simple algebra rules you learned in school, but you are trying to apply them to a mathematical object of a higher sophistication. infinite sets do not add and subtract according to the same simple algebra rules you were taught, because you were taught simple things. You never actually learned modern algebra. Mathematicians work at much higher levels.
now i will return to lurking.
A! = A for an infinite number of values of 1 and 2. 😉
-Q
Good points, AhmedKiaan.
-Q
AhmedKiaan:
This appears to work at first blush only because the way you phrased it is so loose. What you actually need to say is: green+green=more of green. Or more precisely:
quantity x of green paint + quantity y of green paint = quantity (x+y) of green paint.
The only way either quantity x or y can equal quantity x+y is if at least one of the two is zero.
The point is that A+A=A is true, for some nonzero values of A. A gentle joke to nudge one toward the fact that the simplified kind of math most people learn in school is too primitive to handle more sophisticated topics. In real life, if you count photons, they don’t add up. A physical math puzzle may be described by a nonabelian group, where A*B =/= B*A. Thinking you have a good handle on things when you barely remember the basics of Classical Algebra is very cute. I’ve intruded too long. Please continue to do what you do.
AK, equivocation. The laws of identity, non-contradiction and excluded middle require that he same things in the same sense and circumstances be the subject for discussion. KF
DS,
Your GB link works for me, and I note how on the first page, Sophia is already running into a problem of asserting an infinite oscillating universe in order to try to deny a beginning.
The instant problem here is such runs into entropy issues (as I pointed out above and which you never answered properly . . . there is a problem of buried stages in such discussions), as entropy increase and dissipation of concentrations of high quality energy are ongoing all the time due to the nature of physical interactions at relevant scales. As a result an oscillating universe runs down and is not eternal. Where, evidence points to an observed cosmological expansion and density beyond the oscillating values and currently to an accelerating rate of expansion if anything.
Next, such past multiverse models are UNOBSERVED, i.e. they are metaphysical speculation not science, never mind the lab coats in evidence. The only actually observed world strongly points to a singularity/bang some 14 BYA, on many different lines of reasoning.
Next Sophia speaks to how infinite past time is about intervals, with remarks that in effect time is a continuum (an unknown, at quantum level . . . ) and that between finitely removed points there is an infinity of “instants.” This is not material (we are not dealing with the issue of infinitely dense continuum and infinitesimals etc here); but what is, is the issue of accounting for duration between specific points that were once present but have now receded into the past as the causal, dynamical process of successive cumulative, causally connected stages proceeds.
And, you will note that I have consistently spoken to stages or steps of finite scale, following in cumulative succession.
This is where if there is an infinite actual past, then there is a duration from some w that was once the present tat is vastly, endlessly beyond any large degree of past time of finite remove from now, k.
Now, on the next page, using years as units, Sophia speaks to how the number of past years endlessly continues through all the [counting] numbers.
This is exactly the problem of conversion of the direction of reckoning that has been discussed above. It leads to the subtle error of replacing an actually completed unidirectional stage to stag cumulative, causally connected flow of time from past to present, with a potentially infinite past succession of counts.
The problem remains, if there was an infinite past duration, there necessarily was some w that is such that time thereafter had to successively span an endless succession of steps of finite size to get to some finitely remote k, which has then gone on to or present in a finite succession of steps.
Nor does redefining infinity as the metric of all the numbers in the series help, time has a specific characteristic of duration that depends on a causally connected stage by stage flow. The duration or distance in time is a relevant consideration, and the need to transition from one stage to the next and to cumulatively build up to the present, are material.
These still point to the problem of bridging endlessness from some w in the forward flow of time in stages of finite size to reach k then our time (where again the 4-dot ellipsis denotes endless succession]:
. . . . w+2, w+1, w [transfinitely remote point], w-1, w-2 . . . . k [finitely remote point], k-1, . . . s0 [singularity], s1, s2 . . . sn [now] + –>
Sophia on the next page gets into the blunder of saying there is an infinite number of finitely remote years in the past. The problem is the obvious one, as has been highlighted ever so often over many months now.
For, first, we cannot exhaust endless stepwise finite stage succession, as reaching to any finite k from 0 in +1 steps or the like will always still have the endless succession ahead. Time, specifically, is a stepwise succession of this general form, but it holds for any metric that is accumulated in a similar stepwise fashion.
(How we get to there is an infinite succession is by definition that beyond any finite k, there is onward endlessness, which then creates the infinite span. You will recall that I have for months emphasised the significance of endlessness and noted how the order type of the natural numbers, omega, is based explicitly on inability to complete endlessness, leading to a new type of transfinite quantity, which we then give a name to. That endlessness is what haunts this discussion.)
Beyond this point the exchange just builds on the pivotal errors in the beginning.
KF
PS: Remember, if all actual past points are finitely remote, then the span to such must be finite. That is, such a claim implies a finite duration past. For there to have been an infinite duration past, by definition of infinity there would have to be values of past time (say, w) endlessly beyond any given finite past time, say k, however far back such a finite k is. It is when such is put with the stepwise, causally connected forward flow of time that we see that to get to now from such one would have to cross endlessness stepwise. Which is a futile exercise. We are only warranted to speak of a finite past of origins.
M62, we can construct a mathematics — logic of structure and quantity — of infinity. Or, better, the transfinite. Indeed, we can construct the surreals as a context for understanding numbers great and small. Key format, a tree structure with jaws gripping a particular value from L and R: {L|R}. As a part of that, we see how ordered succession from {} –> { | } –> 0 gives us ordinals with an ellipsis of endlessness pointing to the new category of quantity, omega. { 0,1,2 . . . | } –> omega. We can go beyond and beyond. We can go to all but zero numbers too, the infinitesimals. And so on. Much of this relates to practical reality, some of it is an abstract exercise in logic. What is relevant is that trying to suggest an infinite past physical world ends in patent absurdities as outlined. Time, to reckon with that and with the credibility of a world that began a finite time ago, requiring a begin-ner. One, capable of accounting for responsible, rational freedom that allows us to reason under moral government of truth and right. Where, a world cannot credibly come from utter non-being but must be rooted in necessary and adequate being, which as a world undeniably is and as time clearly had finitely remote beginning, points to eternal, necessary being capable of moral government as root of reality. The desperation not to go where such issues point, is revealing. KF
AhmedKiaan not true Mike. In the real world, when i mix paint, green+green=green.
Category error. You’re using “+” with reference to an nonspecific volume and not a specific numerical value. In your case, “green” really means “some quantity of green paint.”
Some quantity of green paint +
Some quantity of green paint =
Some quantity of green paint
You were joking, right?
KF,
I have responded to this point many times, though. These are all conclusions based on empirical science, and hence are provisional. In addition, the modern cyclic model(s) are said to avoid any problems with the laws of thermodynamics. The bottom line, though, is that I’m not addressing empirical arguments here.
Yes, I think we can safely ignore the statements about time being a continuum. We are dealing with a proposed discrete sequence of moments in time, a subset of the past. The question is whether the duration of such a sequence could be infinite.
No, there need not be such a k. This is where we apparently cannot agree on what an infinite past would look like mathematically, so I don’t think our discussion can proceed from here.
KF,
No, this is not consistent with the definition you posted above:
Notice the bolding on the “preassigned”. According to this definition, the test for an infinite past is: If you first give me a finite number M, I must be able to respond that the duration of the past exceeds M years, say. This needs to hold regardless of your choice of M. And it does; that’s exactly how I define “infinite past”.
You have to supply me with a finite number first.
For example, you offer M = 100 billion. My response: Yes, the duration of the past exceeds 100 billion years.
You can try again and again and again, but I can always respond that the duration of the past exceeds M years. Hence Merriam-Webster and I agree on the meaning of “infinite past”.
If you cannot count from a finite value and ever reach the full set of aleph null, how can you count from the full set of aleph null to some finite value (such as now)?
Fail.
That’s exactly what would have to be the case if the set of pass time intervals are aleph null.
Asking admins again: what happened to the edit function?
mike1962,
Are you running NoScript or something similar in your browser? I’ve had the editing option disappear sometimes, I’m guessing due to that.
In any case, I still have the ability to edit posts, so it apparently still exists.
DS, just to pick up, if ALL past time-points are finitely remote, then trivially none is transfinitely remote. Where as a counting sequence can be used as yardstick that is readily shown. My real point is, to claim an infinite past, one must have a span to once “the present” moments or stages w, such that through stepwise, stage by stage cumulative causal succession, such times are now transfinitely past. The problem being that you cannot span the required endlessness in finite stage successive steps. Where stepping back stage by stage in a potentially endless but always in fact finite process [how, in the end we measure duration] does not address the needed FORWARD dynamic causal cumulative progress stage by successive stage. FROM the infinite past as claimed, step by step to the present. Across endlessness, step by step. Futile. KF
PS: Entropy fundamentally is molecular/microscopic and drives time’s arrow. So long as molecular processes of dissipation exist, energy concentrations deteriorate across time running down the “spring” for oscillations of any type subject to dissipative forces; including a cosmos. This is driven by probability in configuration spaces. The result would be slowing down the cycle, which in reverse winds it up pointing back to an initiation. Besides the evidence we see is of a cosmos that is flat dense, i.e. below threshold to recollapse. Indeed, expansion . . . flying apart . . . seems to be speeding up if anything.
KF,
The definition you posted does not say this.
DS, the definition is of infinite and in effect is that an INFINITE quantity will endlessly exceed any arbitrarily large but finite value. That is exactly what I am addressing (again). In the case, your remarks speak to all past time values as finite and I pointed out the import, none is infinite and the span to all past values can thus only be finite. On my own reasoning, if there was an actual past infinite time, its value in steps or duration of past w must endlessly exceed any arbitrarily large but finite value say k. That is what I have represented. Recall, duration from past to present is a property of the specific past time value, not a property of a set having infinitely many members. So, for infinite past time there must be specific past times that are infinitely remote. Or else infinite is reduced to a synonym for finite but rather large. The problem then is to move in stepwise, finite stage succession to reach the present, and that must fail once one is claiming endlessly remote past times. That is all actual past times must have been finitely remote. Which then leads to a point of beginning, a start point for time that by causally successive stages becomes the present. Just, such cannot span endlessness. KF
KF,
I don’t know what motivates me to keep debating this point; probably just because it allows me to avoid working.
If you delete the word “endlessly”, I’m fine with this. It’s nowhere to be found in the dictionary definition.
It is slightly interesting that to settle the question of whether a value is infinite, one need only compare it to finite values.
Yes, this is true.
Now I believe you are saying that for the past to be infinite, there must be some point in the past such that the duration of the interval from that point to the present is greater than any finite k. You’ve reversed the order of the quantifiers.
Take a look at my post #184. The dictionary’s definition has the form represented in #2. You are now using form #1, which is not the same.
Debates about the application of the mathematics of infinities to cosmology are as pointless as using non-Euclidean geometries to do the same.
So tell me. What’s a third of the Planck distance?
-Q
DS, it is obvious that any particular large but finite value k can be followed successively by k+1, k+2 etc. Thus, only endless succession beyond such a value will make sense. The P/B case illustrates the problem. Endless succession is key to the infinite structure of the set of counting numbers, and the reals of course are interwoven as is familiar. The relevant point is, you have claimed an infinite past. Either that is endlessly beyond any particular finite value of past time, k, or it becomes meaningless. But once that is so, the endless succession from such a time say w to move forward stage by finite stage to achieve some finitely distant past stage k, much less today’s state sn then becomes impassable to stepwise causal succession as the endlessness cannot be traversed one step at a time. We have no good warrant to infer an infinite actual temporal past of the world. And as duration is to particular times, if every (note, this implies ALL) past time was finitely remote this is tantamount to the past was . . . finite. KF
daveS @229,
Let me just recap what I said in 227:
You responded:
Let me try to clarify what I’m talking about with respect to this infinite “domain” of the ladder, and, by extension, the alleged infinite past.
The infinite and the finite are opposites. In a real sense, each can be and is defined by simply not being the other. The finite is absolutely bounded. It has a definite boundary to its magnitude on all “sides”. Conversely, the infinite is absolutely unbounded. It has no boundary to its magnitude on any “side”. The finite is contained. The infinite is uncontained. The infinite is ‘one big thing’, a set that, if it exists, exists in its entirety all at once and that cannot be built up to over time through discrete finite additions. The finite is a set of individual pieces that can be added to over time, potentially forever, in order to measurably increase its magnitude. In other words, the finite and the infinite exist in mutually exclusive and disconnected domains, definitionally, descriptively, conceptually, logically, etc.
With this in mind, consider the notion of a ladder with a finite stopping point sitting on the earth but extending upwards to an actualized and completed infinity at the other end. This would be an object that somehow spans and combines two completely distinct and mutually exclusive domains. An infinite object that is absolutely bounded on one end or ‘side’. A finite object that is absolutely unbounded and infinitely actualized on one end or ‘side’. This is an incoherent object at its very core. However, if we wanted to overlook that and somehow posit the existence of such a bizarre object, we cannot simply deny the distinct ‘domains’ it inhabits at its opposite ‘ends’. One end is truly finite, the other truly infinite. If we start at the finite end we can start climbing and count off each rung as we ascend forever, never reaching infinity. However, if we attempt to proceed down the ladder from its infinite domain, we have nowhere to begin, we can make no progress, we can count off no rungs, because we cannot reach the finite by crossing infinity in discrete intervals anymore than we can reach infinity by crossing the finite in discrete intervals. It just doesn’t work. It just doesn’t make any sense.
And this brings me back to an objection that I’ve raised several times across multiple threads and that others have mentioned as well. Your proposal that it is possible that an infinite chain of events was traversed, step-by-step, in order to arrive at the present because each step was finitely removed from the next is the equivalent of proposing it is possible to count down from infinity to zero because each number if finitely removed from the next. And yet, counting down from infinity to zero is impossible. It is a task that can never be started, much less finished.
For some reason, at least as far as I’ve seen, you’ve never really addressed this problem. It’s time for you to do so. If you agree that it is impossible to count down from infinity (positive or negative) to zero, why do you think it is possible to traverse an infinite number of past events to finally arrive at the present?
On your model, I agree, and that’s precisely the problem. It is the reason that the conclusion of my argument in #187 necessarily holds. At least, you’ve given no reason so far why any part of it does not hold necessarily.
HeKS, maybe, speaking of a transfinite far zone rather than “end” may help? The point is, the far zone must be endless beyond any given finitely high rung no matter how large the number of steps to it from the ground. (Think, numbered and marked rungs, just to be concrete: 0 flat on the ground, -1 18 inches higher, -2 18 inches above that, and so forth endlessly. Note, I am showing a negative count away to the negatively infinite zone . . . ) Where of course descending a ladder is a cumulative, stepwise causally connected finite stage process. Just like the pink and blue tapes I have used, hard end to left, extending endlessly to the right. And, making the point of the problem of endless succession from that far zone to reach the near zone. Notice how DS is always speaking of an already completed infinite traverse, and finds it hard to address the point that whatever onward endlessness may exist there must be some remote w that is transfinitely remote from the near end if there is indeed an endless ladder. Climbing onward past w and endlessly down to reach the near zone then becomes the focal issue. KF
PS: I think the key conceptual error we are dealing with is the notion that when finite stage increments are chained, we can infer from every particular value we can count to can be exceeded by further steps so is finite, so the issue of ENDLESS CUMULATIVE SUCCESSION to reach the transfinite can be set aside. Notice above, the objections to my highlighting endlessness as a crucially important characteristic.
KF,
Yes, what you’re calling “zone” is essentially what I was referring to as “domain”. When I speak of the infinite “end” of the ladder I don’t mean it in the sense of some terminal rung but simply as being that part or aspect of the ladder that is opposite to the finite end, the part that must be considered to be within the infinite “domain” or “far zone”.
Yeah, I did notice that.
HeKS 261,
Thank you. Great post. The ladder comparison is a treat.
And this question brings us to the core:
HeKS,
I have read a little about infinities and yet never have come across this notion that infinite things are “absolutely unbounded” in the sense you describe. Consider a ray, sometimes called a “half-line”, in Euclidean geometry. Rays have infinite length but are partially bounded in that they have a single end. I suppose you will object that this is not an “actual” infinity, but that’s how many if not most mathematicians think of them, I gather.
In any case, whether actually or potentially infinite, a Euclidean ray does have infinite length according to the Merriam-Webster definition; given any natural number M, there exist points on the ray separated by more than M units. Likewise, given any natural number M, there exist rungs on the ladder separated by more than M steps. And under the simple model of the past, given any natural number M, there exists a point in the past such that the duration from then to the present is more than M years.
Looking up at your post #263, where you clarify the term “infinite end”, I agree that if you stand at a particular rung, then the view up will be totally different than the view down. There are rungs “forever” upward, but only finitely many below. This would be a bizarre thing if it physically existed (and likely physically impossible in our world), but I don’t think the concept is incoherent. I don’t believe you can derive a logical contradiction by assuming its existence, for example.
I disagree that traversing an infinite past (according to my simple model) or descending the infinite ladder is equivalent to counting down from infinity to zero. I interpret “counting down from infinity to zero” to mean that at some particular point, you actually are an infinite number of steps from zero; if this does occur at any point on the journey, you will indeed never finish, according to my understanding of time. But it doesn’t (necessarily*) occur on the infinite ladder and definitely doesn’t in the simple model of time I assume, therefore I don’t have to consider this case.
*The dialog I linked to does address the possibility of rungs infinitely far from rung 0, but since this does not occur in the model I’m using, I won’t discuss it unless it becomes necessary.
DaveS,
But it obviously is.
You are mistaken. Your problem is that you never get “at some particular point”. You don’t get on the ladder.
Unfortunately for your position, there is no journey at all — unless you solve the problem of how to start the journey. Put another way, where do you start “counting down from infinity”?
There is no “on the infinite ladder”.
– – –
*there is no $100 bill*
Origenes,
Please see the distinction I pointed out between “counting down to zero from infinity” and descending the ladder. The situations are very different.
There is no start. In this thought experiment, the man has been descending the ladder throughout the infinite past.
I’m just asserting that you can’t derive a purely mathematical/logical contradiction from this assumption.
daveS @265,
I would say that there are many cases in which “infinite” is used but what is actually meant is “potentially infinite”. I think that a potential infinite could probably be described, basically, as any finite quantity of any size that, at least in principle, could be added to indefinitely, where the addition results in an overall quantity that is measurably and countably larger than it was before the addition. In many cases where people say something is infinite, I think they really mean is that it constantly approaches infinity as a limit, without ever actually achieving it.
With respect to the definition of “infinite”, try just going to Google and typing in “definition infinite”. Here’s what you get:
This is something that works as an abstract concept, not something that can be actualized in the real world. Furthermore, even if it were possible to actualize an infinity in the real world, as I said, it’s an all-or-nothing deal. It exists all at once or not at all. It cannot be built up over time. You cannot transition from the finite to the infinite (or vice versa) in finite increments.
And by the way, if you instead search for “definition infinity”, notice the mathematical definition:
If you are saying that the past is infinite then you are saying it extends to infinity, and according to this mathematical definition, you are thereby saying that the past extends to some moment having a number that is greater than any assignable quantity or countable number. As far as I can tell, this is actually exactly what KF has been saying all along.
And this once again makes the mistake of conceptualizing a claimed actually infinite past in a way that one would envision a potential infinite. As long as you start at the present and work backwards M number of moments / years / whatever, this whole concept will seem to make sense to you, because you can picture some arbitrarily large finite number and then imagine there being another moment (or rung on the ladder) after that, and you’ll tell yourself you can just keep adding one more moment or rung, or a billion and then one, and say, “Yeah, at that moment the past was still there”. To do this is to envision the past as a potential infinite that you can keep building up in your mind indefinitely, simply moving along the number line in the negative direction and picturing one more moment being there. But that’s not how the past works in an infinite past. That’s how the past works with a finite past. You see, to the extent that the future is a potential infinite, so is that past. The past is being added to every moment, growing ever larger, and if the future extends forever, so will the past right along with it. But the past will never form an actual infinite. Instead, its quantity will continue increasing towards infinity as a limit, even while being fully finite at all times. So, to a certain extent, the way you keep representing the past, moving backwards in time, works conceptually with a finite past. For any number you could give, the past will eventually be larger than that given the assumption that the universe exists indefinitely into the future. But as soon as you claim the past to have been an actual infinite, this no longer works, because an infinite number of moments need to already exist before any moment can ever be called “the present”, and for any given event or link in the past causal chain, an infinite number of events or links in the causal chain will have had to have already happened before that, proceeding backwards into an infinite regress.
Well, again, that’s precisely what I did in #187 directly with an infinite past (rather than by way of the ladder analogy). According to that argument, it holds necessarily that either the past is not infinite or else the past includes an infinite number of moments that were never the present. You’ve said you disagreed, but you haven’t shown any reason why this isn’t true as a matter of logical necessity.
I’m not sure what to say about this. I find it a little mind-boggling. Everything you’ve said so far about your “simple” model of an infinite past could be mapped onto the negative integers on a number line. If the past is infinite like in your model, then past moments are like negative integers on an actualized number line (as opposed to one that merely exists as a conceptual abstract where logic tells us that for any given integer [positive or negative] another can logically appear after it, even if it would be impossible to instantiate an actualized number line in the real world). As such, your model of the past either works exactly like an actualized number line in which arriving at the present means an actual and ‘completed’ infinite number of past events were traversed one-at-a-time, just like counting down from infinity to zero, or else your model of the past is not infinite. Nothing about the way you’ve described your model of the past avoids the problem of an infinite regress of events or links in a causal chain that must have been traversed in order to arrive at the present … which is just another way of saying ‘count down from infinity to zero’.
So when you say this:
It also entails that for any given past event or link in a causal chain leading to the present, there exists some other event or link in the causal chain that would have to have occurred before it, ad infinitum. As with the descending of the ladder and the passing of the $100 bill, no step in the process ever occurs or can ever occur because there is always some other step that would need to happen before it, and another before that, and another before that, and another before that, and another before that, and another before that, and another before that, and another before that, and another before that…. stretching back to infinity.
HeKS,
I only have a few minutes today, but let me address this point, and I’ll get to the rest asap:
I am saying that the duration of the past is infinite, meaning that the duration exceeds any finite number. That’s because, under my hypothesis, given any number M, there exist time intervals in the past whose duration exceeds M.
I am definitely not saying there is any particular moment in time such that the duration of the interval from then to the present is infinite. That is not required by any of the definitions we have so far.
HeKS,
I have a few moments, so will continue:
Would you agree with the statement “rays in Euclidean geometry have infinite length” then?
I do agree, and have been assuming, that you cannot transition from finite to infinite in finite increments; in particular, under my assumptions, there is no time at which the past transitions from finite to infinite. Whether this could actually exist in the world, I don’t know, but I don’t see any mathematical reason why not.
That’s not at all what I’m thinking, though. And I don’t really have anything to say else to say about this; what really matters is whether this very simple picture I have of the past (which as you point out, maps to the nonpositive integers) entails a mathematical or logical contradiction.
