In most theologies, it is said that God created the material world. It is also said that God is (1) omnipresent, (2) omnipotent, and (3) omniscient; that God knows the future and the past. It is also said that God is an unchanging, eternal, immaterial being and the root of all existence.
Unless God is itself subject to linear time, the idea that God “created” anything is absurd. The idea of “creating” something necessarily implies that there was a time before that thing was created. From the “perspective” (I’ll explain the scare quotes below) of being everywhere and everywhen in one’s “now,” nothing is ever created. It always exists, has always existence, and will always exist, from God’s perspective, because all those things would exist to God as “now.”
“Matter” cannot exist if God is an immaterial being because God “is” everything from a theological perspective. There is no place or state “outside of God” or “unlike God,” because there is nowhere else to exist, and nothing else to comprise anything that is said to exist. If God is fundamentally immaterial being, then everything is fundamentally immaterial. Matter cannot exist in that situation.
All spiritual or religious doctrines extend from the perspective of assigning “not-God” characteristics and perspective to God. IOW, they are characterizations of God and the assigning of attributes to God that inimical to the logical ramifications of the attributes assigned to God by those same metaphysical perspectives.
The idea that God “chose” to create this specific world and limit the experiential capacity of all sentient beings to, basically, a single architecture out of infinite possibilities is absurd because God cannot have a “perspective.” “Perspective” requires a point of view. God cannot have a point of view.
Furthermore, God cannot “make a decision.” A decision requires context, organized sequential experiences, and a perspective – none of which God can logically experience, at least not from the state of “being God”
Even if we ignore all that, let’s say God instantaneously examines all possible experiential architectures “before” he “chooses” one – let’s say the Christian architecture – to limit sentient beings to. The problem with this is that a Godly “examination” of all possible experiential pathways would necessarily mean instantly knowing all possible experiences in every possible architecture – IOW, experiencing every possible life of every possible person in every possible architecture. That’s what omnipresence and omniscience would necessarily entail.
But God exists in a complete state of omniscient, eternal “now-ness, always experiencing all of those other possibilities as those beings in those other possible reality architectures. That’s what eternal omniscience and omnipresence necessarily means. God cannot then decide to “unexist” those other individual experiences in other architectures – they eternally exist as beings experiencing other architectures. Other realities. In the only place and as the only thing any such reality can ever exist – in the mind of God.
If the “perspective” of God is “all possible perspectives at the same time all the time,” then God (from the “God perspective) doesn’t have a perspective. If the nature of your being is “always fully experiencing all possible experiences all the time from every possible perspective,” no experiential decisions can be made; they are all fully being made eternally. There are no “others” to make experiential parameters for; all possible decisions from every individual perspective always fully exist eternally AS those individual beings in the mind of God – the only way anything ever exists as “real.”
Every possible experience, every possible experiential pathway in every possible experiential architecture always and eternally exists as real as any other. As individual consciousnesses, we can only be observational aspects of God, “exploring” an ocean of fully real possibilities, only limited by what is possible in the mind of God.
IOW, no four-sided triangles or 1+1=3 experiences or the like. But that’s the only kind of limitation to what is available to experience. As observational aspects of God, everything is ultimately “within” us. All possibilities. All other aspects conscious aspects of God – other people with individual perspectives, are in this sense “within” us.
Interesting Comment – maybe not too accurate.
Problems or issues:
1 – God is omniscient, I am not omniscient. How can I expect to understand all there is to understand? The writer places himself in a very lofty position.
2 – God is omnipotent. That means God can do anything not logically inconsistent with His divine nature. We may only have the power to recognize things around us, understanding some but not all of what He does and how He does it (see #1 above).
3 – Most theologies do not have God creating out of nothing. This is a unique characteristic of the Hebrew God. The unique position of Christianity (derived from Judaism) is that God is fully transcendent and fully imminent at all times. Most religions have divided the two – transcendence and immanence.
4 – There is a difference between God being in and supporting all things verses the pantheistic idea that all things are just part of God. One of the real mysteries is that God created other creatures to share His life with Him.
God Bless
GCS said
Not really. I offer a logical extrapolation from the assumed innate qualities of God. Your same objection can be made against any characterization of God. I posit that my characterization is more logically sound, given the assumptions. It’s no more “lofty” than any other characterization.
See response to #1.
Care to explain what those things mean and what the difference between the two perspectives are in relation to my post?
So, God lives a linear time existence where he creates things? Does ‘mystery” indicate an inability to logically track that from the given assumptions about God’s nature?
@GCS
It’s obvious the writer of this article is a believer of New Age B.S. and from his writings you can understand he really thinks is a kind of god .He already knows everything and he write to help other people understand “the reality”. :)) coincidentaly what snake was doing in the Garden of Eden.
These are legitimate and interesting questions, but extremely difficult to answer for the following reasons. Let’s start with a perspective:
1. From what we observe through scientific investigations, God’s creation is profoundly complex considering all the different codes in a cell, all the complex chemical cycles, the programmability of our genetics, and so on.
2. One of the most fundamental assumptions of science is that we have the capability to understand it entirely. For example, our current speculations involve additional dimensions and parallel worlds. Can you visualize a rotating hypercube with four linear dimensions? I’ve seen one generated by a computer program and could almost understand it. Furthermore, it’s extremely difficult to imagine either no time dimension or an infinite number of time dimensions.
3. Human IQs top out at around 200. Let’s say that God’s IQ is a million. If we have trouble understanding someone with an IQ of 200, understanding God will certainly be a problem for us.