But it simply doesn’t follow. My “axioms” include at least the following:
If you think there were moments in the past which were never the present, can you give me an example of one, for example the most recent one? All these moments are finitely many seconds from the present, so illustrating using the nonpositive integers should be feasible.
True, it’s an utterly trivial “model”. If by “counting down from infinity to zero”, you simply mean traversing all the nonpositive integers in numerical order [actually traversing all these past moments in time order], then that’s fine, I agree that that is what is happening.
Just as long as we’re clear that we’re not counting down through any infinite values, which is sometimes what people mean by that phrase.
Well, my “hypothesis” just states that these links in the causal chain did occur. Is there a mathematical/logical contradiction here? I don’t think so.
nevermind!
I’ve been making some diagrams. I’m still finishing them up and trying to figure out how I’ll link to them since I don’t know if I want to bother creating a whole new post for this.
HeKS, sometimes I have simply put up a brief post with the pics, a few words and comments off. Then link the discussion thread. Did that with the Ehrlich field of numbers diagram. KF
KF,
Good idea. I may do that. I considered actually making a video but ultimately decided that the diagrams should make the point clearly enough.
KF,
I’m not sure how to disable comments on the post. I don’t see an option anywhere.
Diagrams / infographics visualizing the logic of the argument in #187 above can be found here:
Re: The Viability of an Infinite Past
Very nice diagrams, HeKS! I will read through them more carefully tomorrow and respond then.
Glad you like them 🙂 Sounds good. Have a good night.
thought I’d pop in to give a little assistance:
“4) If an infinite past entails that any moment that was once the present was necessarily preceded by an infinite number of moments already constituting the past then it entails the existence of infinitely many past moments that were never the present”
This is hardly a “premise”. It’s a convolutedly worded sentence where you conclude “then it entails (the opposite of what you said the past was)”. There’s no premise here, just your conclusion written into a “premise”.
The problem is you can’t abide an infinite past because you want to turn infinity into a human thing you can start from or reach to. Infinite negative numbers exist, though they conflict with our primitive intuitions.
Honestly the discussions here are bizarre.
If you believe there is a Creator, then think about this:
Nothing exists that God didn’t create, except for God Himself.
If Time was always there, then God didn’t create it.
Since the only thing that God didn’t create is Himself, then
Time is God.
I believe that God created Time. Which means, of course, that Time had a beginning and there is not an infinite past.
I couldn’t really understand the diagrams but the 100 dollar bill analogy helped.
Davem,
Who is your comment directed to?
An infinite past (for me) has an endpoint – the present. An infinite future (for me) has no endpoint. My future infinity is greater than my past infinity. Eternally longer:)
HeKS, scroll down the main box for composing, and as you pass it you will see a little box with comments on/off. Flush left, box with text. KF
HeKS,
Very nicely done diagrams, well thought out.
I suggest regarding your 4th premise, that there lurks an ontological and metaphysical discussion. In a nutshell,
Where, also, such a being must be able to account for a world in which responsibly and rationally free contingent beings such as we must be to simply be able to genuinely discuss, are. That points to mind and to being adequate to sustain moral government.
None of which is palatable in many quarters today.
But, we need to rethink.
KF
Excerpt from ‘The Case Against Infinity‘ by Kip K. Sewell:
This argument against an infinite past is valid against the materialist concept of a universe that operates via material cause and effect sequences. If there is no original cause, then causation is pushed infinitely backward on the chain and no present can ever be actualized. An actualized present could not be causally explained. If one has to go to extreme measures to show this to someone, they are denying the obvious for ideological reasons.
However, the argument has no power over a universe where material causation is not actually what moves past into present, but where causation is an observational artifact of mind moving from one potential universal “moment” to an adjacent such “moment”, where there may be many such “adjacent” moments; indeed, where the leap from one such moment to another is limited only by the scope or nature of that which is doing the observation.
However, this would not be a materialist framework, so either something non-material and non-temporal generated the starting point of the material and temporal sequence of cause and effect, or space-time causation is an illusion of mind. Either way, materialism fails.
HeKS, the argument against an infinite regress in time of course is, and always has been, a sound one. Moreover, this ancient philosophical argument against an infinite regress is now empirically verified by General Relativity and the Borde, Vilenkin, and Guth theorem
Of further note,
I think it is fairly obvious, i.e. intuitive, that we all know that an actual infinity must exist. In fact, it was by studying the ‘logic of infinity’ that Godel was able to pick up the pieces where Cantor left off and finally derive the proof of the incompleteness theorem,,,
,,, Thus, I think it is fairly obvious that we all know that an actual infinity must exist or else how could Godel’s theorem have possibly ever been proven? The proof itself is based on the assumption that we all intuitively know that an actual infinity must exist. Moreover, the argument that Atheists use against the impossibility of an infinite regress also rests on the assumption that we all intuitively know that an actual infinity must exist. Atheists simply don’t want that actual infinity, that they themselves assume to exist in their argument against the impossibility of an infinite regress, to reside outside space-time. i.e. that is to say they don’t want the actual infinity to be God. Yet since, as you and others have rigorously shown, an actual infinity cannot exist in time, then the actual infinity, that we all intuitively know must necessarily exist, must necessarily exist outside of time.
Moreover, the actual infinity that must necessarily exist outside of time is exactly what we find evidence for in quantum mechanics.
First off, in drawing this point out, it is important to note that, very much unlike General Relativity which is based on space-time, Quantum Mechanics does not take space-time into consideration.
Moreover, the ‘uncollapsed’ photon, in its quantum wave state, of the ‘fundamentally spaceless and timeless physics’ of quantum mechanics, is mathematically defined as being ‘infinite’ information:
Moreover, this ‘infinite information’ quantum qubit is also mathematically defined as being in an ‘infinite dimensional’ state:
Thus every time we observe/measure, (i.e. collapse a quantum wave of), a single photon we are actually seeing just a single bit of information that was originally created from a very specific set of infinite information, that exists outside of space-time, that was known by the infinite consciousness that preceded material reality. i.e. information that was known only by the infinite Mind of omnipresent, omniscient, omnipotent, eternal God!
Also of related interest to finite space-time and infinite quantum mechanics, Richard Feynman was only able to unify special relativity and quantum mechanics into Quantum electrodynamics by ‘brushing infinity under the rug’:
Feynman rightly expresses his unease with “brushing infinity under the rug.” here:
I don’t know about Feynman, but as for myself, being a Christian Theist, I find it rather comforting to know that it takes an ‘infinite amount of logic to figure out what one stinky tiny bit of space-time is going to do’:
The preceding line of thought is summed up in this short video
supplemental notes:
HeKS,
I still have (approximately) the same “objection” that I raised in a previous post, concerning these statements:
I definitely agree with this, just to be clear.
This is the part that I complained about before. I will revise my position a bit and say this statement is true, but that it is actually consistent with an infinite past where every past moment was once present.
At first glance, it might seem that the statement implies there is an “infinite tail” on the left, consisting of past moments which were never present.
However, under my scenario, it is true that no present moment occurs before an infinite number of prior moments have already occurred, each of which were at one time the present. That’s essentially an “axiom” that I’m assuming—from the point of view of any moment, the past is already infinite, and consists entirely of moments which were once the present.
In other words, it is always the case that “there is already an infinite number of preexisting moments”, so this condition ends up not constraining the possible present moments at all.
Now if there were supposed to be a first moment-that-was-ever-a-present-moment, this argument would show that is impossible, but that doesn’t occur in the situation I envision.
DS, duration is from time to time. Unless there is at least one w such that it is an actual past time that was once the present but due to stage by stage causally connected change since, it is now transfinitely remote, there is no coherent meaning to saying there was an infinite past. But the very point that time proceeds forward step by step cumulatively then leads to the challenge that such will require step by step traversal of the transfinite intervening domain. This is not reasonable and we are not warranted to speak of infinite past time. Also, if all past times were finitely remote, then this means the duration of past time is finite also, unless finite and transfinite as well as duration lose reasonable meaning. KF
KF,
Well, I don’t think HeKS is invoking that premise in his argument, anyway.
HeKS,
Incidentally, have you considered writing up your argument and submitting it to a journal? I don’t think I have seen this particular one in print yet (I haven’t done an exhaustive search, admittedly).
In an effort to understand this statement more fully, I will attempt to rewrite it in a different, but logically equivalent form:
I will use “t” to represent an arbitrary moment. I understand the original statement to mean:
Then this is logically equivalent to:
which is part of what I am assuming, so I again affirm that I do agree with the original formulation.
Continuing with the argument from the diagram:
I do agree with this also, as at every point in time, an infinite number of past moments already exist.
What I disagree with is that all this implies there is/was a first past moment that was a present moment. I think under my assumptions, all past moments were once present moments, and that all this is consistent.
translation of daveS’s post at 289:
“I would rather embrace what is patently absurd than ever admit that God is real.”
there, all better! 🙂
281
HeKS
To anyone contemplating whether time was infinite or not, and believed in God.
bornagain @ 292: Well translated. Brings to mind the following truths:
The fool says in his heart, “There is no God.” — Psalm 14:1
Although they claimed to be wise, they became fools. — Romans 1:22
Atheists look more and more foolish by the day. Glad I am not one!
AhmedKiaan @279,
As far as assistance goes, your comment was not particularly helpful.
Sure it’s a premise. I understand there are a lot of words there, but the complexity of the statement should be somewhat offset by the fact that the first half of (4) is merely a restatement of the latter half of (3). I worded it this way to make sure the logical link from each step to the next was apparent. Furthermore, the “then” portion of (4) appears to really be nothing more than a restatement of the “if” portion. In other words, it is like saying, “if X entails A, then that is really no different than saying X entails B, as B essentially appears to be nothing more than a different way of stating A”. Of course, anyone is free to disagree with this claim, but I’ve shown in my diagrams why this appears to be necessarily true, so demonstrating it to be false will require more than simply saying, “I disagree”.
Umm, no. As I’ve been saying all along, an infinite past makes it impossible to start and makes the present impossible to reach.
And yet, compare the flow of the negative integers to the flow of time. If zero is “the present”, in the negative integers the lowest one is closest to zero, but with time it is the reverse, which I drew attention to in my diagram. Mentally mapping an infinite past to the negative integers is what causes one to mischaracterize it in their minds and think it to be a more coherent concept than it actually is. When you follow the flow of the arrow of time the logical problems become apparent.
2nd Law of Thermodynamics that is scientifically measurable REQUIRES a starting point. A very PERFECT starting point.
Sean Carroll explains….
https://m.youtube.com/watch?v=yKbJ9leUNDE
DS, whether or not he does, the issue is a substantial one. KF
WJM @286,
I agree. The point of the argument was to show that a materialist version of an infinite past cannot exist even if we grant the possibility of an actual infinity existing in the world. Interestingly, what my argument suggests is that if an infinite past actually exists, it was created wholesale and then a finite temporal past of cause-and-effect relationships was butted up against it. And what on earth could do that except for God? So the argument shows that either there is not an infinite past, or if there was it could only be the case that God created it. And so yet again we come to God as Necessary Being
daveS @291,
I’m not surprised you haven’t come across it. It just occurred to me the other night while I was brushing my teeth 🙂
I’ll respond to some of your other recent comments later tonight or tomorrow.
I would like to point out a hidden assumption in the term ‘the present moment’. To assume there to be ‘the present moment’ in the first place, i.e. a ‘present moment’ that is distinct from all other moments, you have to assume an observer with distinct perspective, i.e. frame of reference, outside the passage of time. An observer outside the passage of time with a distinct, separate, ‘psychological time’ in order to be able to bestow on each moment as it passes in front of him ‘and this moment is now’.
This sharp distinction between what is termed ‘psychological time’ and ‘physical time’ is one of the main reasons why Einstein never received a Nobel prize for relativity.
To give some background, Einstein had an encounter with a famous philosopher, Henri Bergson, over the proper definition of time. In fact, that encounter with Bergson over the proper definition of time was one of the primary reasons that Einstein failed to receive a Nobel prize for relativity:
A few years after Einstein’s clash with Bergson, another philosopher, i.e. Carnap, asked Einstein,,,
Einstein’s answer was categorical, he said:
Quote was taken from the last few minutes of this following video.
And here is a bit more detail of the encounter with Carnap:
What Carnap meant by ‘the Now’ can also be read in full context in the article:
Moreover, the statement Einstein made to Carnap on the train, ‘the now’ cannot be turned into an object of physical measurement’, was an interesting statement for Einstein to make to the philosopher since ‘the now of the mind’ has, from many recent experiments in quantum mechanics, now undermined the space-time of Einstein’s General Relativity as to being the absolute frame of reference for reality.
I’ll re-reference this experiment I listed in post 288 to illustrate the point:
Thus ‘the now of the mind’ is apparently far more important to physical measurement than Einstein thought possible. i.e. ‘the Now’, as philosophers term it, and contrary to what Einstein (and Jaki) thought possible for experimental physics, and according to advances in quantum mechanics, takes precedence over past events in time. Moreover, due to advances in quantum mechanics, it would be much more appropriate to now phrase Einstein’s answer to the philosopher in this way:
For anyone who may be interested, here is a video on the subject
daveS @289,
I hate to beat a dead horse, but this only seems like it works when you move backwards through time from one moment to the next saying, “The moment before this one was the present, and the moment before this one was the present, and the moment before this one was the present”, ad infinitum. It seems to work because you can retroactively apply “present-ness” to each previous moment starting from the present and working backwards towards infinity as a limit [1]. When you move forward through time and consider the logical “initial state” of an infinite past then it quickly becomes clear that it simply cannot be the case that every present moment throughout all time was already preceded by an infinite number of “prior” moments while each one of those prior moments was at one point the Present.
The mere fact that you have delared something an “axiom” of your model doesn’t mean it is coherent. What you’re saying here appears to be tantamount to claiming that it is an axiom of your model that it does not entail any logical contradictions, and so it is no problem if your model happens to entail certain conditions that plainly seem to be mutually exclusive, because, after all, it is axiomatic that your model doesn’t suffer from contradictions. You might as well just make it an axiom of your model that it is true and correct.
If you wish to maintain that (4) in my argument is incorrect you will need to show how it could be possible that an infinite number of moments would have to already exist before any moment can be the Present while it is also possible for each of those moments to have once been the Present. Furthermore, you need to do this without resorting to stepping backwards through time and retroactively applying “Present-ness” to each prior moment and then asking us to extrapolate backwards indefinitely. On their face, these two propositions are mutually exclusive right at the foundational level of defining the model.
I’m not sure if I’m understanding you here, because I would say that what my argument shows is that even if there was an infinite past, there still had to be a first moment that was a present moment and that that’s the only way it could even be possible for there to be an infinite past (allowing, for the sake of argument, the possibility of an actual infinite existing in the world). If there is an infinite past, it consists of two distinct parts: 1) an infinite number of moments that were never the Present but that were created all at once, and 2) a finite number of moments that were once the Present, forming a finite history of cause-and-effect relationships.
———
[1] Note that you can actually play this out in the Nth Moment of my Infinite Past diagram, retroactively assigning “Present-ness” to all moments in the model, including the infinite number of moments that were never actually the Present at all. This, however, can only be done by moving backwards from the Present towards the Past rather than the other (proper) way around.
Infinity: a concept solely existing as symbols of human invention. Nothing else. That’s all that can be demonstrated.
I think this topic is done, eh?
HeKS,
I also prefer not to keep repeating the same things, but once more, I’m not at all looking at this situation from the perspective of moving backward in time. Rather, I’m asserting that all these moments in time occur in the proper time order, and am essentially asking you or someone else to point out the mathematical/logical problem.
Exactly. In effect, I’m saying “here are my axioms, now you try to show they are inconsistent”.
If my axioms imply A and not-A for some A, then my axioms are inconsistent and you win. That’s what I’m looking for you to do.
I don’t know if it’s possible for me to do that, but my understanding was that (4) was provable from (1)–(3), each of which I have agreed to. I don’t see how it follows, however. If you exhibit a proof, again, you would win.
This is the fundamental question I have: How does this proof of the existence of a first moment that was a present moment go? Is it the logical priority argument?
It is easy to imagine an infinite future. Otherwise there’s a last second. Okay, but what happens the next second? So time is almost certainly eternal, which means an infinite future. Since the laws of physics at the most fundamental scales are invariant with respect to time symmetry, the most elegant and unavoidable answer, is that the past is also eternal.
That is physics. All else is mere mumbo-jumbo.
AhmedKiaan,
You are mistaken.
First, the future exists only as pure potentiality, not actuality. Second, what you are describing is a potential infinity, not an actual infinity. It is not an actually infinite existing quantity but an entirely finite hypothetical quantity representing the number of moments that will eventually have become the Present. That amount will continue to increase towards infinity as a limit while never actually achieving it, even if the universe continues to exist endlessly. Also, as you will have noted if you looked at my diagrams, the Past is also potentially infinite for precisely the same reason, because it consists of a finite number of moments that will continue to increase as each moment of Future potentiality becomes an actualized Present and then fades into the Past. So the Future is a potentially infinite hypothetical potentiality (there’s a mouthful) and the Past is a potentially infinite actuality.
Also, it apparently needs to be said yet again that an endless future possesses none of the logical problems of a beginningless past.
AhmedKiaan,
Time (or space time) emerged at a distinct trillionth trillionth trillionith etc of a second way back when (6000 years ago give or take 14billion). And will be snuffed out upon heat death way way way out in the future. Way way out.
Nothing lasts forever, not even time. That is the actual physics but you are free to imagine otherwise. Nothing wrong with imagination. Fanciful.
Once upon a time, many years ago, the doorbell rang at midnight. There, in the doorway, stood your left door neighbor holding a $100 bill. He instructed you to keep it for 24 hours and then give it to your right door neighbor. And so you did.
The other day you asked your left door neighbor how he got the $100 bill and he told you that the exact same thing happened to him: midnight, left door neighbor, $100 bill and the same instructions. He also informed you that all his neighbors on the left had the exact same experience.
The question is: can the existence of the $100 bill be explained by an infinite number of neighbors on the left? Is it the case that we do not need a $100 bill producing machine, when we have an infinite number of neighbors on the left?
HeKS:
Telling:
Infinity is turning out to be a pivotal issue in all of our reflections on origins science.
KF
KF,
Note that I’m trying to be as clear as I can about what my “axioms” are in order that anyone challenging my view will know what they have to work with. The proofs that I’m interested in (mathematical or logical) that would refute my view would involve showing my axioms are inconsistent, so I’m obligated to be upfront about them. Obviously I’m not asserting that merely because I take some statement as axiomatic, it is automatically actually true.
Material worlds don’t get cause and effect for free. One would expect that if we had an infinite past of cause and effect, exisetnce would have long ago used up all of the significant available work energy and all there would be to “experience” (even though complex living creatures would be long gone) would be a cold, motionless state.
The fact that this is not the state of existence contradicts the idea that we have an infinite cause-and-effect past.
Yes, nicely stated.
We can measure the rate(s) of the earth slowing its rotation as does anything in the universe with angular momentum.
Isn’t it amazing then that assuming an infinite past that there was a time when everything “musta” rotated twice as fast, ten times as fast, or even at the speed of light!
Of course that would mean that gravity also “musta” been stronger to keep things from flying apart at the speed of light.
And then before that, as we travel back in time and velocities and frequencies increase, the speed of light “musta” been a lot faster then as well to allow for speedup up or to prevent infinitely small wavelengths, which would bump up against Planck distance.
So, my question then with all this stuff whizzing around, when did the speeds of things and gravity stop being infinite so we can now measure them? In other words, when did the infinite speed of light slow to half and then half again to become a sluggish 186,000 miles per second?
😉
-Q
Querius,
I think those arguments are excellent for showing that our universe must have had a beginning in the finite past. The problem with those empirical arguments is that they don’t necessarily tell us whether it would be possible for some physical superspace or multiverse to have existed into the infinite past. I’m assuming that’s why daveS is looking to be presented with logical/mathematical contradictions rather than empirical arguments. That said, the types of arguments cited by you, WJM and ppolish are certainly valid in responding to AhmedKiaan’s attempted argument for an infinite past from a false application of Physics.
Thank you, HeKS.
Even the existence of Planck distance falsifies the notion of an infinite universe analogous to or corresponding with a a continuous n-dimensional manifold.
Conjuring a superspace, multiverse, trans-dimensional oscillating plasma, or some other fantasy, has no higher rationality than a cosmic turtle whose eggs form universes. It’s simply word substitution based on imaginative speculation rather than any measurable evidence.
Such speculations are not science. Ideological superstition is the closest description that I can think of . . .
-Q
DaveS
Perhaps the more classical arguments deal with the impossibility of moving sequentially across an infinite past. Also, the more simple axiom that a sequence that has no beginning can never have been started.
If it required an infinite amount of time to arrive at today, then today never would be able to occur. Because you cannot arrive at a termination point (today) in an infinite string. You might say that the string is potentially infinite in the future, so you could simply add days to it, thus adding today.
But the problem is that the string is an actual infinite in the past. Nothing can be added to an actual infinite. An infinite past has fulfilled all potentiality. Today cannot arrive in a string because all possible points in time have already arrived. Or better, no present point could ever arrive since it would take an infinite amount of time for it to exist.
You would have to wait an infinite amount of time for today to exist. That’s the difficult part – thinking about a non-beginning to a sequence that proceeds for an infinite amount of time.
Or to rephrase the OP’s comment: For any present moment to exist, you have to wait for an infinite number of past moments to exist.
In order to have a sequence of numbers, for example, it must have a beginning. So, a sequence of moments must have a first moment.
When I am asked to count a sequence, it must have a beginning.
The only way I can say I have a sequence that has no beginning, is if I never started counting (and thus the sequence does not exist and I am wrong to claim that I actually have a sequence.
But that’s a practical test. How do you add a number to a counted sequence that never was started?
If daveS is going to abandon causal work-energy laws in order to have his superspace infinite past (and avoid superspace heat deat), then one wonders why he would insist that time would be configured, perceived or act like it does in our particular physical-law, entropy-obeying universe?
Unless superspace materially behaves much like our own universe, space-time cause-and-effect as we understand it would not be applicable. He doesn’t get to have it both ways – a superspace unlike our universe in that it has unlimited work-energy resources yet like ours in that the space-time continuum progression of cause and effect is the same.
Silver Asiatic,
These indeed are the types of arguments that I am interested in (mathematical, logical). But I believe I’ve come across responses to most or all of them, and have put forth counterarguments against them myself.
If by “never been started” you mean “could never exist”, that would do it; if you mean you can’t ever start traversing a beginningless sequence, that is true (by definition), but I don’t think that implies such a traversal is impossible.
Well, I’m saying that I’m assuming that such a traversal of infinite past time has occurred, and asking for someone to then state what logical contradiction this leads to (when taken in the context of my other assumptions). Is that possible? If you can prove not, then the above argument would work.
This is not at all obvious to me. The diagram which HeKS provided illustrates an actual infinite collection of past moments, and as time elapses, more and more moments get added to the list. That’s at least conceivable to me.
You can (and people do) speak of sequences without a “beginning”, or “first element”. For example, the set of integers is a bi-infinite sequence: (…, -2, -1, 0, 1, 2, …), in the usual ordering.