God created space-time among other things. We can collapse a spatial dimension by geometric projection. Can we convert all time into space or vice versa?
God describes himself as I AM. Is it possible that God can move in temporal dimensions as easily as we move in spatial dimensions?
We can imagine and build finite state machines, which are not dependent on time. Can we imagine an infinite state machine also not dependent on time? That doesn’t mean that a state machine is not in motion. State machines can oscillate and form consistent patterns. Have you ever seen The Game of Life (cellular automata)? You can try it online here:
https://playgameoflife.com/
Before launching it, click a complex pattern not too near the initial “flier.” Notice that it’s rules-dependent, not time dependent.
God describes himself as changeless. This includes being changeless in justice, mercy, purpose, intention, character, and so on. But, the fact that there was an “In the beginning” indicates a difference between a non-existent universe to an existent universe.
This leaves us with many possibilities that are by definition incomplete and untrustworthy. Here are two possibilities:
a. God lives mostly in another set of space-time dimensions, but created a simulation reality that we exist in. Ancient Jewish thought includes the concept that God fills reality but withdrew somewhat to allow us to exist.
b. God always maintains consistency but changes “in conversation” that might result in things that are new but not requiring time. This would be like the time-independent state machine of the Game of Life.
-Q
as to:
Wow! Just Wow. I didn’t even read past that hubris parading as intellect.
First God is not a ‘itself’, He is a person, i.e. a ‘himself’. Secondly, God is ‘eternal’ and is above time.
And if you have a problem with the person of God creating time from his eternal perspective, then I guess God stepping into time, (i.e. subjecting himself to time), to become a human and conquer death, will completely blow your little finite mind out of the water.
Verse and music:
Querius,
Yes, there are things that would be extremely difficult to imagine, perhaps impossible from this perspective, but logic about it can be pursued. Assumed states of being have both logical limitations and consequences. I don’t see how certain theological claims in these various doctrines can be logically reconciled with these presumed states of being. They make sense from a limited perspective, linear-time framework, but from a “god” perspective as posited?
William J Murray @6,
My first question is whether you tried creating and running some random patterns using the rules based, finite-state machine known as the Game of Life? I’m not suggesting that God necessarily operates like a state machine, but I’m just suggesting that decisions and actions don’t necessarily require time.
So, for the sake of argument, let’s assume that God is revealed in the inspired text of the Bible and let’s do a partial inventory about statements made by or about God.
Let me suggest that this image for humans is of sovereign moral agents capable of real choices, including love, hate cooperation, rebellion, and meaningful dialog. Dialogism as expressed by M.M. Bakhtin is prominent in many parts of the Bible.
The word, “strive” in Hebrew can mean contend, but most often means to judge.
Nevertheless, God can communicate with humans on their level just as a human can communicate with a beloved pet. Now I once “tried” explaining quantum mechanics to my beloved tabby, but she had a short attention span and her math was pretty basic. She did like to be petted some, definitely liked treats, and she could tell me when she wanted to be let out.
Gödel’s Incompleteness Theorems demonstrate that not all propositions can be verified or falsified from any single self-consistent mathematical system. Deductive logic is one such system. Logic is not enough and even studying the logos of God, while helpful, is not sufficient.
To me, logic is like building a bridge of books off the end of a table. Without tangible supports, one cannot get very far due to the shifting center of mass. This is the problem I had with Spinoza. Supports would have to be additional evidence that’s not derived from logic alone.
-Q
God is also perfect, and I don’t see how it’s logically possible to change the mind of a perfect, omniscient being.
I happen to think the other omnipowers of God are more about what humans want to believe than what God has actually said. God is portrayed as a very emotional, quick to anger, and at times ruthless being in portions of the Old Testament. That doesn’t square well with the Omni characteristics.
What if there’s a dialog between God and another sovereign moral entity with free will such as a person?
Perhaps the omniscience of God is misunderstood. If we can collapse a wave function by observing it, why hasn’t God already collapsed it? Maybe because it’s because God chooses not to do so, leaving it as a wave function.
Maybe this is part of his granting us free will.
“There’s some good news and some bad news in physics. The good news is that we finally detected God. The bad news is that it turns out he’s a mathematician.”
-Q
@Rhampton7
Of course God is not emotional, but humans ARE… so sometime God communicate like a Leader ,not like Data from StarTrek because nobody would listen.
Secondly ,how do you judge someone is rutless? 🙂
If a swat team kill few terorists to save innocent people ,are they criminals or heroes? They killed. If you wouldn’t know the final objective you would judge they are killers. Do you know what objectives had God ? If not you are in hot water.
WJM,
I do think you have created an internally-consistent description of things here. But it seems to have been created in order to be resistant to falsification.
As far as theology, you do seem to press some assumptions on to God, however:
>“Matter” cannot exist if God is an immaterial being because God “is” everything from a theological perspective.
Not sure where that comes from. God may be over all, but you are saying he can’t can’t create anything outside of himself. I would say he can’t create anything he can’t control. But to use a definition of God that says he can’t create anything outside of himself seems like taking it too far.
>There is no place or state “outside of God”…
He cannot create a place outside of himself?
We take the things of theology, which are dumbed down for us. We try to reason with them, and end up in some strange places.
EDTA:
What are the logical ramifications of “omnipresence?” If I take an empty cylinder and fills it with a gas until that gas is omnipresent in the cylinder, what does that mean? Is there room for anything else? If there was, would the gas actually be omnipresent? If you pout a marble in there, would the gas still be omnipresent? Ultimately, “omnipresent” means god is everything.
If we examine this from the immaterial, mental reality perspective, what does “omnipresent” mean when space and matter don’t actually exist? Where is God “omnipresent?” In all information, throughout mind, and in all experience, and in consciousness itself. God is omnipresent and omniscient because God is everything.
Mental reality theory isn’t resistant to falsification; it’s impervious to it (at least mental reality as a general theory) because the basic premise is self-evidently true. Self-evidently true statements or concepts cannot be falsified.
Perhaps existence and reality are really very simple things to understand once you agree to stop denying the obvious and just apply some simple logic extending from self-evident truths.
Omnipresence is an over-simplification, a first approximation. I don’t take it to be a mathematical absolute that we can reason from, as you are attempting. We like single words for concepts; it makes us feel like we fully grasp something. (And it gives philosophers something to attempt to argue from.) But I don’t take God to be omnipresent in the literal, absolute, mathematical sense. He’s not present in hell, for instance.
He’s not absolutely omnibenevolent, because he doesn’t do every possible good thing that we think he should do. He doesn’t prevent pain, for instance. So his omnibenevolence is just a first approximation, a generalization. He is ultimately very good to those who put their trust in him.
If we allow omnipotence to include doing contradictory things, then he’s not that either.
We want to ascribe the highest, most good, things to him, so we use the above words as short-hand for what we can’t otherwise delineate. Any attempt by us to actually list or delineate the exceptions would be futile, because we lack the knowledge. But the concepts are not things we can/should reason from. They’re too vague and fluid.
EDTA @13,
Yep. Well said!
The Bible quotes God through a prophet, saying that we cannot understand God’s thoughts. It sounds like we’re being told that we shouldn’t try. We have as much chance of getting it right as a news reporter trying to explain first-year calculus.
Putting it another way, let’s assume that most people don’t understand the details of physical chemistry, algebraic geometry, and artificial intelligence filter schemes. What chance do they have of understanding a spirit being with an IQ of a million?
The anthropomorphisms are plentiful. “If God is old, he must have a long white beard.” “If God didn’t live on earth, what would he breathe?” “Is God limited by the size of the universe?” “Can God make a rock that he cannot lift?” “If God cannot lie, cheat, and steal then he can’t be omnipotent.” “God cannot be omnipresent because the stars and planets take up space.” And so on.
But we can have a relationship with God–but on God’s terms. A lot of “trust me” is involved as well.
-Q
WJM
First, appreciate all the good stuff you have written over the years.
“It always exists, has always existence, and will always exist, from God’s perspective, because all those things would exist to God as “now.””
I’m not sure about “perspective”, but I do agree they exist to God as now. As a point of clarification. Are you saying that if everything exists to God as “now” that means the actual state of affairs of my existence is not temporal and logically contradictory?
Vivid
Querius & EDTA:
Unfortunately, appeals to the incomprehensibility of god shut down all rational discussion about God. My argument is based on logical extrapolations stemming what were common theological perspectives that were represented to me in the past.
Vividbleau,
It means that from an objective, universal “perspective” there is no linear time; from the subjective perspective, sequential experiences are a necessary aspect of continuity of identity and free will.
I’m not sure what you mean by “logically contradictory” at the end of your question.
This universe is made entirely for manifestation of free will . All other elements are only props. Starting with all fine-tunned universal constants, carbon chemistry, life as a carrier of information(DNA) and as a carrier of consciousness (through which will choose to be with /without God. ) We have absolute free will to choose whatever we want only on a tiny tiny range . Like a warehouse (our body) have thousands of automatic switches ,breakers , relays our free will is only a small switch which God let us to activate or not .
Querius and EDTA,
From my perspective, most theological and spiritual perspectives are a lot like belief in materialism, which is why I often refer them as versions of materialism. Materialists must apply “incomprehensibility of the gaps” or offer promissory notes to sustain materialism, and also basically live in de facto denial of the same self-evident truth as most religious or spiritual doctrines.
Most theological doctrines, like materialism, live in de facto denial of this self-evident, inescapable truth: we live entirely within a mental reality. This is true whether or not an actual external physical world exists. The denial usually justifies itself by making an appeal to consequence. I’ve shown that appeal to be invalid because the consequence they appeal to is not a necessary ramification of mental reality theory; in fact, it’s actually a categorical error.
The “incomprehensibility” argument is also, as far as I can tell, a convenience that is used to patch up theological doctrines where needed. Apparently, God is comprehensible enough to support the doctrine, and incomprehensible to just the right degree, in just the right ways, in exactly the right places to allow the validity of the doctrine to survive where logic finds an issue.
It seems to me that these convenient incomprehensibles, whether utilized by materialists, spiritualists, or in theological frameworks, are really all rooted in the same thing: denial of the self-evident truth of the nature of existence. This essential denial cascades down into all sorts of issues that cannot be resolved except by invoking “incomprehensibility of the gaps” or by offering promissory notes.
I really don’t know what to make of WJMs recent extended foray into his ‘mental reality theory’. Some parts I really like, but some parts strike me as extremely absurd.
The main flaw, for me, in WJMs argument(s), seems to be that he is making gargantuan deductive inferences with minimal reference to empirical evidence (i.e. to inductive logic). As I noted previously elsewhere,
In sum, WJM is very much pronouncing on how the world should behave with insufficient attention being paid to how the world does in fact behave.