I’m not sure what “counted sequence” means in this context. I am assuming an actual infinite collection of past moments, and whenever a present moment ceases to be present, it gets “added” to this actual infinite set. I really don’t think there is an issue with adding elements to an already existing infinite set.
Q @ 313 wrote: “Such speculations are not science. Ideological superstition is the closest description that I can think of . . .”
Well said!
Go to a math department and ask them to explain whether the sequence (…, -2, -1, 0, 1, 2, …) is a “counted” sequence or not. They will tell you that you are babbling, and please learn some basic math.
Ahmedkiaan @ 319: ???
Can someone point me to some other Intelligent Design blogs that aren’t just Discovery Institute fronts? This is basically the only one I’ve found.
I would like to just see Intelligent Design blogs, though, not Creationist ones.
daveS
That’s one way to look at it. When we say a material thing exists (or a process involving material things), the term “exist” requires boundary information. An actual past infinite cannot be known as a “thing” given it lacks the boundary necessary to identify it.
You use the term “impossible” so we’re talking about potentiality, possibility and probability.
First, I find it positive (knowing your worldview) that you’re willing to assume that an actual infinite entity could exist. We do the same thing when we say “assume that God exists”, and I don’t think you have a problem with that. You’re assuming entities that cannot be circumscribed by human reason or logic, so it points to a mystery beyond science and even beyond metaphysics or philosophy. A beginningless entity, actual infinite, possesses all potentiality. Thus we have a classical understanding of God.
However, is there a logical contradiction with your assumption that a “traversal of infinite past time has occurred”? Yes. It has to do with the nature of an actual infinite. An actual infinite of time-sequence for example (as assumed for the past) has several properties that make a movement to a termination point (today for example) impossible.
First, as said above, if you had to wait an infinite amount of time for something to happen, then it could never happen. If we had to wait an infinite amount of time for today to exist, it could never exist.
The reason for this is that an actual infinite is an entity that is a fullness or completeness. In that sense, an actual infinite is unchangeable.
To ask, “is it possible to add a new day to an actual infinite past of days”? is to look at the probablity. But the probability/possibility of adding a new day to an actual infinite of days is zero.
To understand if something is possible, we consider that certain conditions need to be met. “How could it be possible to add a new day to an actual infinite of days”?
To answer that, we might say “if there was a new point in time where an unrealized day could exist, then a new day would be added”. But in an actual infinite, there cannot be any unrealized potentiality. There cannot be any conditions yet remaining to be fulfilled. If an event cannot occur in an actual infinite number of chances, then the event is, by definition, impossible.
A new event cannot be added to an actual infinite sequence of events because the possiblity for that event was already exhausted an infinite amount of time ago. In other words, if it was possible for today to exist in an actual infinite number of days, it would have already existed. New possiblities cannot be realized, thus new days or new events cannot be added.
The occurrence of today can be considered a mathematical chance event. In an actual infinite sequence, what is the probability that day 1000 already occurred? Obviously, it’s 100% certain it must have occured.
In an actual infinite series of events, what is the probability that day 10,000,000 already occurred? Again, it’s 100% certain it already must have occured. Why? Because every possibility has already necessarily been realized. There are no potential days that ever could occur that haven’t already occurred.
To then ask, what is the probability that day “infinite plus one” occurred?, is also to say necessarily that it already occurred, with 100% certainty. If it was possible to occur under any possible circumstances, then in an infinite number of chances those circumstances already arrived.
What if it is not a “new day” but merely a repetition of a day? The same holds, in an actual infinite, how many times can a day repeat itself? If it was possible to repeat one more time, then it already has done so an infinite amount of time ago.
These are some of the characteristics of an actual infinite sequence.
Yes, but those symbols are not representing a sequence of events that occur in time. The elipses require an actual infinite to already have occured. You’re actually adding -2, -1, 0 to the end of the sequence. But in order to do that in real time, you have to have a countable sequence where you would know how to position -2, -1, 0, 1 etc. Otherwise, it’s assigning arbitrary symbols.
If the sequence never had a beginning, then it is inexplicable in scientific or mathematical terms. Actually, strictly speaking it is somewhat inexplicable in logical terms.
For a sequence to move, it must begin to move at some point.
An actual infinite past would be an entity without an origin – an always-existing entity. As such, it would be inexplicable and it would obviously be illogical to talk about the origin of such a thing. How did it get there? what caused it? Why does it exist? Why does it still exist?
Ok, just to close – there is the other classical argument:
If it was possible for an actual infinite sequence of days to stop existing, then it already would have stopped (as above, all possiblities must be realized under infinite opportunities).
So, the choice here is:
1. It would have stopped existing, thus wouldn’t exist now.
2. It is impossible that the actual infinite series of days could not exist.
If #2, then you’d be saying that the infinite past was necessary, and not contingent on anything else to keep it in existence.
Again, we arrive at a theological argument about a necessary being.
@ Silver Asiatic, DaveS.
The concept “actual infinite” is in need of an explanation. Kip S. Sewell (see #285) wrote:
Perhaps DaveS will attempt to elucidate the concept.
AhmedKiaan @319,
Umm, did you happen to notice that the sets of positive and negative integers both start at zero and then ascend from that starting point? That is why both the positive and negative integers can be counted towards infinity as a limit, though infinity is never reached. If you had to start counting from negative infinity to positive infinity no counting would ever take place at all.
daveS @317 & Silver Asiatic,
If you look at my diagram again you will see that the set of infinite moments is sectioned off from the set of finite past moments that includes the first moment that was the Present. In fact, you will even see that in my Infinite Past diagram, under “The Past” where I show the size of the set of past moments, I show two distinct sets, one infinite, the other finite. So my diagram doesn’t have the set of infinite moments being added to, but shows the Past as a collection of two disconnected sets.
Ahmedkiaan @ 322: ??? (again). Are you really so stupid?
HeKS,
Sorry for the misrepresentation. In any case, I hold that present moments are being added to an actually infinite past as time elapses.
Origenes,
There is a wikipedia page on the actual infinite which does elucidate the concept. I will point out that the majority of modern mathematicians accept actual infinities. They (and I) do consider the set of natural numbers, for example, to be an actually infinite set.
However, I’m attempting to let that sleeping dog lie, and work under the assumption that sets such as {0, 1, 2, …} are potential infinities for our discussion here.
Edit: I took a look at Kip Sewell’s paper “The Case Against Infinity” here. Sorry to say, but the parts I looked through seem to be full of misconceptions. Maybe later when I have more time I will post a couple of them.
Silver Asiatic,
I’ll try to get back to your post later; I’m going to be offline much of the weekend though, and right now can only read and respond to the briefer posts.
Origenes
from Kip Sewell @285
I’d only disagree with Sewell here that the infinite is not a “coherent notion” simply because it does not conform itself to mathematical analysis.
In fact, I think he proves it is a coherent notion by moving through the analysis he does. But just because the analysis of a thing produces contradictory results, does not mean the thing itself is incoherent. Instead, what it means is the analysis is flawed. What we learn from applying mathematical thinking to an absolute infinite is that mathematics is not capable of comprehending an actual infinite. It’s a false assumption to conclude that if an entity does not conform to mathematics, then it is incoherent.
We also learn that if an actual infinite exists, it transcends human reason. This is important. It’s a clear proof that human reason is limited in what it can understand. Logic itself cannot be used to understand an actual infinite, although logic gives us more knowledge of an infinite entity than mathematics alone does.
So, to say that “anything that does not conform to human reason cannot exist” is to make a very big assumption without proof.
Why is that a more true statement than: “it is possible that certain things exist which transcend the power of human reason to comprehend”?
The only way we could say “it is not possible for an actual infinite to exist” is if we defined “to exist” as applicable only to things that can be bounded by human reason.
The fact that we can conceive of an actual infinite, at least in part, and that we can make calculations about it, and argue (as philosophers have done for centuries), means that an actual infinite has some reality at least in human cognition. It is understood what properties an infinite must have. In that sense, since this is commonly known to humanity, there is some possibility that it could exist.
Going farther, it is actually necessary that an actual infinite does exist since all potential infinites and all contingent/dependent entities much find their origin in that which is non-contingent and unbounded.
Or we could say “for an entity to exist, it must begin to exist at some point”.
That may sound rhetorical. For example, like saying, “that sequence never got started”. If it never started, then it wouldn’t be a sequence.
But the argument is not that it “never started” but that it never needed to start since it always existed.
I find it somewhat acceptable to posit infinite entities that are inexplicable, have no origin and are merely assumed to exist.
However, those entities open up many other serious questions that cannot be avoided. It’s not only “how did that infinite sequence exist”? but “what does it depend upon for its existence”? Whatever that is, must also be actually infinite and complete in its potential.
All sorts of infinite entities must also exist along with an actual infinite sequence of time. Most importantly, it is the relationship between these entities that has to exist infinitely. The balance and regularity that creates an ordered sequence, also has to exist in an actual infinite. But the laws creating order have no function unless there are the material properties to act on.
So, there are several actually infinite (completed potential) of relationships supporting an infinite sequence. The actual infinite does not explain itself, it cannot exist without support from other actual infinite entities.
Thus, we have many “godlike” infinite qualities and entities, all unexplainable which must be assumed to exist. Not only the entities themselves, but the forces, laws and processes that are joined to this sequence remain unexplained.
This is where it is necessary to compare the assumed existence of these actual infinite entities and relationships with the existence of God.
With God we have the infinite source of being, without beginning and independent of any contingent support. God is the necessary being that explains all other contingent being. What is the better explanation? Multiple unexplained entities creating an actual infinite sequence that must be assumed to exist, or the arguments of classical theism?
“Umm, did you happen to notice that the sets of positive and negative integers both start at zero and then ascend from that starting point?”
you are imposing primitive human notions like ‘start’. The set (…-2, -1, 0, 1, 2…) does not start anywhere. It just is. This is basic stuff.
Anyway, I’m looking for an intelligent design blog to read. I don’t want anything by the Discovery Institute, they are a right-wing propaganda organization headquartered about an hour from me in the PNW. They are funded by bad people. And I don’t want to read creationist blogs. Is there a blog which focuses on Intelligent Design, where there are scientists discussing it?
I agree that there must be a First Mover. And I agree that this First Mover is fundamental to everything — including space and time. However to argue that — since the First Mover is fundamental to space and time — he has to be infinitely in space and infinitely in time is IMHO a mistake.
To be outside of space, to be independent of space, does not equate with having an infinite diameter. Similarly, to be outside of time, does not equate with being infinitely in time.
The First Mover created time and space, but what that means is that his existence cannot be captured (understood) in the context of neither space nor time. To say that the First Mover is infinitely great or eternal would be a futile attempt to do just that.
IOWs the First Mover doesn’t fit a space time context, and when we attempt to do so anyway it shows …
And you’ve been posting here for a while.
I bet there are a lot of left-wing “non-propaganda” organizations headquartered more than an hour from you in the PNW funded by uber-good people.
Here are some. 😉
Definitely a troll.
Ahmedkiaan @ 333 said: “You are imposing primitive human notions like ‘start’. The set (…-2, -1, 0, 1, 2…) does not start anywhere. It just is. This is basic stuff.”
To which I say: “Get off your high horse you arrogant prig.”
Ahmedkiaan @ 333 said: “I’m looking for an intelligent design blog to read. I don’t want anything by the Discovery Institute, they are a right-wing propaganda organization…”
To which I say: “You hypocritical left-wing elitist fool.”
Ahmedkiaan @ 333 said: “They are funded by bad people.”
To which I say: “Go to hell. You are the bad person.”
Ahmedkiaan @ 333 said: “I don’t want to read creationist blogs.”
To which I say: “Then get lost.”
Ahmedkiaan @ 333 asked: “Is there a blog which focuses on Intelligent Design, where there are scientists discussing it?”
To which I say: “You foolish, foolish primate. Are you really that stupid?”
I should add that if he’s talking about some sort of materialistic actual-infinite, then that would be incoherent.
Another follow-up thought:
Or even better, with an infinite, beginningless past, when did day 1000 occur? 1000 days after the first day?
Origenes @334
Good clarification. If it’s a question of defining the First Mover strictly with space-time-material categories, then that doesn’t work. I believe that’s what the Sewell quote was referring to also. An actual infinite is an incoherent concept within a space-time paradigm.
On an IPad so flexibility is limited.
I have not read any of the comments so if what I post is redundant I apologize.
Any argument to infinity of time or universes falls apart due to absurdity. Namely, because nothing is really impossible. Name things that are not possible. Please no 2+2=5 logical absurdities.
This means that all possible worlds have existed and not only have existed but have existed an infinite number of times. Including this discussion with the current cast of characters but also with an infinite number of other characters/creatures. If one says no, then justify your reasoning.
If one wants to subscribe to such a possibility then there also an infinite number of worlds with intelligences so large that we could not tell the difference between any one of these numbers of beings and what we call the Judeo/Christian God.
And an infinite subset of these intelligences will say “Let there be light” and a new universe will come into being. And to emphasize the absurdity an infinite subset of these declarations will take place in English.
If one wants to entertain infinity of time or universes then this is what you are subscribing to.
Silver Asiatic,
Responding to some of your post #323:
If there were a particular point in the past infinitely remote from the present, then this would be a good argument, I think. But the “standard” model of an infinite past assumes that any two points lie within a finite distance (in time) of each other, so there is no waiting an infinite amount of time (from any particular point) to the present.
I don’t see that this is obvious at all, in fact I don’t see the problem in adding moments to an infinite past as they change from present to past. Certainly in mathematics, people have no issue with this.
Well, adding days to an infinite past is not a chance process as far as I can see; rather, it’s deterministic. Given that an actual infinite collection of days has already transpired, then the “next” day is not chosen randomly from some sample space. The next day is always the immediate successor of the most recent day in the past.
If we really were going to do some sort of probability analysis, then I would want to see details of the sample space and the chance hypothesis.
This isn’t actually true, mathematically. Say you have chosen a countably infinite sequence of real numbers, all between 0 and 1, and you consider this an actually infinite set. Then it would be impossible for you to have chosen every number between 0 and 1, because this is an uncountable set. In some sense, you have barely scratched the surface.
I don’t think there is a natural notion of “day 1000” in this setting, since there is no “day 0”. You could set one, but it would be an arbitrary choice.
If we did arbitrarily identify a day in the infinite past as day 1000 and then speak of choosing days “randomly” in this past, then there is another problem, which is that you can’t define a probability distribution on this set such that every day has equal likelihood of being chosen, which presumably you would want to hold.
The bottom line is that I don’t think a probability analysis would be very useful in this context.
What DaveS said.
This is not terribly hard stuff to anyone who understands the fundamentals of Real Analysis. But trying to discuss these concepts without a basic education in the subject is, as can be expected, producing vastly more words than understanding.
“I don’t think there is a natural notion of “day 1000” in this setting, since there is no “day 0”. You could set one, but it would be an arbitrary choice.”
watching people try to impose “start” and “end” on (-?,?) is amusing, but sad.
i guess the board sofware is not intelligently designed to handle lemniscates. 🙁
daveS
The infinite past contains an infinite amount of time. If it contained a million days, then you could choose a particular point a million days ago. Instead, it contains an infinite # of days. Logically, you should be able to pick a point “infinite days ago”. But that is not possible. There’s the contradiction.
Mathematics cannot model what happens in real time over an infinite span. An actual infinite quantity of something, contains 100% of the thing. That’s the difference between actual infinite and potential infinite. An actual infinite of days is a set that contains all possible days. Again, this is what is meant by possible (you used the term ‘impossible’).
It may be confusing where I spoke of probability and possibility in the same regard. They mean the same. First of all, if you mean that every new day must necessarily exist (deterministic), then you’d need proof for that or else it is yet another assumption you’re adding to your model (first assumption, infinite past exists, second assumption, each new day must necessarily follow deterministically forever). In this, you’re assuming both an actual infinite past and necessarily an infinite future.
But again, days don’t follow necessarily on their own. Days are dependent on many contingent factors. This is why we refer to what is possible. What you seem to be saying is that “it is impossible for days to stop being added forever, infinitely”. Again, that’s an assumption. Many factors could break down an infinite string of days or time itself. So it’s not impossible for that to happen. We speak of ‘possible’ when we consider the conditions and factors.
As above, this seems to claim that it is impossible for time as we know it, marking days, to cease. But if time can come into existence (as most physicists believe it did), then it can cease to exist. Thus we talk about whether and how this would be ‘possible’. In an actual infinity of days, necessarily – everything that is possible must have occured. That, by defintion, is how we understand possibility and impossiblity. Over an infinite time, if something that was considered ‘possible’ never actually occured, then that fits the definition of ‘impossible’.
Over an infinite amount of time, today was possible to have occurred already, an infinite amount of time ago. But it didn’t occur, thus the past cannot have been actually infinite.
Again, this not a question of ‘randomness’, but rather the conditions present and what happens over an infinite amount of time.
The sample space is an actual infinite. All probability is based on this. In order to determine if something is possible, it is measured against an actual infinite.
No matter what you are measuring, if your sample space is infinite — in other words, you take an actual infinite number of chances — then the probability of any ‘possible’ event is necessarily 1, or 100%.
The hypothesis for an actual infinite number of chances is always either 1 or 0. The reason for this is that an infinite number of trials exhausts every possible circumstance that could cause an event to occur.
I’ll restate it again because it is important:
“If an event that is claimed to be possible, does not occur after an actual infinite number of opportunities, then it is — by definition — not possible, or impossible”.
To claim that a new, unrealized day with new conditions, is possible after an infinite number of permutations and conditions that cause days to exist already occurred is a contradictory claim.
Again, whatever conditions that cause the day to occur, must have necessarily already occurred an infinite amount of time ago – thus the day must have occurred.
Every possible day that could have occurred, must have occurred in an actual infinite of days. If not, after all possible conditions that create days have occurred, then by definition – that day is impossible.
If you disagree with this, then you have a contradictory notion of the term ‘possible’. We accept something as possible only if it could occur within an infinite number of attempts.
If after an infinite number of attempts, it has not occurred – then it is not possible. That’s the nature of possiblity. You can’t wait “another infinite amount of time” for the event to occur.
All of the conditions that caused you to exist as a person on earth today, must have already been in place an infinite amount of time ago. After an infinite amount of time, nothing new can occur.
As above, probability requires possibility as the first criteria. With possibility we have necessary (deterministic) as well as impossibility.
If you cannot measure the probability of an event, then on what basis do you claim it is ‘possible’?
Anything that is possible must have a probability greater than zero. So, you’ve made that claim. How did you measure that and conclude the event to be possible?
In three coin flips, what is the probability of getting 3 results? Obviously, it is 100% certain. In fact, it is ‘necessary’.
In three coin flips, what is the probability of getting 10 results? Obviously, it is zero. It is impossible.
In an actual infinite of coin flips, what is the probability of getting at least one head?
Here, we use “what is possible”. If it is ever, under any circumstances, possible to get one head – then, necessarily, under an infinite number of attempts, the probability of getting a head is 100%.
What is the possibility of getting an entirely new pattern of heads and tails after an infinite number of attempts?
The answer is zero. Because under an actual infinity of flips, every possible pattern must necessarily occur an infinite number of times.
jerry
The argument against this view requires acceptance of the principle that “nothing can come from nothing”.
Is it possible for nothing at all to exist? We see things come into existence and go out. Why not everything going out of existence?
If not, then we’d be saying (with no proof) that it is necessary for something always and forever to exist. In other words, it is impossible for all things to go out of existence. Some things can, but not all. This is an assertion, not proven.
If however, we say “yes, it is possible that everything could cease to exist” … then this is a problem.
As I explained above to daveS — anything that is claimed to be ‘possible’ must necessarily occur in an actual infinite number of opportunities.
Thus, if it was possible for nothing to exist, everything would have ceased to exist after an infinite number of opportunities.
Then, with the principle above “no thing can come from nothing” — everything would cease to exist, and nothing would ever come from it.
The fact that we exist today proves that there cannot have been an infinite amount of time in the past.
By the way, speaking of simple math, Happy Hamilton Day.
i^2 = j^2 = k^2 = ijk = -1
Yes, Silver Asiatic. An infinite amount of time is needed to have passed just for us to get to the present!
A lot of things die out after an infinite amount of time. But this is not a problem for materialists who simply conjure billions and billions of new stars as needed out of nothing. Their theory is based on more faith than my own in the Messiah.
Ahmed,
Mathematics is a wonderful tool for precise descriptions, but not all mathematics is applicable to the real world. Non-Euclidean geometry is a good example as is “infinity.”
Otherwise, the number line could be made into a convincing argument by analogy that Planck length doesn’t exist. Wouldn’t you agree?
-Q
Ahmedkiaan (everywhere): You are a monotonous bore. How did you survive natural selection?
Q
True, Querius. Today would be “infinite plus one”. But that’s obviously a contradiction since “infinite plus one” would be a larger quantity than an actual infinite — and that is illogical and absurd.
An actual infinite cannot get bigger since it is already the maximum possible size it could ever be. As you quoted previously from Sewell, an actual infinite is “complete”. (It is complete with no boundaries – meaning it fills every possible space to its fullness and cannot continually expand).
That is why it cannot be traversed. It has reached the fullness of potential with no unrealized states possible and cannot have edges upon which something more can be added.
So, yes, in order to exist today, an infinite amount of time would have had to elapse!
Belief in an actual infinite past is belief in an entity that is inaccessible to mathematics, science and logic. It requires many assumptions that must be asserted without proof — they’re just statements of faith. It’s far more a blind-faith position than faith propositions in any of the major religions which, for Christianity especially is based on testimony evidence as well as miracles and prophecy.
Faith in a actual infinity in the past is blind-faith, irrational, incoherent and contradictory. There is not only zero evidence that it exists, but to defend its existence one has to admit that it cannot be explained rationally.
LOL. I will tell Steinhardt next time I see him, he is wrong because an anonymous person used lots and lots of adjectives to say an infinite past is wrong. And very confident clauses and phrases! Surely those are as good as knowledge!
Rudimentary errors w/r/t real numbers do not interest me though. I’m interested in PaV’s ideas about virology, and I await his post describing his position thoroughly. That could be exciting! This other stuff, not so much.
Ahmedkiaan @ 351: Good idea. Go run and tell Steinhardt. LOL. My God, you are a child.
Silver Asiatic,
Good points. The fundamental flaw with all of these arguments is the assertion that if something exists in mathematics, it exists or is even possible in reality.
-Q
Silver Asiatic,
I do appreciate your posts, but I think our views on this topic, including even the definition of “actual infinity” are too far apart to have much productive discussion.
Q
Exactly. And in parallel, anything that exists can be fully and coherently explained by mathematics. But math is a limited tool and we end up with contradictory results when applied to an actual infinite.
A thing that lacks boundaries cannot be circumscribed, cannot be compared with anything else, and cannot be fully explained.
daveS
Well, thanks for reading my comments anyway.
One key area you avoided was how you concluded that something was “possible” and at the same time claimed that there was no way to analyze its probability.
Another example might help.
Assigning random letters from the 26 letter alphabet to the notion of infinite past. Each day is randomly assigned a letter.