And as I have pointed out previously elsewhere, WJMs ‘mental reality theory’, and the primarily deductive form of logic that it takes, (if it would have been the primary form of reasoning that we would have used at the time), would have prevented the discovery of scientific theories which presuppose an objective existence that is outside of our inner subjective mental experience.
For instance, General Relativity, Special Relativity, and Quantum Electrodynamics all presuppose an objective existence that is separate from our inner subjective experience.
Thus, as far as empirical science itself is concerned, WJM mental reality theory would be highly antagonistic to what is already established science.
WJM, could claim that his subjective mental theory supersedes those objective theories, (and that could be true to a certain point), but it still would not, in a rigorous and scientific manner. unify those ‘objective’ theories that are already established outside of his mental reality theory.
Again, that is not a minor flaw in WJMs mental theory as far as empirical science is concerned.
On the other hand, Christianity deals with both the objective and subjective theories of science in a rigorous manner in order to ‘unify’ them.
As stated previously,,
Thus in conclusion, while there are parts of WJMs theory that I like, (and parts I find to extremely absurd), I simply find his theory to be incompatible with empirical science itself.
As I asked WJM before, if your mental theory would have been in place as the major form of reasoning that we used, (where there is no objective existence apart from our own inner subjective experience of it), would quantum electrodynamics have ever been discovered?
Verse:
BA77,
Mental reality theory is built using a combination of deductive and inductive reasoning. Science under mental reality theory would employ both. As I responded before, just because I originally made an argument for mental reality theory deductively from self-evident and necessary truths, doesn’t mean that’s the only form of logic that can be used to support it or to employ in scientific endeavors under that premise.
As to whether or not we would have discovered what science has discovered so far under external-material reality theory, who knows? That’s pure speculation. But, let’s assume that we would not have discovered quantum physics under MRT (for whatever reason.) So what? One theory often leads to another theory, which leads to another theory that characterizes things in an entirely different way and opens the door to kinds and arenas of research that weren’t even imaginable before.
WJM,
There are two distinct things going on here. First is our human propensity to generalize, and then re-specialize. This happens all the time. Someone is bitten by a venomous snake, so we generalize that all snakes might be venomous. We see another snake, and we apply the generalization to the new specific case. Such useful reasoning becomes troublesome in abstract areas like theology and morality: “Thou shalt not bear false witness.” This generalizes to “never tell a lie under any circumstances.” Then when Kant’s hypothetical murderer comes to the door seeking to kill your friend, a re-specializing of the dictum leads to “Well, I guess I have to tell him that my friend is indeed inside.” That’s fallacious, and it gets applied to all the omni-* characteristics of God, leading to the pseudo-problems that Querius points out above. We just need to recognize this fallacy, and avoid making it.
Second, is our finiteness relative to God. He knows things we don’t, therefore, he has to talk down to us and simplify everything if he is to convey anything to us at all. We get what are necessarily generalizations (and examples and metaphors, etc.), because that is all we can handle. Same thing as when a parent speaks to a young child, but magnified proportionally.
Our puny “doctrines” will always fall short of fully capturing God. But if we can avoid fallacious reasoning and presuming too much, then we won’t have as many doctrines that need “patching”.
WJM,
I had earlier asked for some evidence for MRT. Let me be a little more specific. Can you access any information, and provide it to us, such that we could, say, a year from now, verify by other means?
A few examples:
– Give us additional digits of precision of one or more “physical” constants–beyond what we know them to be today.
– Give us the 10^14 through 10^14 + 33 decimal places of pi.
– Give us the closing values of the S&P 500 stock index on the last day of each month, for year 2021.
A hundred bits of information should suffice.
Of course, being unable to do this does not disprove MRT. But it would be spectacular if you could do it.
[“A wicked and adulterous generation looks for a sign, but none will be given it except the sign of Jonah.” It’s Sunday, and I couldn’t resist!]
EDTA @ 21: You express a theological perspective I don’t share.
EDTA @ 22: Did I give you the impression that the algorithmic expression process was short in terms of linear time?
William J Murray,
Sorry, I’m with EDTA and Bornagain77 on this one.
As I said before, a fundamental assumption of science is that we can comprehend it, and we’ve done a reasonable job at successive approximations overall. However, there are indeed some people who can’t and others are brilliant and can comprehend more.
God, by definition, is far more brilliant than humans. So, does it seem plausible to you that we should assume that we’re able to comprehend God using the tools of logic, a branch of mathematics?
If God encompasses all facets truth, would you deny Gödel’s Incompleteness Theorems?
https://plato.stanford.edu/entries/goedel-incompleteness/
-Q
Querius,
No need to apologize! I don’t offer my thoughts in the hope that the are agreed with. I enjoy the challenge.
Why is God “by definition” far more brilliant than humans? Do you mean “intelligent?”
I’m really not in the habit of eliminating possibilities due to assumptions. I’m more of a “increase possibilities by getting rid of assumptions that limit or deny possibilities” kind of guy.
There’s a difference between what is knowable and what is provable.
William J Murray,
Ok, I’m glad to hear that.
By intelligence, I mean the God’s capability of designing and programming things compared to ours.
Let’s say you went to a conference and listen to a presentation by a scientist who found a way to produce a variety of living cells through direct synthesis of DNA and epigenetic programming by use of an innovative mathematical system. This scientist was able to create the multitude of interlocking chemical cycles not limited to only those found in nature, intracellular transport, defense mechanisms, metabolism, reproduction, electromagnetic communication, and the programming necessary for interacting with the environment. In addition, the scientist also had another session on creating self-modifying code among the two dozen or codes so used within cells, including DNA.
Would you say that scientist was “intelligent”?