In the actual infinite:
What is the probability of the letter ‘t’ being randomly assigned? 100% Why? Because t is ‘possible’ under some condition. With an infinite selection, every possible condition will arise. Thus ‘t’ is 100% certain to arise.
What is the probability of the word “the” arising? As above, that pattern is possible. So, 100% certain in an infinite number of chances.
How about “Methinks it is like a weasel”? Again, 100% certain to arise.
Now, how often will the phrase “Methinks it is like a weasel” arise? Answer: An infinite, uncountable number of times. If it was possible one time, it was possible multiple times. If multiple times, under an infinite number of chances it will arise an infinite number of times.
Now, what is claimed when it is said “a new day can be added to an actual infinite string” is that the phrase, for example, “Methinks it is like a weasel” never occurred in an infinite number of chances to occur.
Perhaps last week we had “Methinks it is like a wease”. But we wait an infinite amount of time for the unique phrase that includes the last “l”.
That’s what it means to wait an infinite amount of time for today, a unique day, to arise. It’s obviously false.
We may say, “No, today is not unique. It’s merely a repeat”. In that case, as with any phrase – the entire collected works of Shakespeare, in fact, the entire literary output of the entire human race – all of that, in perfect sequence, will Necessarily appear in an infinite number of chances. Why? Because it is possible. You could calculate the odds somehow – no matter how astronomical, those odds necessarily will arrive in an infinite number of chances.
But not only that! Every possible pattern will necessarily appear an infinite number of times.
Thus, to say “today is a repeated pattern” is to claim that the exact configurations that make everything that is “today” necessarily already happened an infinite number of times already.
So, your life, exactly as it is today, would be a reincarnation of an infinite number of identical lives you already lived.
However, unlike random letters (or numbers) which have no real existence, your life could cease entirely and never be reincarnated. If so, as above, your life would cease and never exist again.
jerry
Just to highlight @339 – this is essentially what I said above, and yes – correct.
Belief in an infinite past creates a kind of religious, mythological state where everything has been repeated infinite times and anything that was possible has already happened. As you point out, it requires the belief in the existence of gods, if not God Himself.
Your challenge: Anyone who wants to sign-on to that belief system is really just stating their blind-faith belief in the mythological religion of scientism.
I did offer even a refutation of that mythology at the same time @346.
Silver Asiatic,
Your example in #357 is a very interesting one, and illustrates a point I attempted to make above.
It is true that the probability of a “t” being assigned to at least one day is 100%. And similarly, the probability of no “t”s being assigned is 0.
However, that does not mean it is “impossible” for no “t”‘s to be assigned. That outcome is entirely consistent with the rules of this experiment.
The probability of every day being assigned the letter “a” is zero, but it is nevertheless possible for that to happen.
In fact, every specific sequence of assignments of letters to the infinitely many past days has probability zero; (…, a, a, a) is just as likely as any other specific sequence of assignments.
daveS
Here’s where your idea is contradictory. If the event is possible, then the probability of it occurring under an infinite number of trials is 100%.
The definition of “impossible” is that under an infinite number of opportunities, the event can never happen. If the event could happen, under an infinite number of chances – then the probability is not zero.
So, as above, you’re claiming something is ‘possible’ and at the same time stating there is zero chance in an infinite number of trials that it can occur.
Of course, in the model I provided, it assumes a randomizer. This is an artificial construct. No, it is not possible for a alphabetic randomizer to produce an infinite number of ‘a”s. If it did, it would not be a randomizer. It would be biased and false. A randomizer contains certain parameters that prevent various outcomes.
But days following days require the support of non-deterministic forces, in order for them to exist (as I explained and you avoided already). If days followed necessary/deterministically, then you’d be assuming that days will always exist. That’s a blind-faith assumption that you’re adding to your first assumption (of an infinite past).
It’s clear to me that you understand fully what I said. I believe I made it crystal clear. Querius and Jerry had no problem understanding it. I would suspect that very few IDists on this blog would have any problem understanding the points I made.
Silver Asiatic,
Well, I don’t recall seeing that formulation before.
In any case, could you describe a particular sequence that is possible in this experiment?
daveS
That’s the output of a random generator of some kind.
The probability of a unique new random arrangement (all ‘a’s is not a random arrangement), never before having occurred is zero. It is therefore impossible. If it could have occurred (if it was possible) it necessarily would have occurred. If it could have occurred once, it necessarily would have to occur an infinite number of times. If it was possible under any circumstances, under an infinite number of opportunities, all of those circumstances must arise – thus it necessarily happened.
Now, when applying to the addition of “new days” …
The probability of a unique new day occuring after an actual infinite number of days already occured is zero. There is no possibility for a new day, since everything that was possible already occurred.
I’m sorry dave, I may have to agree with your previous post. We are not able to understand each other.
I cannot understand your question. You again, (as you started the conversation) use the word ‘possible’. You’re claiming also that something is “possible” that has zero probability of occurring under an infinite number of trials.
If an event does not occur within an actual infinite (boundless) set of opportunities, where every possible condition that could ever arise has already been met, then the event is ‘impossible’. That’s what the word ‘impossible’ means. It could never happen within an infinity of opportunities. You cannot wait “another infinite amount of time” for the event to occur. An actual-infinite number of anything is the maximum possible number. If an event did not occur, then there is zero possibility that it ever could occur.
This is where you’re contradicting yourself. You’re claiming a possibility where there are zero chances in an infinite number. Where did this possibility or potential come from? If it was possible, it must necessarily occur. Otherwise we must conclude it is impossible.
An actual infinite contains every possible result. If it was missing one result, for example (like the unique day ‘today’), why is is missing? Why didn’t it already occur? Could we wait for some new conditions to arise, after an infinite number of opportunities with every possible configuration of conditions already necessarily having occurred? If so, then we would have to wait (traverse) an actual infinite number to arrive at today. Again, illogical and contradictory — and not possible. You can’t wait an infinite amount of time for an event to occur because an actual infinity does not have bounded space which you can reach by waiting.
If the conditions that produced today did not occur in an infinite amount of time, there is no possibility (zero chances in an infinite number) that it ever could occur.
An infinite string of days already completed every possible day. If the day did not occur within an infinite string, then the day was never possible to occur. It could never occur in a “future of the infinite” since the actual infinite itself has the maximum possible opportunities. A “future of the infinite” cannot provide more.
Again, an actual infinite is a complete set. You cannot add anything to it. It already, necessarily contains every potential event, every possibility must be realized — why? Because an infinite number of opportunities to realize that event have already happened — an infinite number of times.
Silver Asiatic,
Yes, we may be at an impasse.
But do you acknowledge that every single outcome of the experiment you describe, that is, every infinite sequence of letters assigned to days in the past, has probability zero?
Even those outcomes which do have “the” and “methinks it is like a weasel”, etc., all have probability zero.
daveS
You said:
Then you said:
So, I don’t know which you would like me to acknowledge since you offered contradictory statements.
Silver Asiatic,
But they aren’t contradictory.
1) The probability of the event of at least one “t” occurring in the sequence is 100%.
2) The probability of any specific outcome (sequence) occurring is 0.
Do you agree with either of these?
One in 10^40, not zero. In an actual infinite, a one in 10^40 selection will appear with 100% certainty, and it will appear an infinite number of times.
The probability of every possible sequence occurring is 100%. If it could not occur over an infinite amount of time, then it is not possible.
Silver Asiatic,
Are we talking about the same experiment, where there are an infinite number letters in the sequence (one for each day in an infinite past, for example)?
We’re talking about an actual infinite string of randomly generated letters. It’s the same approach as used in the wiki article.
Silver Asiatic:
“If an event does not occur within an actual infinite (boundless) set of opportunities, where every possible condition that could ever arise has already been met, then the event is ‘impossible’. That’s what the word ‘impossible’ means. It could never happen within an infinity of opportunities. You cannot wait “another infinite amount of time” for the event to occur. An actual-infinite number of anything is the maximum possible number. If an event did not occur, then there is zero possibility that it ever could occur.”
I have not followed the discussion, but I think this is an interesting point, and I would like to offer a couple of thoughts.
Here you seem to interpret “impossibility” (probability 0) in purely frequentist terms.
While I am a frequentist too, that seems probably too much.
I would say that, when we speak of probability 1 or probability 0, we are usually speaking in terms of “necessity”, not probability.
IOWs, let’s say that I state that if I drop a stone in the gravitational field of our planet, it will never go upward. In a sense, that statement is motivated by the repeated observation (although certainly not in an infinite time) that such an event never takes place. But, in another sense, we have developed some wider map of reality (for example, newtonian theory of gravity) which does not include that kind of event as “possible”. With some confidence (but not certainty) we accept that map of reality as true. In that sense, we assign probability 0 to that event, even if we have not an infinite frequentist support for it.
The concept of “law” and “necessity”, IMO, go beyond a frequentist approach.
Of course, we can never be “certain” of any empirical laws. But that is true for any inference, whatever the number of, even infinite, observations that support it. Even if infinite observations of some event, or non event, are done in some context, there could always exist a different context where such a regularity of observation is violated.
However, such a lack of certainty has never stopped us from making science, and from having good results in that, both at a cognitive and at a practical level.
So, I would say that if we accept a law as best explanation, and if that law implies some 0 probability, or 1 probability for some events, we can safely accept that kind of necessity as a consequence of our law, and we don’t need an infinite frequentist confirmation.
However, it remains true that any law can be falsified, at any moment, by new observations.
Of course, if we go at quantum level, the discussion becomes more complex. But I would not go into that now. 🙂
And I don’t agree that:
“An actual-infinite number of anything is the maximum possible number.”
As we know from mathematics, there are many infinites, and many kinds of infinites. It’s rather trivial that something can be true for the (infinite) set of natural numbers, and not for the (infinite) set of real numbers. It is equally trivial that infinites can be compared, and that some infinites are bigger than others.
Silver Asiatic,
In the weasel experiment, I believe the strings all have length 28.
“a new day can be added to an actual infinite string”
And there’s the crux. Nothing new can be “added to” an infinite set.
Infinity + 1 = Infinity
The “1” is “absorbed”, and made irrelevant, by the fact that infinity already contains all natural numbers prior to the add (otherwise it would not have been infinite.) This is why the idea of infinite time intervals in the past is nonsense IF we also say that intervals are “added to the set”, in the manner that we obviously experience. Nothing can be added to the infinite set of all times intervals. Therefore no new intervals can come to exist. Yet, we know they do by direct experience.
Contradiction by definition.
No infinite set of past time intervals.
The misunderstandings and absurdities arise because what infinite (alpha null) are simply matters of what finite values exist in the set. For example: is 23 included within the set? Answer: yes. And will always be yes for any natural number. By definition. But without that question, “is this in the infinite set?”, infinity means absolutely nothing, whether it be in Cantor’s original formulations, or ZF set theory, etc.
All of the other metaphysical stuff is beyond the scope of the technical mathematical specifications about infinity’s relation to finite values.
gpuccio
First of all, it is impossible to achieve an infinite number of observations. So this proposal is false and contradictory from the start. An actual infinite cannot be circumscribed. It is limitless and boundary-less. It is impossible to finally arrive at “an infinite number of observations”. Any set of observations is necessarily finite, since it is bounded as a set. An actual infinite extends without boundaries and cannot be counted.
The idea that “there could exist” different (new, unrealized) contexts, within an actual infinite, means that over, infinite time, some new context could arise which has not arisen.
But if it was possible for that context to arise, over an infinite time, it necessarily would have already arisen an infinite number of times. Whatever conditions caused it, if possible in any way, must be fulfilled. If the event never occurred under an infinity of time, it never could occur.
How much time would it take for the new context you’re referring to, to exist? You are given an absolute infinite amount of time. But how much more time than that is needed for a new context to exist? Clearly, that’s incongruous. You can’t have a greater amount of time than an actual infinite.
If you have an infinite amount of time, every possible event necessarily would exist. Again, if it did not exist after an infinite number of opportunities, it is not possible. I did not see how your explanation refuted that.
An absolute infinite of something that contains the maximum quantity of the thing. Nothing new can be added. As such, every possibility under every possible condition, must necessarily be realized in an actual infinite. As stated, you can’t wait for “another infinite amount of time” for a thing to occur. If you have one actual infinite, then you have everything possible (within that set).
Mathematically, one can show that an infinite set of real numbers is greater than a set of natural numbers. But this is evidence that mathematics cannot model the reality of the infinite. An infinite set of natural numbers is limitless. It is exactly the same size (unknowable) as any infinite set. Mathematics offers the illusion that this is not the case, but logic proves otherwise.
An actual infinite cannot be circumscribed. As such, it cannot be measured. That’s the nature of it. It it limitless and complete (see Sewell’s explanation above).
mike1962
Exactly. If days were numbered, then no new numeric day could be added to an infinite set. All possible numerics are already included before today. That’s what an actual infinite is.
You get this clearly and exactly. It’s impossible to add new data to a set that already contains all of the possible data.
This remains irrefuted (I’d say irrefutable). I’m disappointed that daveS has claimed not to understand it.
Mathematical approaches to the question are illusory. Mathematics cannot model the reality. Nor can science or logic or even human reason in itself. An absolute infinite cannot be bounded, and as such, cannot be measured. Calling an actual infinite a “set” is inaccurate, since it is not a fixed quantity. It is limitless. A set is something finite.
daveS
The word “the” has a length of 3 characters. So, there are better odds that it will appear. But it doesn’t matter. Both are 100% certain to appear over an infinity of generations. Over an infinity, a one in 10^40 will necessarily appear — and it will appear an infinite number of times.
Every possible finite string of characters will necessarily appear. All have the probability of greater than zero. If it is possible ever to appear one time, then under infinite opportunities, it must necessarily appear. Otherwise, it fits the definition of “impossible”.
When we say something is impossible, it means that over an absolute infinity of time (limitless, uncountable, completeness of all potential of time), it never happened.
You might object, that an infinite past is not “all time”. But an infinite past is not “an infinite amount of time”, but rather “infinite time”. It’s all possible time, unbounded. No greater amount of time can be realized since, by definition, you cannot have a greater quantity than an infinite (which is an unmeasurable quantity for that reason).
Clarification. I’m mixing real events in time with randomized abstract symbols in a string.
No, if an event is possible, then it will necessarily occur at least one time in an actual infinite number of opportunities. Otherwise, it is impossible.
However, as explained before that if the event was possible to cease existing, then it would have already ceased to exist.
If the argument is that yes, it would have ceased, but something then created it again – well, that is talking about multiple entities, and thus more unexplained, asserted, assumptions being added into the model.
gpuccio
I’m using the concept of “what is possible” alongside of probability.
I think you’re correct to point out that under some possible conditions (that could exist in some way), the stone could go upward.
Measuring the probability under known forces and conditions, we say that probability is zero. However, knowing that there is some potential of another result, given other unknown forces that could exist, we can assert that another result is “possible”.
The event can be said to have 0 probability under known conditions. 0 probabiliy is equivalent to impossible, as I stated. But only under what is known.
But that is different from a measure of the probability under currently unknown conditions.
In that case, we decide something is “possible” because it has a probability of >0 under some (unknown, or perhaps never existing) conditions.
If those conditions never arise, the event remains impossible. If the conditions do arise, the event falls under a different probability measure.
What you seem to be saying (and I would argue incorrectly) is that we can say there is 0 probability that any, as yet unknown, conditions may exist which would cause different results.
That would be saying that “it is impossible that any other forces or conditions could exist”.
So, it’s not a measure of the probabiliy of the event, but rather of the possibility that there are unknown factors that may change things.
In that case, since we (most of us) would conclude that other factors “are possible”, then the probability that another result (rather than stone dropping) is not absolute zero.
In that case, as you said, we do not have certainty. The probability is not zero for another result. It is not 100% that the expected result will occur. This is based on the finite number of experimental trials we’ve evaluated.
The problem we’re looking at, however, is when you already have had an absolute infinite number of opportunities.
In that case, probability measures are either 1 or 0. If the event is possible, it necessarily must happen. Otherwise, we know it is impossible – by definition.
If it did not happen in the maximum amount of time that is possible, then it is impossible, it cannot ever happen.
Silver Asiatic:
I disagree with many of the things you say, but perhaps it’s not so important. I am not sure that I have expressed well my points, so I will make another attempt.
You say:
“First of all, it is impossible to achieve an infinite number of observations.”
And I obviously agree. Indeed, my statement:
“Even if infinite observations of some event, or non event, are done in some context, there could always exist a different context where such a regularity of observation is violated.”
was simply a reductio ad absurdum. My point is simply that you cannot derive scientific concepts from philosophical reasonings about the poorly defined concept of “infinite”, least of all using a frequentist approach to derive laws of necessity.
Our scientific laws are inferences, and inferences are more than simple probabilities. They are maps of reality. That was and is my point.
Moreover, I think you are confused in some of your points about the “infinite” nature of sets. Infinite is a rather ambiguous word. If we stick to its mathematical meanings, which are in themselves not simple, the when you say:
“Mathematically, one can show that an infinite set of real numbers is greater than a set of natural numbers. But this is evidence that mathematics cannot model the reality of the infinite. An infinite set of natural numbers is limitless. It is exactly the same size (unknowable) as any infinite set. Mathematics offers the illusion that this is not the case, but logic proves otherwise.”
You are simply wrong. In the mathematical sense, infinite sets are not equal, they have different cardinality, as shown by Cantor. This is not at all an “illusion”, but a very precise mathematical truth. I am really surprised of your statement that “logic proves otherwise”. What so you mean? Logic is a deductive science, strictly connected to mathematics. Why should it “prove otherwise”?
Even stranger is your statement:
“Mathematical approaches to the question are illusory. Mathematics cannot model the reality. Nor can science or logic or even human reason in itself. An absolute infinite cannot be bounded, and as such, cannot be measured. Calling an actual infinite a “set” is inaccurate, since it is not a fixed quantity. It is limitless. A set is something finite.”
What do you mean? If mathematics and logic cannot “model” the reality, what on earth can do that?
You seem to ignore that “models” of reality are simply maps created by human reason, and that they are created using the fundamental laws of logic and mathematics. That’s why they are called “models”.
IOWs, the map is not the territory. And models are maps.
But, if you refute mathematics and logic as tool to design models and maps, what are you left with? Especially in science?
So, again, my point is: empirical science is about models and best explanations, and it uses mathematical and logic models as tools to build those explanations.
The concept of “infinite”is either a mathematical concept, rather well defined, and then your statements are false, or it is a philosophical concept, which has no specific and univocal meaning, and then your statements are undefined.
In all cases, a frequentist debate about probabilities in infinite sets of potential observations is not the best way to do empirical science. Instead, realistic reasonings about empirically small probabilities in finite contexts are perfectly useful in empirical science, and that’s exactly the kind of argument that ID theory uses.
gpuccio
I think I understood your points, and I certainly disagree with you but I appreciate the clarifications.
First of all, if you’re able to provide an analysis of what I meant as “infinite”, and then draw conclusions, then the concept is not poorly defined. You state “even if ..” and then make a proposition, which ends with an absurdity. But as I said elsewhere, the reason it is absurd is because the tools you are using to understand the infinite are incapable of handling the task. In any case, if you cannot derive scientific concepts from philosophical reasonings about the infinite, then you can’t derive mathematical conclusions from it either.
I note that Querius, Origenes, Jerry and mike1962 understood exactly what was meant by an actual infinite. In fact, Origenes cited Kip Sewell’s paper which said exactly the same thing (although I disagree with some of Sewell’s conclusions, he provides philosophical defintions of infinity and argues, correctly as I see it, against the mathematical notions you are defending as being contradictory and absurd). So, that’s a group of us that have no problem with what was meant by an absolute infinite. Your disagreement goes beyond just with me in this case.
I don’t agree that we should stick with mathematical meanings since they are totally inadequate (as mentioned, Sewell’s paper, and simple logic shows it).
Yes, that’s exactly what I said. In a mathematical sense they are not equal. But in a real sense they are exactly equal. Thus, the mathematics simply doesn’t work. It provides a false and contradictory understanding of the infinite.
First of all, numbers are symbols. They are not real in the sense of occupying some space or dimension in material reality (unless they are expressed on a medium). Numbers only have meaning assigned to them by humans — as such, they are imaginary.
An actually infinite set of symbols, is exactly the same size as any other infinite set of symbols. Call them real numbers, natural numbers, odd numbers, negative numbers. They are all exactly the same size. It’s only in the imaginary world of mathematics that they can be different. That imaginary world does not represent reality, or real things.
In fact, all of those symbols are dimensionless. You can “fit” an actually infinite number of symbols in no space at all since they do not exist.
Thus, in reality, you cannot “have” an infinite set of symbols (and “set” is an incorrect term also since it indicates a finite boundary) unless they occupy some dimension in the real, material world. The mathematical approach to an actual infinity is imaginary in that sense.
So again, an actual infinite of anything is exactly the same as any other.
It’s a precise truth within mathematics but completely false in terms of reality. An actual infinite cannot be circumscribed. It is unbounded. It cannot be measured. That’s what it is by its nature – by definition. Again, as one example, in the disputed claim, “Infinite + 1 = Infinite”. You cannot have a larger or smaller infinite. In fact, you cannot even measure or determine the size of an infinite. Logic shows this. Math does not. Thus, the math is incorrect.
Logic is what is used to judge mathematics. Mathematics can produce numbers that cannot be represented by real things. Math does not tell us that, only logic does. Logic is superior to mathematics since math relies on logic but logic does not rely on math. Math can arrive at incoherent but mathematically correct conclusions. The simple example given, when you subtract the infinite set of odd numbers (again, impossible because a “set” is finite and all the odd numbers are therefore not a set) from the set of natural numbers, you remain with two infinites. That is illogical and contradictory. Even as math speaks of “infinite sets”, that also is logically absurd. Or in the simple example given, the infinite set of symbols called “natural numbers” are seen mathematically as a smaller quantity than the symbols called “real numbers”. Again, logic proves that to be false, because by definition, an actual infinite is limitless and cannot be measured, circumscribed or compared. Both actual infinite sets of symbols, logically are exactly the same.
So, logic proves that the math is incoherent.
But even logic, which is superior to mathematics, cannot represent an actual infinite. An infinite cannot be represented because it is limitless. The act of describing a thing requires knowing what it is. But the infinite is not an “it” in the sense that it does not have boundaries by which it can be defined. Any claims to reduce an infinite to a “set” or “a quantity” or any sort of “thing” that can be comprehended is reducing an infinite to a finite quantity – thus contradictory and false.
By “model” I mean describe, explain, illustrate.
Do you think Jesus Christ can explain what reality is better than Georg Cantor could? Do you think that Christ, who said “I am the Truth” knows what reality is? Do you think that Christ requires mathematics to communicate the nature of reality? Reality is that which exists. Existence is being, and its source is ultimate pure being. Again, without some context (external to math), mathematics has no way to distinguish between reality and imaginary concepts.
There are many sorts of non-mathematical models that map reality. Again, spiritual revelations about the nature of reality are, in fact, maps that can be used for understanding.
When one is trying to understand a concept that transcends human reason, one cannot expect the tools of human reason to give a complete or even accurate model of the concept.
An actual infinite transcends the capability of human reason to understand. It cannot be circumscribed (comprehended) by finite methods (science, logic, mathematics). It can only be known in a spiritual sense, at best. Some pointers can go towards it from philosophy and math, but in the end there are many contradictions.
Again, as said earlier – just because math and logic arrive at contradictions when analyzing an actual infinite, does not mean the entity is flawed. Instead, it means the methods or tools used in the analysis are flawed.
Again, you seem to think that mathematics should be able to accurately describe all of reality. Where did you arrive at that notion? Again, I think we have even mundane examples within human experience – poetic insight, prophetic intuition, conscious awareness … to the more esoteric like the resurrection of Christ. These are all significant aspects of reality which are completely inaccessible to mathematics. Would you use mathematics to model the poetic beauty of Dante’s Divina Commedia? Is that not obviously (almost literally!) a map of reality? Even if you disagree with his notions, are you going to describe the beauty of that work through mathematical understanding?
The same is true of an actual infinite. It transcends human understanding.
And again, it’s a false assumption to think that every aspect of reality must necessarily be accessible to mathematics, or even that mathematics is the best tool for understanding all of reality. Again, even simply, mathematics cannot be used to understand logic, which must be a priori accepted before mathematical work can be performed.
I disagree. The infinite has been discussed and understood philosophically since at least the time of Aristotle.
A few mistakes here — I wasn’t talking about doing empirical science, which is simply impossible to do on an actual infinite. Secondly, the frequentist approach uses the same starting point as the philosophical which is whether an event is possible in some way.
As stated, and you haven’t refuted — an event is possible if it will occur in an actual infinite number of trials. It is impossible if it does not occur after an infinite number of trials.
As I asked you already when you claimed that after an infinite number of trials (a mistaken notion in itself since there never can be an “after an infinite”) that some new data or new event could occur … “how much more time than an actual infinite would you need for the new event”?
Can you see the contradiction here? You cannot add time to an actual infinite. There can be no “future time after an infinite elapsed”. That’s why you cannot traverse an infinite.
I give you an actual infinite amount of time. Your event doesn’t happen. Now you want more time with the claim that maybe then it will happen?
That is absurd, illogical and contradictory. You cannot have more time than an actual infinite amount.
I already gave you the maximum possible amount.
gpuccio
I failed to mention, most importantly, that HeKS’s model (note, philosophical) and his comments through out the thread (see #268) for example are all basically elaborations or parallel explanations of exactly what I was describing.
Silver Asiatic @ 379 & 380: Wow. Impressive work.
Q: If adding future days to a past infinite – in the past actual infinite set of natural numbers in sequence does the number 23 appear?
A: No. It cannot appear because in order for a sequence of natural numbers to contain 23, it has to begin at 0 and move 23 places to 23.
But an actual past infinite cannot have a beginning at 0, thus it can never arrive at 23.
If it contains 23 in a sequence, then it had a beginning at 0, and thus it is not an actual past infinite.
Yet again, one of the many contradictory impossibilities in dealing with an past actual infinite.
Thanks TWSYF! – and a great user name you’ve got which is very liberating and true! 🙂
I just have a further comment relevant to infinity. Infinite or infinity does not actually exist in the physical world. It is an abstract concept with no physical reality.
In the abstract world of mathematics the term infinite is used to explain something that is without a bound. We can imagine this but because we can imagine it does not mean this concept has any existence in reality. Another mathematical concept that does not exist is irrational numbers. Are there any irrational numbers? Not really. It, like infinity, is a very useful concept but so are imaginary numbers. I could argue there are only discrete particles in any universe so in any universe there is only a finite number of particles or an integer.
When one uses the term “infinite” in the universe sense, it is not a universe without bound but a series of universes that does not seem to have a bound. Either in one after the other or an unlimited number of simultaneous universes or I guess some combination of each.
We have seen that this latter use of infinite leads to the absurd conclusions that everything had to happen an infinite number of times including an infinite number of Judeo/Christian like gods (who by the way should have the power to interfere in this universe creation process. If this infinite number of Judeo/Chrisitan like Gods does not exist then one is imposing a limit on the intelligence/power an entity can attain. Something that is not consistent with and infinite number of universes.)
I assume the people who hold this absurdity do so only to explain away the fine tuning of our universe. But what an extremely high price they pay (subscribing to idiocy) in order to avoid the obvious. But apparently they are being idiots an infinite number of times.
Silver Asiatic @ 360 noted,
Correct. Similarly, DaveS has convinced me that he doesn’t understand probabilities when dealing with infinities.
Gpuccio, how familiar are you with Kurt Gödel’s incompleteness theorems?
I agree with Silver Asiatic that mathematics can only model reality, not replicate it.
Imagine a number line that’s one meter in length. Mathematics tells us that there are an infinite number of unique points on it. Next, imagine this number line superimposed onto space-time. It no longer has an infinite number of points. Does anyone know why?
Silver Asiatic wrote,
Ok, maybe not 24. Yeah but what about 25? 😉
Jerry @384 mused,
Brilliant!
-Q
Querius,
Did I make a mistake? Would you mind pointing out the errors? Thanks.
DaveS,
Haha, you’re joking, right?
If you’re unfazed when Silver Asiatic clearly and succinctly points out your non sequiturs, I would have no hope.
-Q
Silver Asiatic:
“Your disagreement goes beyond just with me in this case.”
I am OK with that.
“In any case, if you cannot derive scientific concepts from philosophical reasonings about the infinite, then you can’t derive mathematical conclusions from it either.”
I have no desire to derive mathematical conclusions form that specific philosophical concept.
“I don’t agree that we should stick with mathematical meanings”
We should, when we are dealing with scientific empirical models, which are built by mathematics.
“simple logic shows it”
Again, I can’t see how logic can be against mathematics. They are essentially the same thing. Of course, some specific philosophical reasoning certainly can. But a specific philosophical is is not “logic”.
“But in a real sense they are exactly equal.”
I really don’t understand what you mean by “a real sense”.
“First of all, numbers are symbols. They are not real in the sense of occupying some space or dimension in material reality (unless they are expressed on a medium). Numbers only have meaning assigned to them by humans — as such, they are imaginary.”
I agree with the neo-platonic view of mathematics, so in a sense I partially agree with you. Mathematics is inborn in human mind, and not empirical. But it is the only means we have to build rational models of reality.
Again, the map is not the territory. Cognitive models of reality are not reality. Science is a model of reality, not reality.
“Thus, in reality, you cannot “have” an infinite set of symbols (and “set” is an incorrect term also since it indicates a finite boundary) unless they occupy some dimension in the real, material world. The mathematical approach to an actual infinity is imaginary in that sense.”
We have infinite sets in mathematics, and they work very well. Even if I believe that mathematics is not empirically derived, I certainly believe that it is part of reality.
“It’s a precise truth within mathematics but completely false in terms of reality. An actual infinite cannot be circumscribed. It is unbounded. It cannot be measured. That’s what it is by its nature – by definition. Again, as one example, in the disputed claim, “Infinite + 1 = Infinite”. You cannot have a larger or smaller infinite. In fact, you cannot even measure or determine the size of an infinite. Logic shows this. Math does not. Thus, the math is incorrect.”
I really think we must agree to disagree. You have given no definition of what you call “an actual infinite”, and yet you try to explain it by a mathematical argument, just to say that math is incorrect, and state its nature “by definition”. OK, I disagree. Let’s leave it at that.
“By “model” I mean describe, explain, illustrate.”
So, what can explain scientifically reality better than math, for us humans?
“Do you think Jesus Christ can explain what reality is better than Georg Cantor could? Do you think that Christ, who said “I am the Truth” knows what reality is? Do you think that Christ requires mathematics to communicate the nature of reality? Reality is that which exists. Existence is being, and its source is ultimate pure being. Again, without some context (external to math), mathematics has no way to distinguish between reality and imaginary concepts.”
OK, you put it on the religious plane. But that is not a scientific argument.
I will try to explain what I think. I certainly believe, like you, that there are sources of cognition that are different from math, or empirical facts, or logic, or reason. Religious faith can be one of them. But I also believe that we have many intuitive cognitions, which are not in themselves confined to reason, logic, models and external facts.
OK, but that is not science. Science is the building of models of reality using reason, logic, math and facts.
That is not even philosophy, because philosophy too is about building models, even if its “rules” are somewhat different.
You speak of “infinite” from some inner intuition that you have. That’s fine with me, but you cannot use that intuition to share an argument with others, unless you move it to the plane of human reason, logic and math. Then it becomes something you can use in science.
So, we have a scientific concept of infinite, and it comes from math. As far as I know, that’s the only concept of infinite we can use in a scientific discussion.
And we have many different concepts of infinite in philosophy, including obviously religious philosophies. Those are certainly important, but they are many and different. Unless formulated in some mathematical form, you cannot use them in a scientific argument. You can, of course, use them in some philosophical argument, and others can counter your argument with other philosphical arguments, based maybe on different philosophical concepts of infinite.
OK, I have nothing about that. That’s what philosophy is about. But I certainly have a lot against your apparent certainty that your personal intuition, or imagination, of what infinite means in philosophy is something everyone should agree upon. I certainly don’t. I find your vague concept of infinite flt and unappealing, philosophically.
“The same is true of an actual infinite. It transcends human understanding.”
But it seems not to transcend your personal understanding, given that you use it in your arguments, try to define it and to convince others of how it should behave.
“And again, it’s a false assumption to think that every aspect of reality must necessarily be accessible to mathematics, or even that mathematics is the best tool for understanding all of reality.”
I have never said those things.
“When one is trying to understand a concept that transcends human reason, one cannot expect the tools of human reason to give a complete or even accurate model of the concept.”
But if a concept transcends human reason, you cannot “understand” it by reason. You can believe it by faith. Or you can have some intuition about it. But that’s different form what we usually call “understanding” when we share our concepts. So, let’s say that we are using “understanding” in two different ways, both acceptable, but very different.
“Again, even simply, mathematics cannot be used to understand logic, which must be a priori accepted before mathematical work can be performed.”
Math is based on logic, and logic implies math. There is no contradiction between them. This is one of the points I cannot accept in your arguments. You seem to confound spiritual intuitions, or scripture based faith, with “logic”. I cannot see why.
“An actual infinite transcends the capability of human reason to understand. It cannot be circumscribed (comprehended) by finite methods (science, logic, mathematics). It can only be known in a spiritual sense, at best. Some pointers can go towards it from philosophy and math, but in the end there are many contradictions.”
In a sense I agree with that. But I would say that, exactly for those reasons, nobody can claim that he really knows what “an actual infinite” is. And math, logic and philosophy cannot really deal with it. It’s not a problem of contradiction, but simply of limitations. And, certainly, logic is no better at that then math or philosophy. and, certainly, logic does not contradict math.
“I disagree. The infinite has been discussed and understood philosophically since at least the time of Aristotle.”
I agree with “discussed”. I fully disagree with “understood”. And many of those discussions, however, are about the mathematical infinite.
“There are many sorts of non-mathematical models that map reality. Again, spiritual revelations about the nature of reality are, in fact, maps that can be used for understanding.”
Spiritual revelations are, indeed, “revealed”. If they are models, they are not models that we have built. We can use them, but we do not build them.
“Again, I think we have even mundane examples within human experience – poetic insight, prophetic intuition, conscious awareness … to the more esoteric like the resurrection of Christ. These are all significant aspects of reality which are completely inaccessible to mathematics. Would you use mathematics to model the poetic beauty of Dante’s Divina Commedia? Is that not obviously (almost literally!) a map of reality? Even if you disagree with his notions, are you going to describe the beauty of that work through mathematical understanding?”
Certainly not. As I have said, we have deep intuitions of reality which go beyond reason, logic, math and philosophy. I call them intuitions, for that reason. I have never said that science is the only way to understand reality.
But poetry, intuition, feeling, are more similar to “facts” than to “models”. Artistic works are hints at those personal experiences, that other people can use to live a similar intuitive experience.
Science is a specific field of knowledge, and it is based mainly on models built by logic and math about observed, outer facts. That’s what makes it shareable in a very specific way.
While I don’t believe that science is fully shareable (I am, after all, a Polanyite), I do believe that being mainly shareable is what makes science science.
So, you see, I have nothing against you idea that we have intuitions of reality from personal inner experiences and from faith, or what else. I also believe that we can share much about them in some forms (art, poetry, religion, etc). I simply say that we cannot use those personal experiences as a foundation to share scientific maps of reality with others.
That’s all.
“I give you an actual infinite amount of time. Your event doesn’t happen. Now you want more time with the claim that maybe then it will happen?
That is absurd, illogical and contradictory. You cannot have more time than an actual infinite amount.”
This is a good example of what I mean. You seem to build an argument using a concept, the concept of time, that we really don’t understand. Maybe even less than the concept of infinite. It is an empirical concept, and I think that nobody has a really given some final theory of what time is, either in science, or in philosophy. And yet, you boldly build an argument on what time should be, or how it should behave, according to your personal opinions.
OK, for my part, I agree to disagree.
Querius:
“Gpuccio, how familiar are you with Kurt Gödel’s incompleteness theorems?”
As much, I believe, as a non mathematician can be. Penrose’s argument about it is one of the key points of my personal thought.
“I agree with Silver Asiatic that mathematics can only model reality, not replicate it.”
Whoever has said that math should “replicate” reality? I have simply said that it is (together with logic) the only tool we can use to build scientific models/maps of reality.
“Imagine a number line that’s one meter in length. Mathematics tells us that there are an infinite number of unique points on it. Next, imagine this number line superimposed onto space-time. It no longer has an infinite number of points. Does anyone know why?”
I don’t follow you. Real numbers are a great achievement of mathematics, and they have made possible our understanding of physics, and our present modeling of physical reality. What do you mean by:
“It no longer has an infinite number of points.”
Are you referring to quantum mechanics? As I said, quantum mechanics creates new important problems, none of them really solved.
In traditional physics, space and time are treated as continuous, and real numbers are the only way to do that.
Just to be clear, I don’t believe in a past infinite. I firmly believe in the big bang as origin of the actual universe. But my reasons for that are very scientific, and have nothing to do with discussions about what an “actual infinite” is, or should be.
Querius,
No, I’m not. I’m asking you to identify the specific statements about probability I have made that are factually incorrect.
gpuccio
It’s good you recognize that we have other means of understanding reality beyond science and math.
Science is not an adequate tool to use for measuring transcendent entities.
I note that while disagreeing here, you agree later on, so that is good.
Science is dependent upon philosophy.
I notice that you did not answer my questions about Christ’s teaching – you ignored that for some reason. Perhaps you’re not familiar with it. Christ stated “Before Abraham was, I Am.” According to your view, He was not able to share this idea with others? Notice, his teaching transcends the limits of human reason, logic and math. Do you actually think Georg Cantor knew more about reality than Christ did? You didn’t answer my question. I mean, it’s ok to say what you think, I’m not judging you on that. I’d consider it a bold notion, given Christ’s claims. But I’m assuming you’re some kind of Christian believer, and I apologize if I’m mistaken on that.
To understand that teaching of Christ (I Am), one must be able to understand that an actual infinite can exist and it necessarily transcends what human reason can comprehend. It transcends science and math. Attempts to reduce an infinite to models will always end in something inaccurate and contradictory.
You can use approximations of the infinite in science, but the infinite is not an entity that can be studied empirically. An actual infinite is not a “thing” if we definite things by their boundaries.
First of all, we must use philosophical concepts in scientific discussions. We must decide if something is logical or not. We must recognize if a study “is scientific” or not. Science cannot tell us these things. Only philosophy can.
I already showed, and you failed to refute, that science and probability studies (Bayesian or Frequentist) necessarily use the concept of “what is possible”. This discussion was between me and daveS where he stated that that an “infinite past was not impossible”.
That argument can be studied scientifically, mathematically and philosophically (logically). You attempted to explain this by saying a zero probability is not impossible because conditions can change. I pointed out that you calculate the probability under known conditions. If the conditions change, then the zero probability does not apply.
Again, if an infinite number of trials was possible (as it would be in an infinite past), then anything that is “possible” must necessarily occur. Otherwise there is no basis to claim that the thing is possible.
You’re misreading what I’ve said. Of course I use transcendent entities in my arguments. Of course I try to define them and convince others of how they behave. The end result of these arguments merely indicates that what I call transcendent, does indeed transcend what human reason or science can fully understand. As I stated, and you ignored, science, math, logic — all can be pointers, or give some hints and clues about transcendent entities. That’s what I think has been proven many times by others on this thread also.
Do you think God is a transcendent entity? If so, are you incapable of talking about God, trying to understand God’s attributes and actions that follow logically from what we know about God?
It seems you’re arguing from the point of view of scientism, which reduces all knowledge to that of empirical thought — as if math and science are the only means we have of understanding reality. You seem to resist the notion that “correct math” can also be illogical.
That’s what you’ve been arguing. I stated that an actual infinite transcends reason and you said “that’s not science”.
I have never heard of the term “understanding” to mean “sharing concepts”. I my view (and I believe the ordinary view) we understand something when we know what it is. We may “partially understand” or not understand at all. With a transcendent entity like an actual infinite, we can understand some things, because of its nature, we can never fully understand it. “Sharing concepts” can be a process offering results that are completely illogical, irrational, contradictory and illusory. As I see it, that is not “understanding”.
I’m sorry I don’t understand what you’re saying.
This is better. You’re supporting my view here. Again, if a person argues that an “actual past infinite existed”, then the point you raise above is at least one necessary response. My elaboration and explanation (the reasons I gave that you agree with) was an attempt to prove this very thing. I don’t know why you decided to argue against this until now, but perhaps I wasn’t clear about what I was saying. Again, an actual infinite cannot be fully known by math, science, logic or intuition. None of those methods will work. Each can help in some way, but all end with only partial and often contradictory, false conclusions.
But that has been your argument thus far.
Other methods of knowledge are shareable in their own ways also, but the point remains, science and math give inaccurate and contradictory information when analyzing non-empirical entities (as actual infinites are).
Along with those sources, these intuitions is embedded or a part of the human person, in my opinion. The intuition that recognizes a difference between truth and falsehood, precedes and is superior to all human reasoning (philosophy, logic, math, science, etc). So, the intuition is really the superior and most necessary source of knowledge.
You seem to disagree with what is meant by “impossible”. As I said, if an event would not occur given an infinite number of opportunities, it is, by definition “impossible”.
It’s not a question of defining what time is.
At the same time, stating that we don’t know what time is, could certainly be another good argument against daveS’s view that an actual infinite past exists.
The view I presented, which you agreed with is that we cannot understand what an actual infinite is so it cannot merely be assumed to exist. I gave several reasons why this is true. Again, I was glad to see you agree with me (eventually) in saying “But I would say that, exactly for those reasons, nobody can claim that he really knows what “an actual infinite” is.”
If you want to add, that “nobody knows what time is”, then that’s merely another problem with the same claim that an actual infinite past could exist.
At best, daveS’s view is merely an assertion of an imaginary concept that cannot be evaluated scientifically, mathematically or logically.
As I said earlier, it’s a religious or mythological view, based on imaginary entities.
gpuccio
I invite you to take a look at this thread. Perhaps use your ctrl F “God” (or however you can search the page). You’ll find a lot here.
Posts 91-94 or so and following, introduce proofs of God, discussions on Infinity and Time.
bornagain77, HeKS, Origenes, mike1962, kairosfocus, Querius … all contributed something on the topic.
@298 HeKS states:
Notice, the discussion on an actual infinite is built on arguments, just as I offered, and they lead to an understanding of the transcendent entity we know as God. There are several ways to understand God as Necessary Being, the above is one.
Arguments on potentiality and actuality are others. While the materialist version of an infinite past does not work, a theistic view does.
You may have missed the theistic (you termed it “religious”) component of this thread and assumed that I introduced it into a scientific discussion.
No, that’s not the case.
I’ll guess, you may have quite a lot to argue with as you read through the comments from fellow ID’ers here (or not, I don’t know).
Silver Asiatic,
I want to make explicit one assumption I am making about an infinite past, namely that we have an actual infinite sequence of days, and that this sequence is totally ordered by time.
That is, given two days d1 and d2 in this infinite past, either:
Even if the events of d1 and the events of d2 are identical, if one is in the past of the other, I do not consider them the same day. What I’m debating is the duration of the past, and specifically whether the universe existed more than M years ago, for every natural number M.
Whether some cyclic phenomenon (such as described by the Poincaré recurrence theorem) exists is a separate issue from my point of view.
gpuccio
That is very good to hear!
Now, if you’d like, please give your reasons and arguments for why you don’t believe in a past infinite. Do you think it is “possible but not very probable”? If so, how did you determine it is possible, and how did you calculate the probability of it?
… that was just a suggested path for your answer. Please feel free to use whatever arguments you may have that have convinced you, or which you think will convince others.
Greetings UD community!
Since the discussion on arguments against an infinite past is still active, I would like to recommend my own published work on the subject in which I develop an argument against an infinite past that I find to be convincing. The argument I have in mind was first published in Philosophia Christi under the title “Methuselah’s Diary and the Finitude of the Past”; however, the same type of argument was also given in a less technical (hopefully more readable) style in section three of my open access paper titled “Toward a new kalam cosmological argument” (if you have problems with that link, then try this one).
As I conclude in the latter paper, the reason why there cannot be an infinite temporal regress–so that any countable series of consecutive finite temporal intervals that recede into the past must be finite–has something to do with the fact that we live in a world in which individuals can have real knowledge of the past while also being able to act independently of that knowledge in the present. So there seems to be a deep connection with the causal asymmetry of time at work in this argument.
Silver Asiatic:
I certainly agree that, having not followed the previous discussion (for lack of time), my intervention was probably a source of confusion for you.
However, without debating the many philosophical aspects that you have raised in your last posts, I will try to simply clarify a couple of points:
1) I can conceive of many forms of infinite which cannot be addressed scientifically of mathematically. But I don’t believe that, in that field, univocal ideas can be easily reached. In philosophy, there is no universally recognized truth. Each person has to make his own choices. So do I, so do you. As I said, science is more shareable, but not completely (Polanyite again! 🙂 )
2) I certainly believe in a transcendent God. However, my idea of a transcendent God seems to be a little different from the idea of an “actual infinite”. IMO, transcendence is much more than that.
3) The reasons why I believe that the universe started with the Big Bang are the usual reasons why scientists believe that: the many observations about Cosmic background radiation, and the expansion of universe, which are best explained by Big Bang like theories. As usual, I consider science a search for the best explanation of observable facts, not a search for ultimate truth. I respect science even more for those intrinsic limitations.
4) Personally, I would not use probability in reasonings which are mainly philosophical. It is, already, a tricky tool when we apply it to empirical contexts. That is probably the main reason that motivated me to post in this thread. IMO, scientific inference is not simply a question of probabilities. It is much more. It implies a lot of intuitive cognitions. I do love probability (especially in its frequentist flavour, I will probably never be a Bayesian!). I love it even more for its limitations, and for the big mystery that remains at its core. Like science.