Would you say that you could use your capabilities of logic to independently arrive at the same understanding and results that the scientist demonstrated?
If you asked the scientist about the mathematics he or she invented for driving the algorithms that were used to generate the desired outcomes, do you think you would be able to understand the scientist’s explanation?
Would you be grateful to the scientist for an abstracted outline of the general processes employed and perhaps some guidance on your own research?
Can you give me any examples of what’s knowable and yet not provable through deductive, inductive, and Bayesian logic? I believe there are some.
Consider I Corinthians 1:20-25 (NASB)
From my perspective, I also don’t like the hand-waving, sloppy thinking, and inconsistencies in many theological positions. I’m also an enthusiastic challenger of (usually unstated) assumptions. I also enjoy hamburgers barbecued from sacred cows. But I try to remind myself that my own perspectives of God are going to be limited, incomplete, and sometimes misleading. I don’t make everything a “mystery of the church,” but I pray and probe. I research different translations of the Bible, including Hebrew versions and the Greek Septuagint. I even have a Bible published from the extant fragments of the Dead Sea Scrolls. But there are some things I still don’t understand and leave them to be understood or revealed to me at a later time.
-Q
WJM,
>Did I give you the impression that the algorithmic expression process was short in terms of linear time?
I got (perhaps erroneously) the impression that MRT might provide easier access to information that would be effectively inaccessible under other views. I think that came from a different thread where you answered a question of mine about how I might access new/different things via MRT.
I don’t fully get MRT, but am trying to probe around the edges of it here. Thanks for all your replies.
WJM, you don’t seem to get it.
In deductive logic, you are assuming that your premises are unquestionably true and are then reasoning in a top down fashion to reach your conclusions. Some conclusions which I find to extremely bizarre, even absurd. As kf would state, (paraphrase) your conclusion demands warrant.
As I see it, either one or more of your premises is false and/or flawed, and you are therefore making a faulty deductive logical step following from that flawed premise. Or else you are ‘overreaching’ your premises.
You could remedy that situation by proposing and/or predicting a ‘novel’ empirical test and having your bizarre conclusion(s) substantiated. In fact, that would go a long way towards you rigorously establishing your theory as being scientifically true. Much like Einstein rigorously established his ‘objective’ relativity theory as being true by having it empirically established via a solar eclipse, i.e. validating his ‘bizarre’ conclusion of space-time curvature.
That is one available avenue for you where inductive logic could bring a ‘scientific’ resolution to what I see as, almost, the purely deductive form of reasoning you are using right now to reach (some) conclusions that I find to be rather bizarre, even extremely absurd..
Whereas, on the other hand, in my claim that Jesus Christ’s resurrection from the dead provides a very plausible resolution to the much sought after ‘theory of everything’, I am primarily reasoning in a ‘bottom up’ inductive fashion, from the empirical evidence itself. Indeed, I reasoning ‘up’ to my conclusion from the most powerful theories we have in science, i.e. Quantum Mechanics and Relativity
As stated previously, inductive reasoning is the primary form reasoning that Francis Bacon, (a devout Christian), championed and which lays at the foundation of modern science itself in Medieval Christian Europe,, A ‘bottom up’ form of reasoning which represented a major departure from the deductive form of reasoning that the ancient Greeks used (and which is the deductive form of reasoning that present day Darwinists and theoretical physicists have, apparently, ‘regressed’ back into).
You claim that your premises are self evidently true (i.e. they are ‘unquestionable’). I’m sure you feel that way, and I am also sure that many Darwinists and theoretical physicists today are also absolutely sure that their premises are self evidently true (i.e. they are unquestionable).
That simply is not the way inductive reasoning works. In inductive reasoning all premises, no matter how self-evidently true they may seem to be, are open to question, and it is only by bringing a substantial amount of empirical evidence to bear, not to mention surviving vigorous attempts to empirically falsify your premises and/or theory, that your theory and premises can be said to be on solid scientific footing.
I’ve seen (practically) none of that ‘bottom up’ form of reasoning in your arguments in order to establish your premises as being on solid scientific footing.
Indeed, as mentioned previously, it seems that your theory simply ignores, or even denies the existence of, all ‘objective’ scientific that have thus far been established as being true. i.e. special relativity, general relativity and quantum electrodynamics.
This is not a minor problem for you and for you to say “So what?” in response to me pointing that fact out to you just will not cut it. You need to be able to successfully incorporate and/or explain those theories in your ‘new’ theory.
I’ve seen zero attempt from you to try to do that. Again, it seems your theory simply denies the existence of those ‘objective’ theories, or at least renders those theories, for all intents and purposes, inconsequential.
Of related note to inductive reasoning, and to repeat my argument for Jesus Christ providing a very plausible resolution to the much sought after ‘theory of everything’, i.e. a very plausible reconciliation between quantum theory and General Relativity.
Verse:
Querius,
We have two different premises of God then. I would say that God, being everything (omnipresence), is all-knowing . I don’t think God (or any individual) “created” anything because all things eternally exist.
I think “intelligence” is like “matter.” It appears to be a quality of something from a certain perspective, in certain experiential sequences, but like “Matter” is just an arrangement of thought experiences generated by attention. For example, would you consider an autistic savant super intelligent? Or, is what they do really just their capacity to more immediately access certain kinds of information, like a computer retrieving information off a hard drive?
Self evident truths are examples of knowledge that cannot be reasoned into because they are often the foundation from which reasoning springs. Like the principles of identity and non-contradiction. I cannot prove “I exist,” but I experience it directly. It is a self-evident truth. I cannot prove I have free will, but I know I do.