5) I am a big fan of the cosmological argument for the existence of God. Of which ID is a direct derivation. I am less interested in other kinds of philosophical arguments on that subject. For me, inner conviction of the existence of God goes well beyond philosophical arguments, and is based mainly on personal choices, intuitions and experiences.
I hope that helps clarify my position.
However, I come here almost only to discuss science and ID theory, and I should probably get back to that.
gpuccio,
It certainly does help, as a step (or more) forward, at least for my attempt to understand your view. So, thank you.
[unnecessary addition, deleted]
Silver Asiatic:
Thank you for your patience! 🙂
gpuccio @395:
eccellente caro dottore!
Yes, please, come back and start new science discussions. Thank you!
DaveS,
All of them. I wouldn’t know where to start.
Here’s an idea. Go back and read Silver Asiatic’s posts carefully, and try to understand them.
-Q
Querius @399, just point out one. You’re bluffing aren’t you. You have no idea what your’e talking about.
If you’re interested, Pindi, go back and read Silver Asiatic’s posts. They’re clear, cogent, and convincing.
Actually, I do. But first tell me why I should care about convincing you of anything about me.
-Q
daveS,
I don’t understand something. Pick any present moment. How can an infinite past ever get to that moment? It seems to me to be logically impossible to make that case.
If I may take a stab at this question although it wasn’t directed towards me, the problem here is not a strictly logical one. In particular, there is nothing logically problematic with the notion of an infinite past that is totally ordered by the earlier than relation anymore than with the notion of the integers and/or real line being totally ordered by the less than relation.
In my opinion, the problem you are getting at is that it seems metaphysically implausible for a state of affairs to obtain in reality if an infinite duration of time would necessarily precede that state of affairs obtaining in reality. That is to say, it just doesn’t seem possible (metaphysically speaking) for this sort of thing to actually happen in reality. If this intuition is right, then it follows that if the past were infinite in duration then we have the absurd consequence that the present state of affairs could not possibly obtain. This is how philosophers like Saadya Gaon would argue against a past whose duration is infinite.
However, others have not been not content to stop there and have sought for a deeper metaphysical account as to why this intuition should be accepted. Toward this end there have been two schools of thought on the matter–one saying that the real problem lies in the notion that an actually infinite collection of any kind could obtain in reality while the other prefers to blame the particular notion of an infinite succession of past events (leaving open the possibility that other sorts of actually infinite collections might obtain in reality).
My apologies if these comments have already been made by others in this thread.
Ben
In order to determine an earlier-than-event, one would have to arrive at a point that “comes after an actual infinite”. So, you have to get there somehow. You have to cross an infinite range then arrive at a moment where you can look back.
There can be no distinct point in time where one arrives “at the edge of a boundless field”. If you find yourself there, in a present moment which marks a sequence in time, then why didn’t this moment already occur? Could you wait an infinite amount of time for today to arrive? Do we wait an infinite + 1 for tomorrow?
As discussed above, an actual infinite cannot be circumscibed. As such, it cannot be considered “an entity”. We say “this is a thing” because we define by boundaries.
In order to add an element to an infinite, the infinite would have to be bounded, comprehended, “captured” in some sense.
Of course, it is illogical to claim that an “infinite plus one” is a greater quantity than an actual infinite. It is equally illogical to say that an “infinite plus one” is the same size as an “infinite plus a million”. But that’s what it is.
An actual infinite cannot be measured. As such, new elements cannot be added to it. Any element that could be added is already contained within it. In an actual infinite span of time, whatever could have happened, already happened.
Also, an actual infinite in the past lacks a boundary necessary for it to be included in an additive process.
Just an additional point that I think is very important for you to consider. You stated:
Notice the equivalency you offer. A mathematical, symbolic presentation is basically the same as events occuring in real time?
No, as discussed above, mathematics offer an imaginary view of infinite sequences. Reality is quite a lot different. Mathematical symbols do not “occur in sequence”, they don’t take up any space. They can be manipulated in the mind.
But a real succession of events is much different. Actual things have to persist through an infinite field of time, space, etc.
You can traverse a mathematical infinity in an instant. To do it in real time takes an actual infinity of time, and is thus impossible.
There is no problem with an infinite past being an “actual infinity” because at any specific moment there is only the present. The infinite past never appears in existence at any moment, therefore is not impossible.
Besides, Christians who deny an infinite past have more problems than they are aware of.
PaV, please write up your explanation of the massive fraud in the science of HIV! Very much looking forward to it!
WJM,
I’m actually not making a positive case for this. I am asserting that an infinite past has unfolded as I have described, and am inviting anyone to derive a logical/mathematical contradiction from my premises.
I do agree with Ben when he states:
As I said in my previous comment, the problem with an infinite past is not (strictly speaking) a logical one. There is nothing logically amiss with the abstract notion of an infinite past for the same reason that there is nothing logically amiss with our concept of the integers and the real line (and the usual relational structures that we assign to these abstractions). My contention is that if there is a problem with an infinite past then it must be some kind of metaphysical problem, hence your emphasis in saying that infinity cannot be traversed in “real time.”
How are you going to find your non-DI, non-creationist left-wing “non-propaganda” ID organizations if you spend your time posting such comments in this DI right-wing propaganda ID organization less than an hour away from you in the PNW?
You don’t say?
You are? Perhaps you need to look less ’cause you’re in the wrong thread and PaV posted an article where he clearly stated he’ll be out for a while.
This won’t do because even if we concede the presentist assumption that the only state of affairs that actually exists at any given moment is the present state of affairs, it will still be the case that an infinite series of states of affairs (or events) actually obtained in reality at various past times. So, we will still need to make sense of the situation that such a series actually obtained in the past. All that presentist assumptions can do for us is bring the problem into sharper focus (assuming there is one).
Let me be clear for those who missed my first contribution to this thread, I am persuaded that one can successfully argue against an infinite past. Indeed, I have gone through the trouble to publish a couple of peer-reviewed articles to that effect and have made them freely available for download via the links given in comment 395.
Ben,
I just noticed your post #395; your paper also came up in my post #125!
How neat is that! Thank you for mentioning my work at comment 125.
Ben
An infinite past is usually not posed as an abstraction (at least it hasn’t been in this discussion thus far). So, whatever logical analysis that is applied to it must be done under the context that we’re talking about real time.
Would you agree that there is a logical problem when a notion that is proposed as a real event is evaluated as if it is an imaginary abstraction?
If someone said that there are actually 5 million elephants flying, under their own power, over the city of Los Angeles right now — wouldn’t we conclude that is illogical, even though abstractly, it’s the same as any collection of 5 million imaginary points?
If an infinite past is proposed as a non-existent, imaginary concept then I’d think it would be even more difficult (or impossible) to analyze. Why does it need to have any mathematical consistency? Creating an imaginary concept to mimic the symbolic world of math is the opposite of the task, as I see it.
Math is supposed to model what is real (or at least give understandings).
In any case, I appreciate corrections here. I didn’t/don’t follow the distinction you’re making and I’m very open to the possibility that I misunderstand it.
In the strictest sense, I would not say that the notion of five million elephants flying over Los Angeles is logically absurd. The problem with this notion is not that it contradicts the axioms of modern set theory, for example.
However, I would say that the notion of a flying elephant is metaphysically absurd all by itself since elephants obviously lack the capacity to fly. Moreover, I can also say that the notion of five million elephants flying over Los Angeles is physically impossible on the grounds that there aren’t five million elephants left on the planet.
For a discussion of these modalities–logical, metaphysical, and physical–check out this SEP article. These distinctions are fairly common in the philosophical literature.
Ben,
The problem with your statement is that you cannot depend on successfully applying the logic of mathematics to the real world.
For example, a number line in space (or the curvature of space) cannot be continuous by the mathematical definition of continuous due to the existence of the Planck length.
Additionally, other mathematical systems such as those studied in non-Euclidean mathematics cannot be applied wholesale to the real world either. Mathematics is undeniably a logical structure, but it’s not reality.
When you think about it, Kurt Gödel’s incompleteness theorems also falsify the notion of a complete mathematical description of reality.
-Q
Ben
That was a very good reference, thank you.
As I see it, the distinction between the strictly logical and the other two categories is interesting, but not very useful in a discussion like this. Beyond that, I’d say that it adds more ambiguity than clarity.
What seems to be missing, in the general notion, is that logic is also required in the metaphysical and physical understandings.
It would be better, in my view, to say “it is illogical on metaphysical or physical grounds”, than merely to say “strictly speaking it is logical”. In other words, it sounds as if logic and metaphysical analysis are entirely separate the other way.
We can build a syllogism which shows that elephants flying over Los Angeles is illogical. We arrive, in your terms, at a ‘metaphysical (or physical) absurdity’. True. That conclusion is driven by logic, and the nature of reality or physics, etc.
So, that’s where I’d question whether the term “strictly speaking it is logical” really works, since we can show it is illogical.
This is just semantics and I’m just a layman arguing with philosophical terminology — but sometimes even laymen can bring some new insights.
Perhaps instead of “strictly speaking”, it could be something like, using abstract logic alone – or the term the article uses “sheer logic” alone.
Again, I don’t find that very useful since the discussion focused on the metaphysical and physical reality of an infinite past.
For example, if the first response to my claim that there are presently 5 million elephants flying over Los Angeles was that “in terms of sheer logic there is nothing wrong with that claim”, I’d find a problem with that – at least one personal grounds.
But it does show (as I argued above and others opposed) that “correct logic” can result in absurd conclusions (metaphysically).
The very same is true with mathematics. Correct math can result in absurdities and contradictions in light of what is real.
In any case, in spite of all of that – thank you for a very informative resource! I learned quite a lot from it.
Querius
Agreed. As I see it, that’s the critical understanding that is missed. The argument has been, in several instances, “an infinite past is perfectly consistent with mathematical analysis”.
But that’s kind of a bait and switch. The claim is about a “real infinite past”.
Based on these remarks, I suspect that whatever disagreement we might have is more a matter of semantics than substance, and I am not interested in pursuing a lengthy back-and-forth over how best to word things. This sort of problem is common in philosophy since the discipline lacks an agreed upon foundation on which to theorize, with the latest academic conventions constantly in flux. So please don’t take this as a criticism of your own preferred way of discussing these matters.
I never meant to suggest that the series of past times is akin to a literal continuum; indeed, the arguments I give in the papers referenced in comment 395 entail that such cannot be the case. All I am saying is that if the past is infinite, then there’s no strictly mathematical problem with this notion. This means that I don’t think one can successfully argue against an infinite past by showing that the very notion of an infinite past is conceptually incoherent/contradictory.
Ben,
May we ask questions about your Methuselah’s Diary paper?
Sure. I don’t mind answering questions about either paper.
Thanks, Ben.
I’m looking at section II. Methusaleh’s Diary.
I believe I follow your proof of premise (1); for example I see that there does not exist a function f mapping the negative integers to the negative integers such that (i) f(d) <= d for all d and (ii) f(d + 2) = f(d) + 1 for d <= -3. If I've misinterpreted anything, please let me know.
My question has to do with premise (2). How do I know I have the right to expect the Methuselah's Diary scenario (or the beginningless Tristam Shandy scenario) to be tenable, assuming an infinite past?
My conclusion after reading about the beginningless Tristam Shandy example is that if you assume Tristam is currently writing about his past, then finitely many years ago*, he had to have been writing about his future, which certainly should not be allowed. In other words, the "normal" Tristam Shandy example cannot be extended into an infinite past, even if an infinite past makes perfect sense.
As an analogy, suppose I observe that some quantity (which must always be positive, such as the water depth in a lake) is increasing linearly. Then I certainly cannot hypothesize that the water level has been increasing linearly throughout an infinite past. But of course this doesn't mean the past cannot be infinite.
*I am making some assumptions about the order type of the set of past days, namely that it is not something truly bizarre such as that of (…, -2, -1, 0, 1, 2, …, -2, -1, 0), i.e., the integers "followed" by another copy of the negative integers.
PS to my #423: I just noticed I mistakenly read the “D” at the end of premise (1) as “D_F”, but I think my questions still make sense.
First of all, thank you so much for taking the time to engage my work, daveS. I really appreciate it!
I take it as obvious that (2) follows if the Methuselah’s Diary (hereafter, MD) scenario is seen to be coherent (or logically consistent), as the MD scenario provides us with the right sort of mapping. But why think that the MD scenario is coherent? I address this issue explicitly in the second paper as follows:
The idea is that since we are in a position to determine what is possible for a being with powers and dispositional capacities similar to our own, we can see that the MD scenario is coherent. This is the sort of modal judgment that we make when we, for example, speculate as to what could have happened to someone or other during some period of time that has already occurred in the past.
Also, this is where the metaphysics comes in. The whole point of this argument is to show that an infinite past is inconsistent with what we know to be causally possible for a being like ourselves. Hence, I want to say that the past cannot be infinite on account of the modal structure of the world and not because of some conceptual difficulty with our notion of infinity.
So, others have already demonstrated that a backwards Tristram Shandy scenario is not compatible with an infinite past (see the references I give in the first paper), but it still remained to show that such a scenario should be considered coherent (or logically possible) in order to have an argument against an infinite past (per Morriston). The advance in the MD scenario is that we can reconstruct a kind of backwards Tristram Shandy scenario via the assignment of powers and diary-keeping dispositions that an individual like ourselves could have had (and coherently exercised) during the relevant series of past days, which allows us to conclude that the relevant scenario can be judged coherent (or logically possible).
Ben,
You’re certainly welcome, and thanks for the detailed response. I’ll have to read the other paper and look up the references as well.
One quick question regarding this:
Is the MD scenario compatible with an infinite past in a way that the beginningless Tristam Shandy scenario is not?
Hope you find it helpful.
The MD scenario and the backwards Tristram Shandy scenario are both incompatible with an infinite past for pretty much the same reason. Indeed, it’s that very incompatibility that allows me to conclude from the coherence (or logical possibility) of the MD scenario that the series of past days must be finite. Again, I tried to make all this easier to understand in the second paper, so do give section three of that paper a try.
One more thing, I am not the only person who argues against an infinite past by appealing to what should be causally possible. Check out this paper by Koons for a very different approach involving Grim Reapers.
Thanks, Ben, that’s helpful—I think I understand the thrust of the argument better now. I’ll read the other paper over the weekend.
Thanks for the Koons paper as well, it looks quite interesting.
Silver Asiatic @418,
Consider also the impact of Gödel’s incompleteness theorems on mapping mathematical concepts onto the real world. The conclusion is that at best, there will be true statements undetectable by the mathematical system. It’s also likely that any mathematical system will include relationships that can be falsified in nature.
In short, mathematics is a tool that can model reality to an arbitrary degree of precision, but there’s no possible way to prove congruence, and any mathematical system can NEVER be congruent with nature due to (a) the empirical nature of the testing performed, and (b) the proof that there will be behaviors in reality that cannot be modeled in any one mathematical system.
This leaves speculations and arguments about infinities in the realm of pure fantasy along with magical fairies and rainbow unicorns.
Not to mention of course the logical gyrations needed to create a mildly plausible explanation of why entropy isn’t maximized after an infinite time period.
It’s OK math, but absurd physics.
-Q
Ben (in re 404),
When one projects backwards from the present, reverting to an implicit or explicit ellipsis:
sn [now] –> sn-1 . . . s0 [bang] . . . k, k+1, . . . .
it may not seem problematic to have a temporal antecedent for any k. But this is slipping in a subtle substitution of the potential as opposed to the actually completed transfinite.
The problem is, temporal-causal order does not work that way. Instead, stage by stage, we have a stepwise cumulative causal succession that can be reasonably addressed as finite steps.
On this, we have to account for a transfinite, stepwise finite stage causal succession capable of actually traversing the transfinite.
That’s why, from early on in the thread (cf 65 above), I have consistently put this on the table:
That is one of the key things you need to answer.
KF
AK, in re 406: the problem is incremental, finite stage, stepwise CAUSAL succession. To traverse the past to reach any given present, one has to do just that, move forward in causally successive steps to that point. Then, we have onward stages. To traverse an infinite actual past then becomes a pivotal issue and as I just again cited, this cannot be done in such a stepwise fashion. We can have a potential infinite that is open ended onwards in the forward sense, but we never actually physicallt traverse the transfinite span. KF
DS in re 317:
The assumption fails due to the stepwise, finite stage causally cumulative process inherent to the temporal order, as has been long since outlined. Such a process cannot actually traverse a span that is transfinite, thus endless.
And, temporal duration is inherently a matter of span in time or in quasi-temporal stages between relevant end-points, say t1 and t2, the latter being later. To claim a past that is transfinite, implies that there will always be times that were once the present that are now remotely endlessly past beyond any finite past time t1. This implies that there must be past times such as w in the sequence I have repeatedly used. This then immediately brings up the spanning challenge for reaching some remote but only finitely remote time point or stage k.
Skeletally:
KF
Querius
Great points. It leads me to consider that the math (in this case) is not just ‘partially correct’ but it actually gives a false understanding. I’ve noticed that the first thing that some will do when considering an infinite past is turn to mathematical models – and they basically stay with that through the various arguments that the math provides.
First of all, a number line cannot be equivalent to what we mean as “time”, as with an infinite past. A number line can be self-existent and independent. But time necessarily depends on the movement or change in reality. It measures and requires the persistence of existent things that are not time themselves. So, time is not just a sequence of numbers or symbols.
Time cannot exist unless objects and forces persist. Simple number lines, or the use of set theory, for example, do not model those relationships.
This brings me to the points I was trying to raise earlier – building off of the term “maximized”. That’s actually somewhat (not exactly) the basis of various scenarios like Koons’ Grim Reaper and others. The idea is that an infinite always extends to the maximum but never terminates there.
With entropy it would be the same, as you mention. Any linear, progressive development or process will reach its maximum state.
When an infinite past is assumed to exist, it’s easy to forget that any linear process it contains must have reached its maximum possible value before the present.
In other words, you cannot reach a discrete point in time where “maximum + 1” had not already occurred.
If we look at other qualities like entropy: destruction, speed, refinement, volatility, stasis, strength/weakness of bond — if any of these moved in a linear, additive process then by the present day, they’ve reached the maximum possible.
Two arguments against this are that there is no finite maximum. All of those values, it would be claimed, are potentially infinite. The other argument that the processes are not linear but rather cyclical.
On the first point, if those linear processes were not only actually infinite in the past but potentially infinite in the future, we’d have some unthinkable scenarios in terms of physics. On the second point, something would need to trigger recurring cycles.
Finally, even if conceding the possible existence of an infinite past, what caused all of those forces, objects and processes to exist, in exactly the right balance, to be preserved for an infinite span of time?
Ben (and anyone else interested),
I was doing some background reading before diving into the Koons paper. This Grim Reaper paradox is very cool. The first formulation I landed on, taken from here (with some loss of formatting):
My initial response is that he actually hasn’t shown that it is certain that a Grim Reaper kills you. If (p) holds, then there need not be a “first” Grim Reaper (although there could be!).
With the statement, “as long as one Grim Reaper wakes up between 8 and 9 you’re guaranteed to be dead” and with p = for every time after 8 at least one Grim Reaper wakes up in that time, then, logically, it’s certain the Grim Reaper kills you.
The paradox rests on the notion that “between 8 and 9” is an infinite range that cannot be traversed.
I don’t see how there could be a first Grim Reaper for “every time” within that one hour (built on the notion that the time can be split infinitely smaller).
The only way there could be a first one is if some statement was asserted about the absolute limit of increments that would be included in “every time”.
But if time worked like a mathematical number line, then there couldn’t be any finite limit to the fractions included between 8 and 9. Thus Grim Reapers would forever be waking up and you would both be dead because of that and alive because each Grim Reaper was later than the prior one, on to infinity.
Right?
Backing up a couple paragraphs, Pruss argues as follows: “Then, you’re going to be dead at 9 am, since as long as at least one Grim Reaper wakes up during that time period, you’re guaranteed to be dead.”
However, a key assumption that Pruss neglects to highlight in the quoted passage is that he is presupposing a non-discrete view of time. If time were discrete, then no contradiction follows from accepting (p).
Ben,
Regarding the discrete time case, do you have in mind a picture where the interval between 8 and 9 AM consists of finitely many (or perhaps infinitely many?) moments, much as 1 second corresponds to 24 frames of 35 mm movie film?
This leads me to wonder what would happen if the first two or several Grim Reapers arrived simultaneously (in either the discrete or continuous case), but I guess that could be dealt with by having them draw lots or something similar.
Yes. This is the idea that intervals of time might be composed of chronons, which are indivisible units of time. If this is right, then Pruss’s argument runs into the following problem: If a GR wakes up between 8 and 9 at time t, and the duration of time between 8 and t is a single chronon, then it’s not possible for a GR to wake up at a time strictly between 8 and t on the grounds that no such time exists (contra [p]).
Or we could just refine the scenario without sacrificing plausibility to guarantee that multiple GRs don’t wake up simultaneously.
So, if time is discrete in the sense described in comment 438, then I don’t see how Pruss’s method of argument can be used to derive a contradiction in this case. That’s what I should have said earlier.
Thanks, Ben, that’s what I was thinking as well.
A mathematical paradox, similar to subtracting all the odd numbers and ending up with an infinite … but perhaps better because it’s not possible to remove “all” (which would imply a finite quantity) from an infinite is:
With an infinite past, it would not be possible to calculate a “percentage of time existing” for any given event except for eternal entities.
To determine a proportion of time from the infinite past would require a finite value in the denominator.
For example, what percentage of time from the infinite past does the age of our universe represent? Or, what thing has existed for at least 1/10 of time, but not for all time? That would be impossible because you can’t get 1/10 of an infinite past.
If the past was finite, even if the future was potentially infinite, you could calculate it. Every day would be a certain % of time, and that percent would always get smaller, but would always be measurable.
Measuring a proportion of the infinite past, however, is impossible mathematically. This past year, for example, “should be” some percentage of time but it really cannot be.
Silver Asiatic @433,
Exactly–excellent points all. There are so many problems mapping mathematics to the real world, it simply becomes an exercise in futility.
Or a corollary to your description in 441 . . . If you pick an arbitrary point on an infinite line and add one to it, the line in either direction is still infinite, “proving” that time does not advance. Or to use Cantor’s notation, m + 1 = m.
-Q
Ben,
I did finally get to reading your paper “Toward a new kālam cosmological argument” and you were right, it is very helpful in understanding the point of the Methuselah’s Diary example. I believe I understand the basic structure of the argument now.
The part that I am still pondering is toward the end of paragraph 2 of part 3:
Am I right in assuming that you expect different readers to find this more or less plausible, depending on their views on the status of human powers and dispositions?
If someone, for example, believes that human powers and dispositions are somehow “aligned” with matters of objective truth (such as the duration of the past), then they likely would find this quite convincing, IMHO. [Sorry, I can’t think of a better way to put this; essentially I want to say that if we believe the MD scenario is coherent, there is a good chance it actually is].
On the other hand, someone who is more pessimistic about the powers of human reason in particular, might be less convinced?
“Measuring a proportion of the infinite past, however, is impossible mathematically.”