EDTA said:
I have had my attention focused on certain things for decades now. I think I first came up with MRT on my own maybe a couple of years ago? Before that I still thought in terms of an external world and had basically a mystical or spiritual perspective on how the external world was connected to the internal
This particular algorithmic model is something I came up with about a month ago. One of my focuses of attention now for decades has been on having the most efficient and practical model of reality I could that provided clear methodology towards acquiring my goal. My goal can be summed up as “enjoying my existence as much as possible.”
So, under the premise of my model, the information that the algorithm should be attaching itself to, along with current other identity structures, and processing into my experience, is “efficiently productive models that provide me with best operational capacity to increase my enjoyment life,” as well as just stuff I enjoy along with other features of my identity information.
As I said, this particular model occurred to me about a month ago – if that long. It actually just came pouring through as I was writing something else. I don’t know if you do much writing or perhaps some other creative venture, but I can tell you that for me, very often when I am thinking about something or writing something, what comes through is a revelation to me. I’m sitting there thinking, “where the heck did THAT come from? That’s friggin’ awesome.” It’s like I’m transcribing something someone else is dictating to me.
I can say with completely honesty that, from my perspective, this perspective works for me. The algorithmic model immediately increased my enjoyment of life (which I didn’t even think possible at the time) just because the model utterly released me from any sense that I had to try to micro-manage the process, or even trouble-shoot it by trying to figure out what I needed to do to “help” the “experience manifestation” process out. The algorithm automatically does all that for me.
MRT and it’s predecessors changed my life and generated “miraculous” occurrences that were utterly unimaginable to me.
That’s not to say that other belief systems and views don’t generate the miraculous; of course they do and they have their own explanations for those things that fit into their views. MRT is just not compatible with most experiential architectures. That’s another reason I’m not trying to convince anyone of it.
(EDTA and Querius, something in this near the bottom I think you’ll be very interested in)
BA77 said:
That’s like saying I’m assuming a self-evidently true statement about existence “is” true. You’re right. I am assuming all self-evidently true statements are true. I didn’t always realize the self-evidently true value of the statement “We live in a mental reality,” but once you understand what that statement means, it is irrefutably true. You know this.
Is it wrong to base your theory of “how experiential reality works” on a self-evidently true statement about the nature of experiential reality? Of course not. The rest of the theory is fleshed out using deductive and inductive reasoning.
When you can give me an example of any experience that doesn’t occur in mind, or any line of thought or theory that doesn’t begin, process and end entirely in mind, then feel free to do so and demonstrate that my premise is not self-evidently true. All evidence and reasoning about evidence, models of reality, experimentation and research occurs entirely within mind. You can no more refute that than you can refute “I exist” or “1+1=2” or “there are no 4-sided triangles.
(EDTA & Querius, I think you guys will find this of particular interest because it’s a real-time example of what is, under my model, the result of years of attention to the kind of information I talked about in the previous comment. The following just occurred to me and I was completely shocked at the sheer elegance of it. I never thought of it before)
Yes, you can say “Maybe 4 sided triangles exist.” Or you can say “maybe I don’t exist.” Just as you can say “Maybe something outside of mind exists.” But that’s all you can ever do – say a string of words that represent, essentially, a nonsensical idea. You cannot actually imagine a state that represents nonsensical statements. You literally cannot imagine not existing. You can’t imagine a state of “nothingness.” You cannot imagine a 4-sided triangle. These are the true tests of something that is self-evidently true; a state representing the “non-trueness” of the statement cannot even be imagined.
So here’s the elegant part: You cannot even imagine a world that exists outside of mind. No one can. It’s literally impossible.
WJM
I thought of a few things which you may want to consider.
1 – We often have the wrong perspective when we consider God. For example: we experience love and consider that God’s love is just a greater version of our love. The reality is that our love is a very small reflection of God’s love which is totally beyond us. God’s love in its essence is far beyond our imagination or understanding. The same can be said of our reasoning powers compared to God. God’s reasoning is far beyond anything we can imagine or understand. The most you can conclude is that by your powers and abilities you think something is the case.
2 – You appear to be stuck in the either/or conundrum. While it works for many of the ordinary things we deal with, it is not necessarily the case with God. Errors, especially in theology, often occur because we focus on a truth (or partial truth) at the expense of the whole truth. Duality is a common human way of thinking and it works well for many things in the world we deal with. It is not the same with God. God is both fully man and fully human, fully transcendent and fully human, fully just and fully merciful. He is these things at all times in every way. For us to process them we have to separate them, often treating them as opposites.
3 – In dealing with theological issues we have to have faith. Reason alone never can do it. God has deliberately drawn a fine line. He has given us enough evidence so that if we are seeking, we will find Him in everything. If we are not seeking there is not enough evidence to force us to find Him. Why? Because God wants us to make a free choice to find Him, He will not force Himself on us. He wants us to freely choose to Love Him.
The interesting result of this is that both sides honestly say that the evidence supports their own case. It is also difficult to understand each other when the evidence is so clear to us. If we understand this then we will have more patience with each other.
However, only one side is correct. You have to expand your world to include the possibility of God to find out.
Good luck in your search.
God Bless.
WJM states
Actually it is quite easy to imagine a world that exists outside on my mind. In fact, as pointed out previously, several of our most powerful theories in science assume the objective existence of a reality outside of my, or any other, human mind.
As Mr. Arrington pointed out, your theory “appears on the face of it to entail solipsism.”
The assumption that reality depends on my, or any other human mind, (i.e. solipsism), is simply absurd. As Alvin Plantinga pointed out, “We take good care of the professor because when he goes we all go.”
Now it is another question entirely if the reality that exists outside of my, or any other human mind, is ultimately dependent on the Mind of God, and is where ‘mental reality theory’ would gain far more traction.
In fact, I’ve previously argued for God from consciousness as such:
And I used these following eight lines of empirical evidence to inductively support my preceding deductive argument and to thus put my deductive argument for God from consciousness on solid scientific footing.
Each of those lines of evidence are very interesting to look at in its own right, but to further clarify that it must be the Mind of God that precedes ‘material’ reality, let’s specifically look at the quantum wave function itself.
Prior to collapse, the quantum wave function of a particle is mathematically defined as being in an infinite dimensional state,,,
Moreover, the particle, while it is in its infinite dimensional state, also takes an infinite amount of information to describe properly.
Thus, ‘whatever’ is collapsing the wave function from its infinite dimensional and infinite information state, to its finite state of one or zero, must necessarily possess the attributes omnipresence and omniscience.
Theists just so happen to have a candidate that fulfills those attributes of omnipresence and omniscience:
Man, or more specifically, the finite mind of man, certainly does not have the capacity within itself to collapse the ‘infinite’ wave function. As God asked Job:
And even though ‘finite’ man is certainly not collapsing the wave function, man, via his free will, never-the-less plays a integral role in deciding what type of reality, ultimately, gets presented to him by God.
As Anton Zeilinger stated, “what we perceive as reality now depends on our earlier decision what to measure. Which is a very, very, deep message about the nature of reality and our part in the whole universe. We are not just passive observers.”
As well, with contextuality we find that, “In the quantum world, the property that you discover through measurement is not the property that the system actually had prior to the measurement process. What you observe necessarily depends on how you carried out the observation”
And as Steven Weinberg, an atheist, stated, “In quantum mechanics these probabilities do not exist until people choose what to measure,,, Unlike the case of classical physics, a choice must be made,,,”
In fact Weinberg, again an atheist, rejected the instrumentalist approach precisely because, via their free will, “humans are brought into the laws of nature at the most fundamental level” and because it undermined the Darwinian worldview from within. Yet, regardless of how he and other atheists may prefer the world to behave, quantum mechanics itself could care less how atheists prefer the world to behave.
Although there have been several major loopholes in quantum mechanics over the past several decades that atheists have tried to appeal to in order to try to avoid the ‘spooky’ Theistic implications of quantum mechanics, over the past several years each of those major loopholes have each been closed one by one. The last major loophole that was left to be closed was the “setting independence” and/or the ‘free-will’ loophole:
And now Anton Zeilinger and company have recently, as of 2018, pushed the ‘free will loophole’ back to 7.8 billion years ago, thereby firmly establishing the ‘common sense’ fact that the free will choices of the experimenter in the quantum experiments are truly free and are not determined by any possible causal influences from the past for at least the last 7.8 billion years, and that the experimenters themselves are therefore shown to be truly free to choose whatever measurement settings in the experiments that he or she may so desire to choose so as to ‘logically’ probe whatever aspect of reality that he or she may be interested in probing.
Thus regardless of how Steven Weinberg and other atheists may prefer the universe to behave, with the closing of the last remaining free will loophole in quantum mechanics, “humans are indeed brought into the laws of nature at the most fundamental level”, and thus these recent findings from quantum mechanics directly undermine, as Weinberg himself conceded, the “vision that became possible after Darwin, of a world governed by impersonal physical laws that control human behavior along with everything else.”
Moreover, although free will is often thought of as allowing someone to choose between a veritable infinity of options,,,
,,, in a theistic view of reality that veritable infinity of options all boils down to just two options. Eternal life with God, or Eternal life without God.
C.S. Lewis stated the situation for people as such: “There are only two kinds of people in the end: those who say to God, “Thy will be done,” and those to whom God says, in the end, “Thy will be done.” All that are in Hell, choose it. Without that self-choice there could be no Hell.”
On top of that, in order to support the physical, i.e. objective, reality of heaven and hell, I can appeal directly to two of our most powerful and precisely tested theories ever in the history of science. Special Relativity and General Relativity respectfully.
As I explained in the following post, with General Relativity we find an ‘infinitely destructive’ eternity associated with it. And with Special Relativity we find an extremely orderly eternity associated with it:
The implications for individual humans, to put it mildly, are fairly drastic. We, with either our acceptance or rejection of God and what He has done for us through Jesus Christ on the cross, are choosing between eternal life with God or eternal death separated from God:
I can only plead with any atheists who may be reading this for them to seriously reconsider their stubborn refusal to ever accept God into their lives and to now accept God, even eternal life with God, rather than choosing to reject God and thus choosing eternal life separated from God.
Video and Verses:
Assuming isn’t imagining. I can proceed with all sorts of theories and ideas that stem from the idea that one plus one equals “anything I say.” I can proceed with all sorts of ideas that stem from the idea that triangles can have any number of sides. But you cannot actually imagine those things. You can imagine things exterior to your physical body, but not external of your mind.
I’ve explained repeatedly how it does not.
WJM- Which bible verses are you using when you say God is Omni………
William says, “Assuming isn’t imagining. I can proceed with all sorts of theories and ideas that stem from the idea that one plus one equals “anything I say.” I can proceed with all sorts of ideas that stem from the idea that triangles can have any number of sides.”