If you ever take college-level math classes you will know that the probability calculations for sampling integrals to infinity are not impossible, but rather simple and boring, and were figured out centuries before you arrived. Also you might stop thinking that because infinite sets conflict with your simple Classical Algebra notions of things like proportion, there is something wrong with them, instead of your understanding.
There is so much dorm-room philosophy here when a little education would fix things. I do not know what anyone thinks is being accomplished at this website. It seems to be missing a clear purpose.
AhmedKiaan,
I’ll take this opportunity to tout a couple specific density measures:
Natural density and Schnirelmann density
yep.
Interesting …
Ahmedkiaan = dorm room jerk who thinks he is smarter than everyone else on campus, but in reality is an insecure and marginally intelligent fool who nobody likes or respects.
Yep.
Silver Asiatic @447,
And that’s one big reason why mathematics can never be mapped onto the real world as a congruence. It will at best serve as a useful-for-the-moment model.
-Q
Thank you for telling me this!
Close enough. The idea is that readers will recognize that the powers and dispositions involved in the MD scenario are very much like the sorts of powers and dispositions that we already know to be possible for beings like ourselves. Hence, the MD scenario can be judged coherent (or logically possible) for the reason given in the passage you quoted.
I don’t see how such a response would go. I take it as undeniable that we have powers of memory (some better than others), and that we have the dispositional capacity to consciously maintain such a diary in the relevant manner. So I don’t think there’s any question concerning our ability to coherently exercise these sorts of powers and dispositions.
Thanks for the response, Ben. It’s good to hear I’m approximately right on the first point.
I don’t think I worded the second part correctly judging from your reply, so I will think about it some more, and go over the paper another time. If I can think of a better way to express my point, I’ll do so.
Fair enough, take your time.
TWSYF, please, moderate tone. This is a place for a substantial discussion, not a contest for barbed rhetoric. KF
Kairosfocus @ 453: Got it. Thanks for the reprimand. I was actually feeling bad about my recent “tone” as well. I will do better!
DS, 340:
This is a pivotal problem.
If there was an actual past, every stage or moment of it was once the present but causally triggered a successor stage or moment ultimately accumulating the past to become the present and this continues.
This is a criterion of consistent meaningfulness.
Next, durations between moments m_i and m_j are in effect amenable to a count of succession from the one to the other, at least up to some unit or metric of stages. (This does not depend on whether or not time is a continuum in the micro-sense, it is simply saying in effect we can count back in seconds or years etc as a yardstick.)
Duration is specific, difference or span between particular moments.
To claim an infinite past, is to claim there is at least one past moment or stage say m_w such that it was once the present and is endlessly remote beyond any finite span to a moment of the past.
In short, to claim that there is only a finite span between any two moments in time so far, is to say there were no transfinitely remote actual once-present now past moments. This is tantamount to, the past was finite, which cannot mean the same thing as the past was transfinite.
Again, we find no warrant for claiming or assuming an infinite past that actually occurred as the once present and which then gave rise to a cumulative succession of temporal stages that led to the present.
Moreover, the stepwise finite stage succession implied by the past accumulating to the present, poses the challenge of traversing a transfinite span, step by step to pass from an actually once present past that successively progresses to the present. This is utterly different from how the present may continue the process indefinitely yielding a potentially infinite future, absent the issue of heat death.
the proposal of an actually infinite past leads to incoherence that robs the terms used of reasonable meaning.
We are only warranted to speak of a finite past, and that poses the issue of an actual beginning to the space-time physical world we inhabit and any quasi-physical antecedents it may have had.
All of this then points onward to a necessary being root of reality, as in the end if there were ever utter non-being, that would forever obtain as non-being cannot participate in a causal-temporal succession such as we have examined.
KF
PS: Re sets of Grim Reapers, pardon a back to basics comment. I suggest, time is an independent process that moves on, from 7 to 8, 8 to 9, 9 to 10 etc. by whatever means. The days of the Cold War are past, WW II and WWI before it are even more past, so is Queen Victoria’s reign, and so on back to Julius Caesar and King David and King Tut and beyond. So, if such entities exist with markers set in a finite span, are operational, and are capable of relevant actions at set times in a span that will be traversed as time marches on, they would be triggered by the passage of time, just as a time bomb is triggered by a clock mechanism, whether it is analogue or digital, depending on design. (Think, a clock driven by an ideal synchronous motor and set up so the hands will close contacts at a certain preset time, triggering ignition. it will work, never mind the continuum involved as “motion” in time will traverse an interval even if it is continuous; otherwise time is not time. the same holds if time is granular. Of course, if there are finitely many reapers, we can identify the first one will act. If there are transfinitely many then we cannot define a first one but time will sweep by the markers for these in succession, so at least one will be triggered as t moves beyond 8 towards 9, and will act.)
KF,
Suppose it happens that GR n awakes at 8:00 AM plus 1/n minutes, for all positive integers n. Which GR will act?
DS, as I noted, in cases like that, which reaper will act is not possible to specify, but as time sweeps from 8 to 9, at least one will act providing there is a sufficiently reliable trigger mechanism. I note, it is likely infeasible to physically instantiate such, this is a thought exercise. Where, 8 to 9 is a FINITE span, just that on hyp of a continuum, it will be mathematically infinitely dense everywhere within with legitimate values of intervening time. And, you will note that I have consistently spoken to stepwise, finite stage cumulatively successive incrementing temporal succession where present moments march on in succession passing to the past one after another as the future is actualised stage by stage; precisely to avoid the complications of the continuum. We know time proceeds, whether it is an actual continuum or a fine grained discrete stage process is not pivotal to that self-evident fact. It is that finite stage succession that triggers the issue of traversing the transfinite, on a hypothesised infinite past. KF
PS: Just as an illustration, the time-stamps show how the moment of composition of successive posts marches on in succession, achieving a finite span of successive stages and illustrating cumulative, causal interactions with multiple chains of influence. (Added: notice, a bit under 45 minutes between the just above and the original form of this post, time stamps being 2 hrs behind my local time on the clock.)
KF,
Note that Koons himself states that under the scenario I described, no GR will act:
Edit: Of course he also states that some GR will always act, but I don’t think this actually would be the case if we follow to the letter the “rules” he has laid out.
PS to my #459: Actually it is Pruss rather than Koons who wrote up this version of the Grim Reaper Paradox.
DS,
my concern is that time is ticking and per hypothesis, there are GR’s set to act at time markers. The GR’s individually or collectively cannot stop the flow of time, cannot freeze time. Time will flow from 8 to 9, and in that interim markers are there . . .
Where, once a marker is there and time hits it without an already triggered index, some GR will trigger. By the logic of time passing and markers triggering actions. If that is so and there is an effective process, something should happen.
If not, what seems is there are conditional terms that are locking out action. In short, there is need to clarify what is going on.
But, GR is not my main concern, I think there is something far more basic, which you have skipped over over the past day, again: what does it mean to have had an actual infinite temporal past, and is this reasonable?
It seems, not, given the issue of duration and the need for an actual past to have been once the present succeeded to by causally cumulative stages to now, one after the other.
I cannot reasonably see that an infinite past does not imply stages that were once the present but are now endlessly remote beyond any finite past value.
This imposes the traverse of endlessness in steps problem, which is an impossibility.
KF
KF,
I somewhat agree with the second-to-last sentence here—the conditions imposed on the scenario (including (p)) make it impossible for any GR to act.
I understand the statement “the past is infinite” to mean that the duration of the past exceeds any preassigned finite value (as per the dictionary definition somewhere above). That is, given any natural number M, there exists a point in time which occurred more than M years ago.
As far as I can tell, there is almost unanimous agreement in the published literature that this is a reasonable definition.
DS, the issue is this definition has other implications; as I have pointed out above. First, that a value is beyond any finite value implies endlessness, indeed it must be endlessly beyond any given finite past value. For from any finite k we can go k+1, k+2, etc endlessly in a finite stage succession onward. That is there is no finite K* such that K*+1 = “infinity” . . . the transfinite can only imply endless onward succession in a sequence beyond any finite stage or value we can reach from zero; we then recognise a new category of quantity the transfinite, OMEGA. This being the order type of the natural counting numbers from zero, INCLUDING an ellipsis of endless succession:
{0,1,2 . . . k, k+1, k+2 . . . . } –> OMEGA
And, if there were an actual past point infinitely remote in the past now, it must be that this was once the present, which then moved forward step by step across endlessness to reach now through temporally expressed causal processes. Which endlessness cannot be traversed successfully in finite stage steps, which are what time must take. KF
KF,
We have been through this many times, but please observe that the definition you posted (!) does not entail that such a point would have to exist in an infinite past.
DS, duration is point to point, as I pointed out. You claim an infinite duration, either you have an endless span of actual time SINCE an actual past stage or infinite is subtly being redefined to mean finite. KF
KF,
Yes, of course. If, given any positive integer M, there exists a point in the past such that the duration of the interval between that point and the present (another point in time) exceeds M years, then the entire past (whose duration is at least as long as any such interval) is infinite.
This is all according to the dictionary definition.
DS, the implication of infinite actual past MUST be that there are endlessly remote actual past stages. This actually follows from your summary just now for any finite M is preceeded by M+1, M+2, M=# etc without end in order for there to be a limitless past beyond all finite values. It is this direct implication that leads to the need to span endlessness in finite stage steps to get to the present, and subtly substituting a potential infinity stepped back to from the present misses the basic fact that time moves forward stage by stage through causal links. KF
KF,
Well, as I think I’ve said before, if you really believe this is true, you should publish a proof! Using standard mathematical notation and definitions, of course. I’m fairly certain no such proof has appeared in print yet.
DS, The logic is simple and there for all to see. The issue is that once there is an infinite actual past then there must have been stages that were once present, which then gave rise to successor stages in a cumulative process down to the present. Where, for that past to be infinite at least one of those real, actual states would have to be such that the duration (we can count in steps) must exceed all finite durations. Which means that — counting back from now — it is in excess of any member of {0, 1, 2, 3, . . . k, k+1, k+2 . . . . } from now. Where the four dot ellipsis here stands for endlessness. This then poses the challenge that time succeeds in a forward sense whivch must thus cross the same span. But an endless span cannot be crossed in finite stage successive steps as we have seen repeatedly. We have no warrant to accept the hypothesis of an actually infinite past. KF
KF,
For whatever reason, the simple logic that tells us that under an infinite past, there must have existed a point t_∞ in the past such that the interval between t_∞ and now is infinite, has eluded almost everyone who has published on this topic.
That notion also hasn’t gained much traction here. I don’t believe any of the mathematicians or philosophers on UD who post under their real names have supported the idea.
Do you think it’s possible that your argument for the existence of such a t_∞ is faulty?
DS,
pardon, but do you notice how often you substitute balances of expressed opinions for assessing the logic, underlying concepts and warrant of a case or a claim or view? That an opinion may or may not be popular at the moment has little or nothing to do with whether it is warranted.
The logic at work here is that of how time flows, tied to clarifying what duration of time means (especially between stages), what it means to be a past event or stage of the unfolding of the world, and what it means to have an infinite past of origins.
Time succeeds forward, stage by stage. Duration is in the first instance tied to initial and terminal stages. An actually past stage must have been once the present which has now been transcended through cumulative causally successive stages until we have reached now.
In this specific context, claiming an infinite past implies now infinitely remote past but once present stages; or else it equivocates the meaning of the past, begging a crucial question thereby. That is, were there an actually infinite past then there must have been stages that are by stepwise finite stage succession now beyond any finitely large duration from a past stage to now. This implies endlessness of succession (as, in simple terms, there is no finite K* such that K*+1 –> OMEGA . . . the issue of the transfinite pivots on endless succession onward beyond any finite k that can be matched 1:1 to {0,1,2 . . . . }, e.g. {k, k+1, k+2, . . . . }), and it thus points to a key incoherence in such a claim. No such stepwise succession can have been completed.
And, claims about every successive counting number being finite overlook the challenge of endlessness.
It is safer to claim that every counting number we can reach stepwise from 0 will be finite, but that endlessness of succession continues beyond any such number (i.e. for a finite k, there is endless succession onward that can be matched 1:1 to {0,1,2 . . . . }, e.g. {k, k+1, k+2, . . . . }) and this is material to understanding what it means for a set to have transfinite cardinality.
The need to stepwise traverse an endless succession from a claimed infinite actual past to reach the present will not go away. (And just in case, I am not claiming that there is a terminus; beyond say some w of transfinite past temporal remoteness from now, there would be yet onward endlessness. It too, would have had to be reached stepwise across an endless succession. And so forth endlessly. This points to the issues of getting the $100 bill to pass on etc.)
In this context there is no warrant for claiming an infinite actual past.
Nor will it do to assert such as axiom and suppress the issues implicit in it by substituting a potentially infinite regress for the needed forward traversal of an infinite past in steps to reach the present.
The infinite past claim does not solve the problem of origins.
KF
KF,
I’m not attempting to make an argument here, but rather I’m raising an honest question: Do you think it’s possible you might be wrong? If it were me against the world, it would certainly occur to me that I might be wrong, and I’m asking if you feel the same way.
IMHO, your argument for the existence of this t_∞ is a non sequitur (or perhaps you are invoking some premise that I’m not aware of). I can’t be 100% certain of the problem, because we still have not seen a version expressed using standard (mathematical, presumably) language. For my part, I’m not very motivated to look at it further until all of the forms of “endless” have been replaced with terms more commonly used in mathematics.
That’s partly why I suggested submitting your ideas to a journal, or at least running them by a mathematician/philosopher/some other expert. There are several such people who regularly post on UD, as you know. You might get some constructive criticism regarding how to express your argument in a more, let’s say, “accessible” manner. You could even try sending your questions to William Lane Craig if you prefer.
DS, please address the issue of exactly what an infinite actual past means, what it means for time to move forward and how one proposing an actually completed infinite past can avoid the impossibility of traversing endlessness to reach the present. As for mathematical proofs and notation, math is the logic of structure and quantity. Time has a structure amenable to a step by step sequence, where it is clear that an infinite past must include actually once the present stages that are now endlessly remote beyond any finite value of passage of time. Endlessness — which seems to be your main point of objection, is implied by the simple logic that at any finite past “distance” k, we can go to the onward previous stages endlessly: k, K+1, k+2 . . . if there is an infinite actual past. But the same endless”distance” would have to be traversed in finite stage steps going forward to reach to now. But to so span endlessness as an attempt is necessarily futile. That is what you need to solve and reaching backwards and pointing on further backwards does not solve it. KF
KF,
I have, many times. For any natural number M, there exists/existed a point in time more than M years (or seconds, whatever your favorite unit is) before the present.
I don’t think I differ greatly from you on this point. Time just does move forward. In the discrete sequences of moments we are discussing, the relevant “jumps” can be assumed to all have equal length (1 day, year, etc).
I’m simply not going to get involved in another discussion of “endlessness”. If that concept makes sense, then I think one should be able to translate it into standard language that people use when describing ordered sets or sequences.
It is not clear. At least not to virtually everyone who has published on this subject.
DS, an infinite past must have been endlessly beyond any finitely remote past point. As for endlessneess I am astonished that you find it so difficult a concept as it is directly tied to the unlimited succession of naturals in +1 steps, and to the point that for any given finite k, we can succeed equally without end, k+1, k+2 etc and put in 1:1 correspondence with {0,1,2, etc}. Where the order type of the naturals as a whole is omega, first transfinite ordinal, and the set exhibits cardinality aleph-null. Which, demonstrates the infinity by match with a set known to be infinite. The unlimited succession to infinite degree similar to the counting numbers produced by a von Neumann construction or the like is reasonably described by the term, “endlessness.” Omega of course is never seen as successor by +1 increment to some large finite K*, so that K*+1 = omega. Endlessness as is represented by an appropriate ellipsis [I have recently used four dots to mark a difference from a finite, bounded succession] is integral to all this. KF
Dave, it makes sense to you, and to me, and to philosophers and physicists and mathematicians. That’s going to have to be good enough. It’s just not true that every person in the audience is going to understand everything, and at some point, continuing to explain has diminishing returns.
AK, can you write out — yes, literally — the complete set of natural counting numbers? Why or why not? Why do we usually represent much of that set with an ellipsis? Can you completely climb a ladder with an infinite number of rungs? Why or why not? If every stage of an infinite past has to have physically happened then given rise to its immediate successor and so forth, how, specifically can you arrive step by step at the present? What does this tell us about claiming there was an actually completed infinite past that has arrived at the present? KF
AhmedKiaan,
Yes, this particular line of discussion has generated little or no returns.
KF,
It’s not the difficulty so much as the imprecision. And all the “custom” definitions, the ellipses of endlessness™ (now with four dots!) and so forth. It makes communication very difficult.
DS,
Pardon, but I don’t believe your claims such as the just above at this point; they are far too rhetorically convenient in a context where too much water has gone under the bridge.
For nearly a year, we have discussed exactly this point and I freely acknowledge that you have been helpful to me, e.g. in pointing to the surreals.
We both know that ellipses are routinely used in representing sequences and series, often in a finite and bounded context, sometimes in a context of onward continuation without bound. In this situation the distinction has become important and I have simply used the four dot version for that.
Long since, in the spirit of Turing, I used the pink vs blue 0.1 inch pitch punched tape thought exercise to show how end-less-ness (=endlessness) arises and has crisp meaning and significance.
P: 0,1,2 . . . –>
B: 0,1, 2 . . . –>
Take B and shift-left (ShL) the tape to some finite k (i.e. register transfer type operations), but retain the un-end-ing continuity to the RHS:
P: 0,1,2 . . . –>
B: k,k+1, k+2 . . . –>
That is, the onward continuation continues in 1:1 correspondence, the end-less-ness to the RHS continues to hold even after an equivalent ShR by an arbitrarily large but finite k stages by a unit (say, U) sitting on the tape that moves in +1 increments; bounded by the onward continuation k+1, k+2 etc [notice that representation of the unbounded ellipsis]. This has several implications, but the first is that the cardinality of P and B even after the ShR, k times, is still the same, to wit aleph null. Both are transfinite, countably so.
Secondly, after arbitrarily large but finite steps of advance of U to k, the onward set is in effect a transformed form of the first, much as we see in fairly familiar cases:
0, 1, 2 . . . –>
x 2 in each position:
0, 2, 4 . . . –>
+1 from 0 on:
1, 3, 5 . . . –>
Where all three have the same countable transfinite character. And where the transfiniteness is shown by being able to put a 1:1 match between the full set and what is a proper subset. With, a critical feature being the continuation of the tapes to RHS without upper bound. (NB: It is reasonable to simplify to four dots.)
There is a third significant implication.
Namely, that the end-less unbounded continuation to the RHS implies that one cannot traverse the whole set in finite steps. Using (ShR, k) to summarise the multi-step operation of U of a +1 increment rightward k times, we see that at any finite k regardless of how arbitrarily large it is, there will always be onward k+1, k+2 etc, which can be matched 1:1 end-less-ly with the unshifted tape marked with the counting numbers on a 0.1 inch pitch. That is, no stepwise advance U to the RHS of any arbitrarily large but finite scale, k, can exhaust the endlessness. Which, by now, is again shown as to what it means exactly.
Thus, one cannot traverse endlessness of the type exhibited by the counting numbers in finite stage steps.
Now, time is of like character, where one stage gives rise to another immediately following through a causally tied succession, analogous to the (ShR, 1) by U. Time’s arrow can be seen in the accompanying accumulation of entropy, i.e. degradation of concentrations of energy towards heat death.
Going to time forward from now, we see the distinction between a potential and an actually completed infinity. The former is feasible, one may (ShR, 1) unit U any arbitrarily large number of onward steps, which need not be of equal finite temporal duration (think of this as speeding up or slowing down the clock rate driving the +1 process for U).
Now, extend the tapes to the LHS in a similar pattern, in a mirror image:
P/B: . . . . –> -(k+2), -(k+1), -k, -(k-1) . . . -2, -1 //
0, 1, 2, . . . k, k+1, k+2 . . . –>
That is, the tapes are now endless to LHS also.
Fold B at 0 so that the (ShR,k) by U that pointed R now will match the tape to L in 1:1 correspondence. The shifting unit can now do the (ShR,k) on B from 0, and will match -k as we have folded by 180 degrees. The same property of endlessness and frustration of traversal to completion obviously applies to LHS as to RHS.
But now, we see that just as we cannot climb to the transfinite by successive (ShR,1) finite stage steps of U, a (ShR,1) unit on the tape to far LHS cannot traverse the same span rightwards from the endless, transfinitely remote left zone to reach to k, as beyond any given value say w in that far left zone, there would be the same endless span to traverse.
This I have represented by choosing some w in that zone, for argument:
. . . . w, w-1, w-2, . . . . -(k+2), -(k+1), -(k, -(k-1) . . . -2, -1, 0, 1, 2, . . . s_n [= “now”] . . . –>
The (ShR,1) unit, moving rightwards beyond w will not be able to traverse the endless span in successive, cumulative +1 steps, as we see:
P: 0, 1, 2 . . . .
B: w, w-1, w-2 . . . .
showing the same 1:1 match property to countable endlessness.
Where, reverting to time, a claim of an endless past must imply that there were actual past stages w that were once the present — = the (ShR,1) unit once sat there — but stepwise succession (advance to the next stage of time, repeated and cumulative) has continued to now.
Therein lies the problem, that stepwise succession would have to do what it cannot, successively span an endless span of cardinality aleph null.
Again, we have no warrant to speak of an actually completed infinite past that has by cumulative stages given rise to the present.
Instead, it makes better sense to speak of a finitely remote beginning at a -k point, where of course I have used 0 to mark the big bang event. That is we reckon with claimed quasi-physical antecedents to the present observable cosmos and could readily address branches, budding, fluctuations giving rise to bubble sub-cosmi, oscillating worlds, parallel domains and whatnot.
Finally, I suggest that what has made communication difficult is the path of endless objections and looping back as though previous discussions and clarifications have not happened.
I trust the extended P/B tape discussion above will allow us to now proceed. Especially given its concrete nature and its ability to use the concepts of register transfer algebra and thus of computation.
KF
KF,
A few comments:
1) I think you could easily omit the word “endless” from your argument at this point. It seems you are talking about countably infinite totally ordered sets, so can we make that change?
2) I request that we make no reference at all to traversals of sets of order type ω such as {0, 1, 2, …}. The set of past moments I am considering has order type ω*, and propositions that hold for sets of type ω do not necessarily hold for those of type ω*.
3) It appears to me you are getting this infinitely remote past point w by working with the set {0, 1, 2, …}. In view of #2 above, I would ask that you prove the existence of this w in some other way, without bringing up the traversal of the nonnegative integers.
DS, I suggest, first that endless succession is pivotal, especially when time is factored in. Second, that the pivotal question is what does an infinite past mean in a context of causally connected causal succession from past to build up to present; we do have to face and adjust our analysis to the known properties of temporal, causal succession. Third, that such a succession is amenable to counting, thus to the sort of thought exercise analysis of relevant sequences as above. Finally, a duration is between two stages, e.g. WW2 ran from Sept 1939 to Sept 1945. In this case, to claim an infinite past is to imply that there were moments that were once the present but are now remote beyond any finite and bounded value. It is appropriate to call a day or year or stage of the cosmos or whatever quasi-physical order or domain of reality that preceded it and was beyond that span from now w for reference; w is just a label for an arbitrary stage that ex hypothesi was once the present but now has been succeeded by so many stages that the countable span to it is greater than any finite value we can reach. Where, time then moves inexorably forward in stages from w, allowing us to count, w, w+1, w+2 etc, which then brings up the by reason of hyp infinite and countable span from w to now that would be beyond any finite span. If you don’t like such an actual stage, then stop suggesting an actual physical, infinite past. We may then ask about temporal, finite stage causal succession since w to today, on the claimed infinitely remote past. Where time definitely proceeds in the sort of causally successive stages as mentioned. The challenge of bridging an endless, transfinite span that is of cardinality aleph null emerges. KF
PS: To address omega vs omega-star (or star omega) simply fold the blue tape over at 0 and change the sign. The negatives are the mirror image of the positives — as the virtual half universe (of in principle unlimited extension) behind a mirror points to. And this does not eliminate the issue of an infinite actual past requiring stages like w to have been real. The traversal in steps challenge does not go away.
KF,
Yes, but if you reflect the traversal of {0, 1, 2, …} as well, you end up counting down through the negative integers. That’s the wrong direction. The relevant traversal is counting up through the negative integers.
As I said, I’m not interested in discussing “endlessness”; there has to be a translation into standard mathematical terms.
I’m sorry, KF, but that’s not what your dictionary definition states.
Given any natural number M, there is a w such that the interval between w and the present exceeds M years. That’s what “infinite past” means.
There need not be any particular w such that the interval between w and the present exceeds M years, for every natural number M.
“Given any natural number M, there is a w such that the interval between w and the present exceeds M years. That’s what “infinite past” means.
There need not be any particular w such that the interval between w and the present exceeds M years, for every natural number M.”
Anyone who doesn’t understand that simply does not understand basic Real Analysis, with regard to series and function theory. This is not really arcane stuff, but laypeople generally don’t know it.
But what I don’t understand is why the people who inhabit this site are trying to have conversations about topics that none of them know anything about. It’s like you guys want Bob Oh and DaveS and one or two others to slowly teach you whatever topic you ask questions about, but then you reject the answers. This site is baffling to me.
This site doesn’t even come up in Google searches for “Intelligent Design” anymore.
AK, Google’s biases are notorious now, though not anywhere as bad as the hatchet jobs at Wiki. KF
DS,
I simply first showed why the two order types are isomorphic; can be placed in full 1:1 correspondence, where the span in steps will be the same, and where the 0.1 inch pitch is relevant to showing that we are dealing with finite stage intervals.
Had you looked more closely at what I actually did, I was first highlighting that we have in effect a computational exercise, amenable to register transfer type operations. Per those operations against a backdrop that one is claiming that there was an actually infinite past that through stepwise, right-shift finite stage causally connected +1 increment succession, eventually gave rise to the present.
This means that to claim an actually infinite past, then there was some stage that was actual as present but now has been succeeded by a span that makes the stepwise distance from then to now beyond any finite value, i.e. it is endless given the structure of the naturals. We are not claiming a potential infinity, we are claiming an actual, rightward increment, completed one.
So, symbolise w as a typical time in that transfinitely remote past zone . . . notice, I am not saying it had a leftmost terminus, just the opposite, I am simply saying that ex hypothesi, it was there as actual and suceeded up to now . . . and put a ShR, +1 step incremental operator, U, on it. Let it proceed, w, w+1, w+2, etc to the right, the forward temporal direction.
Will U ever reach some k’, a finitely remote point on the tape [mirror image to the k we used above], left of 0?
Answer, this is the same scale of span that a U cannot traverse in steps on the RHS from k on, as k on is 1:1 matched to 0,1,2 etc. Folding the U on the right over starting at k mirrored in k’, the ShR operator will never lead on to the positive mirror of w, w*. Nothing being changed of material significance, we see no reason why a U would be able to stepwise span from w to k’ on the LHS beyond 0. (While we are at it, let us label for future reference the double sided endless tapes P’ and B’.)
An endless or transfinite span cannot be traversed in sets.
The issue then is, was there a w?
If there was an infinite past span there had to be on the LHS of B’.
But this gives rise to the absurdity of sitting in the present and speaking of how we could not get here.
The obvious answer is, there was no w.
The temporal domain is well-ordered and incrementally advancing from a true zero-point, which we here label k’ for convenience.
Rather like the case with temperatures when it was discovered there is a natural, absolute zero. Counting in years of the Christian Era and going to a down count before it, or doing much the same with the big bang, ends in the same result: these arbitrary zero-points point to an absolute zero point, a beginning to the [quasi-] physico-temporal world we inhabit.
Which points onward to the need for a necessary being atemporal root of reality as required for a world to exist. For, were there utter non-being (a true utter nothing) then as non-being has no causal capacity, such would forever obtain. If a world now is, something, a world-root, always was as a key framework for any possible world to exist. That is the discussion is about necessary beings in the end.
An infinite LHS to the [quasi-] physico-temporal domain is not a credible candidate to be such a necessary being world root.
Job opening: wanted, a necessary being, capable of being causal root of a physico-temporal world, must be a-temporal in character and capable of accounting for the evident signs of design in the physical world and the world of life. Should also be able to explain responsible rational, morally governed freedom required to be able to have such discussions as this.
There is only one serious candidate who will show up for the interview: the inherently good creator God of ethical theism, a necessary and maximally great being, worthy of loyalty and of the responsible and reasonable service of doing the good in accord with our nature.
After centuries of debates and discussions of alternatives, that is where we are back to; before consulting any particular scriptural or traditional system of theology.
And yes, such issues lurk here.
In these waters there be big sharks.
KF
PS: I take it that it is readily seen that an infinite succession of successive finite, finitely separated values from 0 to RHS or LHS, not amounting to an infinite span of thought exercise tape will be seen as absurd. To explore, ponder U as a ShR,+1 increment machine and U’ as the mirror machine tat will traverse ShL, -1 increments, and let us consider that the machines are a flipped switch distinct. In short one and the same incremental step machine can be ShR or ShL by +1 or -1 increments as necessary, just flip a mode control bit. (And yes, I am exploiting the fact that computational machines and systems are physical instantiations of clusters of operators and registers that store variables etc. An operator transforms one or more preimage functions or variables into image functions or variables.)
AK, we are deliberately not dealing with the Reals, but with integers and more broadly ordinals in the wider context of the surreals, to bring out the nature of finite stage successions in ordered sequences. Where the key point is that to claim an actually completed infinite past that arrives at the present, one implies — as opposed to, acknowledges — that there were stages that were once the present [think, U operator sitting there], but have now been surpassed as one stage gives rise to the next causally connected one in sequence, and to the point that now a typical such case w is infinitely remote in time or equivalently is in a transfinitely far LHS zone. You are forced to give up the claim of an infinite actual past, on the consequences of such a claim. A mathematical, conceptual transfinite is fine, a potential transfinite where succession can continue endlessly (but never attains transfinite scale) is fine, but an actually physically completed transfinite succession of stages is not fine at all; it is incoherent and impossible of being as core characteristics stand in mutual ruin: one cannot both span and not be able to span a transfinite real world succession in finite step successive and cumulative stages. KF
KF,
The two sets {0, 1, 2, …} and {…, -2, -1, 0} are not isomorphic as ordered sets, assuming we use the same ordering “less than” on both, if that’s what you’re saying.
When you state:
and
it suggests to me that you’re not appreciating the distinction between traversing {0, 1, 2, …} and {…, -2, -1, 0}, both from left to right.
Simply put, the fact that I cannot complete an ascent of an infinite ladder does not tell me I cannot complete a descent of the same ladder.
That’s why I’m asking you to remove completely any mention of traversing {0, 1, 2, …} from left to right.
(Edit: If your statement about climbing the ladder in your response to AhmedKiaan was just concerning infinite sets in general, and not meant to be connected to the issue of traversing an infinite past, then that’s fine of course. However in your (ShR, 1) illustration, it appears you are saying that because we cannot complete a “shift-right” traversal of {0, 1, 2, …}, therefore we cannot complete a shift-right traversal of {…, -2, -1, 0}, and this does not follow.)
No.
What we do have is an actual infinite collection of past moments, all finitely remote from the present, and for each natural number M, at least one of these moments (in fact infinitely many) occurred more than M years ago.
DS, again, I do know the difference between an endless potentially infinite climb from a start point and a claimed completion to date of an endless ACTUAL descent. You will see that I have taken careful effort to stress that w is not a start-point, the implication is that for any value of a past stage there is onward endlessness before that. So, much of your comment above misses the point. The issue at core is, given the causally linked stepwise sequential nature of time, a claimed infinite actual past must have in it endlessly remote points that then pose the onward need to traverse endlessness to get to now. Such cannot be traversed in finite stage steps. You have no basis for getting the U operator unit to now. As for an infinite succession of finitely remote past stages with finite steps, that is plain out ruin by incoherence in this case. What can be said is that what we can reach to will be finite but there is onward endlessness beyond. But this is not an abstract set, this is a claim about causally cumulative stages of time and there is no basis for accepting that endless past cumulative finite stages can reach now, stepwise. KF
PS: Perhaps I should not have said “isomorphic,” as that was likely to be misread. The positive and negative integers are mirrored around 0, effectively by multiplying through by -1, so they have the same basic “shape” and scale in the sense of cardinality. My use of a tape and fold over addresses this. Climbing down to 0 from an infinitely far zone is as far a span — endless — as trying to climb up to the same sort of remote zone.
KF,
Well, yes, I never assumed, nor did I imply, that w is a start point.
That remains to be demonstrated. You’ve simply asserted such a point “must” exist.
In a finite past, there must exist some natural number M such that all past moments occurred less than M years ago. For example, physical evidence indicates that all past moments occurred less than 15 billion years ago.
An infinite past is one that is not finite.
Under an infinite past, for each natural number M, there must exist at least one moment that occurred more than M years ago. That follows by simple logic, by negating the condition for “finite past”.
No “endlessly remote” points required.
Ds, the logic is simple. Time emerges stage by stage as present circumstances give rise to their immediate successors (including actions by agents who are self-moved). Successors go on to the next stage and of course earlier stages fade into the past. The claim of an infinite actual and beginningless past therefore implies that at any given stage s, there were already past stages that recede in a sequence beyond any finite count, i.e. endlessly. Factoring in time, on this view there have to have been actual once present stages that are now infinitely remote, endlessly remote but which stage by stage succeeded to the present. I simply labelled one such w. Alternatively, as duration is a count metric of some sort per a unit yardstick between stages in the chain, if EVERY past stage is only finitely remote, the past is not infinitely deep. For on this claim, there are no non-finite durations from stages of the actual past to the present. The problem with a stage w is of course that the endless intervening span cannot be traversed in finite stage cumulative successive steps. As is easily seen. We have no warrant to claim an actually infinite past. KF
KF,
Ok, let’s see.
Sounds fine.
Yes.
I would phrase it differently, but we might be in agreement here. At any stage s, the set of moments in the past of s is infinite. For any natural number M, there exists a point t in the past of s such that the time interval between t and s has length exceeding M years.
*Record scratch*
This is where we hit the non sequitur. The existence of these “endlessly remote” stages does not follow from the preceding statements.
No. This is contrary to the dictionary definition which you posted (voluntarily!). Do you now disagree with that definition?
For reference, the Merriam-Webster definition that you posted:
Once again, I feel like I’m shouting at the ocean waves.
Mathematics cannot be mapped against the real world. Mathematics provides a useful model of reality, but it is not congruent with reality.
What is it about Kurt Gödel’s incompleteness theorems that is not understood here?
Ok, let’s have some fun with a sequence that asymptotically approaches 1, namely 0.999…
– If n = 0.999…, does anyone object to 10n = 9.999… ?
– Does anyone object to 10n – n = 9 ?
– Does anyone object to 9n = 9 ?
– Does anyone object to n = 1 ?
– But we originally defined n = 0.999…
– Thus, we can triumphantly conclude that an infinite sequence asymptotically approaching 1 is actually a finite number, and that by projection, an infinite universe must therefore be finite.
Does anyone else think this is a stupid application of mathematics?
-Q
Querius,
It’s certainly another non sequitur.
You started with the equation x = 0.999…, and to understand its meaning, we must interpret the right-hand-side. The usual interpretation is that it’s the limit of a particular sequence, and equals 1. So there’s really no need for the next few lines.
In any case, 0.999… does equal 1.
It is not true that the infinite sequence itself is a finite number; rather its limit is.
How this could be construed to show that an infinite universe is finite escapes me.
DaveS,
The sequence 0.999… is an infinite series and is asymptotic to 1. The LIMIT of 0.999… is 1, but 0.999… is not the same as 1.
The logic here is actually analogous to yours.
We’re simply mapping a mathematical representation of an infinite series onto a presumably infinite space-time universe, performing some mathematical operations and coming up with the answer that since the infinite series is proved finite, thus the infinite space-time universe must also be finite.
So, do you agree that mapping this mathematical representation onto reality is ludicrous?
-Q
Querius,
Well, is it a sequence or a series? Those are two different things. Please tell me precisely what you mean by 0.999… .
DS, if there was an actual infinite past, there were actual once present stages that have been succeeded by stages to now that comprise the infinite span. One that is endlessly beyond any finite counting number. And, given the finite, cumulative stages in the chain an infinite number of such stages will yield an infinite temporal distance for some past stage, say w. To say there were infinitely many finite stages that are all finitely remote is incoherent. This is not a convergent series or sequence. Yes the sequence of partial sums so far as we can calculate will be finite but the very point is it goes on endlessly which is not finite. Where also, time accumulates causally forward step by step, posing the challenge of traversing an endless, infinite span in steps; which is a non-starter. Again, we have no warrant for claiming an infinite actual past for the physical-temporal world. KF
KF,
You’ve asserted this time and again.
You’ve also stated many times that the notion is “incoherent”, but have never backed that up with a proof. If you think you have one, why not write it up formally and post it here?
DS, my assertion is not the issue, the logic of an infinitely long chain of finite stage links is. KF
DaveS evaded the question @497 with
What would you call 0.9 + 0.09 + 0.009 + 0.0009 . . .?
-Q
Querius,
That’s an infinite series. If that’s what you mean in #496, then I would interpret the entire calculation to be about infinite series.
You have calculated:
which results in n = 1 + 0 + 0 + … (which you truncated to n = 1).
You could have also done it this way:
and we are back to n = 0.9 + 0.09 + 0.009 + …
or even:
So n = 1 + 0.1 − 0.09 − 0.009 −…
as well.
I honestly don’t see much connection between this example and our discussion of an infinite past.
DS, kindly explain to us how you get an infinite, forward, causally cumulative past arriving at the present without actually infinitely remote past times. Without, incoherence that for example amounts to there were unlimitedly many FINITELY remote past stages joined in a finite-stage chain — which comes down in crude terms to finite link length x infinite number of lengths –> infinite chain and thus infinite length:
. . . . o-o-o-o-o-o-o- . . . -o-o-o –> . . .
so also chain links at infinite temporal remove from now. If every past point is finitely remote the past as a while is finitely remote because duration is point to point not oh we have a vaguely ongoing sequence. KF
PS: I think the relevant point is that while 0.999 . . . as an infinite series [expressed in place value notation] converges to 1, step by step the finite partial sums are never 1.
KF,
You are the one making the claim that such a scenario is incoherent, so it’s on you to come up with a proof. Specifically, I would expect you to derive a contradiction starting with the premises I assume.
That’s what I want you to prove. Demonstrate the incoherence of this scenario by proving rigorously that it leads to contradiction.
I’m assuming that we have an actual infinite collection of past points, each of which is finitely many “shift-right” steps from the present. Have at it.
KF,
I think he’s (or she) is talking about the question of applying mathematical models to the real world, which is generally a valid concern. But it appears you and I agree to accept certain mathematical models [edited] as “good enough” for the present discussion. Anyone who disagrees will of course find none of this convincing.
daveS
It seems you are assuming that which needs to be demonstrated as coherent. You’re starting with a present that is the endpoint of a past, infinite succession. So, you already traversed an infinite to arrive at today, but you’re just including that traverse as part of your assumption.
Sure, that’s one way to do it, but the arguments against an infinite past argue against the point which you’re proposing as a first premise that must be accepted.
It’s like starting with the proposition that “the universe will necessarily exist for an infinite amount of time” and then trying to see if that could be incoherent in mathematical terms.
Of course it wouldn’t but that analysis would add nothing to our knowledge.
Silver Asiatic,
Well, I’m laying out my assumption for KF or anyone who else claims to be able to prove it’s incoherent
I’m not claiming I can demonstrate it is coherent.
DS, you have built a system on a clearly incoherent claim (shown many ways) and seem to be judging the straight by the crooked. An infinite chain of finite stage links will be infinite in extent; thus some links in the far zone will be infinitely removed from now. Which brings us to the problem of traversing an endless span step by step. Cannot be done. There is no warrant for blanket assuming an infinite already traversed past so being here needs no grounds. That begs the core question and tries to shift the burden of warrant. KF
KF,
Do you have a rigorous proof, where all the “endless”es have been translated?
daveS,
The “good enough” part isn’t. As in my simplistic analogy, there are many ways to go wrong.
Here’s another example.
Let’s say space-time has a spherical curve to it. How would we know? One way is to create a large circle and find the ratio of its circumference to its diameter. The diameter direction is always orthogonal to a tangent to the circle. Larger circles will have smaller values of Pi.
Let’s imagine an extremely large circle . . . in fact, so large that its circumference is infinite. Its diameter would also be infinite, but the ratio of the two infinities would be Pi. In other words, space-time is flat.
From there, we can extrapolate that any linear direction is an infinite circle and the ratio of its infinite orthogonal would always be Pi, which clearly produces a contradiction since the circumferential direction and the diametric direction are arbitrary and interchangeable.
Thus, a flat space-time cannot be infinite.
Am I willing to rest my case on those logical extrapolations? No.
And I’ve not even reminded you of the falsification of mapping a mathematical system on reality from Gödel’s incompleteness theorums.
-Q
Querius,
You don’t really mean dividing two infinities, do you? And getting a ratio of pi? That makes no sense. You must mean some limiting process, considering only circles of finite diameter, right?
If so, why would the limit of this ratio be exactly pi? What if space is hyperbolic? Why would the limit have to exist in the first place?
??
I can’t parse this. “any linear direction is an infinite circle”?
[Edit: I think I understand what you were saying—Any line is an “infinite circle”; one problem is, as I mentioned above, you can’t divide the circumference of an “infinite circle” by its diameter.]
Anyway, as I stated before, I do accept that mathematical models have limitations, if that’s what you’re getting at.
DS,
Pardon, but latching on to a descriptive word, “endless,” and rhetorically pretending it is meaningless or hopelessly vague does not answer to the core issue.
It seems to me you want to have your cake and eat it, claiming an infinite past then trying to suggest per some mathematical fast footwork that his is consistent with ALL past actual times/stages being finitely remote.
That actually already shows the incoherence in your claim. If a chain exists and ALL its links are finitely remote from here and now in steps, then the whole chain perforce must be only finitely remote from here and now in steps. The mathematics you have cited ends up in a fatal ambiguity between finite and infinite. I have long since argued that there is a flaw in the relevant chain of reasoning. Namely, yes, any particular value of counting number we can reach to in steps from 0 or express in some notation (e.g. palace value or scientific) will be finite in value, and any finite k can be exceeded by k+1, k+2 etc onwards without end. Thus, we see that what we can reach is finite but a material part of the structure of the set of counting numbers from 0 is their continuation in succession without end. That is, endlessly.
The infinity lies in that endlessness, not in the fact that we can bound and exceed any given finite value endlessly.
Indeed, I have repeatedly shown:
The term endless as extended to the space-time world, precisely describes that if there were an actually infinite chain in time and/or space, then there would be links in it:
that would be endlessly removed in steps from here and now.
But, that is a logical abstraction.
When we deal with the temporal world of stages or states and their cumulative causal consequences, advancing step by step in a chain, we see the problem surfacing.
To claim that there is an endless or infinite past implies that there were moments say w that were once the present but have been succeeded, step by finite stage step, until now has been reached. But that is not all, it is that the span of those successive intermediate steps has been of endless character, that is of cumulative magnitude Aleph-null (A-0 for convenience).
But as was seen yet again, a stepwise chain cannot span endlessness.
(By way of contrast a continuum is everywhere infinitely dense with points that are valid members. It can have ends but so soon as it has extension in space or in an abstract domain, it has cardinality c, continuum, which is of course in excess of A-0. This is why I have insisted all along on speaking in terms of the stepwise chain with finite stages. Of course, we have had another debate on the use of 1/m = M as a catapult between the very small and the very large. During which, I suggested on the sur-reals, that the hyper-reals were readily seen as representing a range of the transfinite beyond the first span of endlessness to lead to omega, so that we have two spans of endlessness between. Then using the catapult the other way, 1/M –> m, an infinitesimal. Just as a model, one that would in some way fit the way such are used. We then can get the continuum [0,1] and more significantly the span of continuum between (0,1), which then can be shifted by addition to fill in the naturals to get the positive reals, and mirrored to get the negative reals. Of course the sur-reals can be inserted as giving us a vast span of numbers great and small.)
Coming back, it should be clear what I am pointing to, again.
Going on, we have the problem of not only endless succession in finite stages, but of the problem of source. Something cometh not of non-being as it has no causal powers. Were there utter nothing, then such would forever obtain. Thus, if there is a world, something always was.
That root of reality cannot be temporal and successive, so we see that the concept of eternity and eternal, necessary being capable of causing a world such as we see makes perfect sense.
That this sounds a lot like the God of ethical theism (especially when we factor in evident fine tuning that sets up a world in which C-Chem aqueous medium cell based life is possible then actual based on information systems, and as we ponder the sort of moral governance behind rational responsible freedom needed to be able to credibly have a reason-based discussion) is a point to be respected and pondered, not sneered at.
KF
KF,
It’s not that it’s meaningless, but rather that I’ve never been able to get clear on what you mean by it. Is there any difference between “endless” and “infinite” (or perhaps “countably infinite”)? I haven’t been able to find one as yet. Presumably the term doesn’t absolutely defy translation into standard mathematical language. If there is no difference, why not use “infinite” instead? If there is a difference, cite an example of two sets/sequences/whatever, exactly one of which is endless but not infinite (or vice-versa).
Do you agree with the definition of “finite” I gave in #491? If so, then if the whole chain is finitely remote from the “present”, there must be some fixed natural number M such that every link in the chain is fewer than M steps from the present. For example, perhaps M = 100. Then the chain could have at most 100 links, counting the present as a “link”.
That’s what you are saying, correct? Unless there is a particular link infinitely many steps from the present, the chain actually has some (finite) natural number of links, has finite length, and in fact has two ends.
Even if a maximally powerful being attempted to create an infinite space and inside it, a chain with countably infinitely many links, each a finite number of steps from one end, it would fail.
Likewise, if this deity attempted to arrange an actual countably infinite collection of meter sticks end-to-end (say to the right of some initial meter stick), then the deity w