I don’t think that is true. 1 + 1 = 2 and triangles have three sides are based on definitions and they can only be not true if you change those definitions. Saying that triangles can have any number of sides is to negate what the word “triangle” means: for instance, it now means “polygon”. I don’t think those are useful examples.
Viala Lee: Triangle doesn’t by definition mean “three sides.” 1+1=2 is not true “by definition.”
WJM,
I am having focus elsewhere so I cannot really give a lot here.
However a couple of points caught my eye.
1: “Incomprehensible” — immensus
Note Latin text: “Immensus Pater, immensus Filius, immensus [et] Spiritus Sanctus.” That is, beyond measure, infinite beyond bounds. That is the sense of “incomprehensible.”
A classic text on a facet of this is:
Here of course there is a bounded rationality on our part so we can have limited but accurate knowledge of God as he shows himself to us in creation, conscience, the gift of rational responsible morally governed mind and revelation through authentic voices, with record (scripture).
This of course ties to concepts from philosophical theology on the idea of God: inherently good, utterly wise creator, necessary and maximally great being. In short, the concepts in Christian theology are not arbitrary lists of notions but fit into an integrated understanding of what God will be like.
2: Omnipresence
The concept is that God is the active, aware, operating root of every where and every when who upholds all things and in whom all things are held together as a coherent cosmos, so he is not displaced from a locale by say there is a stone or a proton there.
A text or two:
Much more can be drawn out.
KF
Viola Lee: I said:
I’m wrong about the first. What a triangle is, is true by definition. However, 1+1=2 is not true by definition.
The definition of triangle is a polygon with three sides. You can’t imagine a triangle having more than three sides without changing the meaning of the words.
Also, 1 + 1 = 2 is true “by definition” in a more complicated way: a combination of definitions ( the name for the unit, the name for its successor, and the definition of the operation of addition) plus a postulate about successors, but you couldn’t imagine 1 + 1 = something other than 2 without changing some of those meanings.
Perhaps you can explain more what you mean?
Your post about triangles crossed with mine, so we’ve cleared that up.
I explain more about 1 + 1 = 2 above. It can only be not true, or imagined to be different, if you change the meaning of at least one of its constituent parts, which are either definitions or postulates.
One could say that 1 + 1 = 2 is a theorem, proven by a chain of reasoning from a beginning foundation of definitions and axioms (or postulates). But again, it can be something other than it is if you change some of meanings of the constituent parts.
William J Murray,
MRT is precious to you and I won’t denigrate your experience. I had to look up MRT. I logically deduced that you weren’t referring to Mass Rapid Transit. Although mass rapid transit has its strong points, here’s what I think is a better candidate based on your context:
Is this correct and what you’re referencing?
I’m always alerted when someone questions the definition of commonly used words such as “intelligent” and “God.” There’s only one definition that counts, the God who actually exists. Since you enjoy logic, let’s try this out, starting with your premise:
• All things exist eternally.
• Eternally means the past and future are infinite.
• To get to our present point in time, the universe had to traverse an infinite amount of time.
• One cannot traverse something that’s infinite, and besides that, entropy is always increasing, which means that after an infinite amount of time, the universe arrives at something called “heat death.”
• We’re not at heat death, therefore all things do not exist eternally.
This is similar to my relationship with God, my maker and through Jesus, my savior. I cannot prove it but I experience inner peace, love, and joy directly through the Holy Spirit.
Much of our relationship to God depends on perspectives and assumptions. Many of these are imperfect and some are completely wrong.
The terms omni- are not found in the Bible and I don’t think they’re helpful. For example, when Christians pray, “Thy will be done on earth as it is in heaven,” that seems to indicate that God’s will is not currently being done on earth and that God is not omnipotent—or chooses not to be. Furthermore, the free will that we believe we have might often mean that it’s at odds with God’s will.
Again, I’m very cautious about drawing many conclusions about God based on logic alone. I rely on the things that God revealed about himself through the Holy Scriptures. I do operate with reasoning, common sense, emotion, and logic in life, but I recognize the limits to these gifts. For example, what I think might be good for me or someone else might not be good at all.
-Q
Viola Lee,
The study of non-euclidean geometry produces many logical but surprising results.
Similarly, both in Chemistry and sandwich making, 1+1 might not necessarily equal 2, depending on the chemical reaction or the sandwich:
1 slice of rye bread + 1 large juicy slice of pastrami = 1 pastrami sandwich. 1+1 = 1 (lettuce, mayo, and horseradish are optional). Now I’m hungry.
In my high school Physics class, I saw a film of a demonstration that had a profound effect on me in many ways.
The teacher showed a film of four serious looking men in suits sitting at a square table, one on each side. The table and the chairs were all made of wood. One of the men produced a wooden ball from his jacket and rolled the ball toward the man opposite him. However, the ball seemed to curve and arrived at the man at his right instead. That man also rolled the ball and had similarly puzzling results. Then the teacher stopped the film.
“Why did the ball change direction?” he mischievously asked the class.
We all had different theories involving internal magnets, grooves, wires, compressed air, table tilt, motors, gyroscopes, and so on. Very resourceful, but the physics teacher smiled and shook his head. None of the above.
“Why did the wooden ball change direction?” we demanded.
“It didn’t,” he replied. He turned the film back on and we saw the camera view zoom out. The table, chairs, and men where on a large rotating platform. We could then see that the ball rolled straight, but everything rotated underneath it. Perspective (frame of reference) is everything.
Same with God.
-Q
In responce to,,
,,, WJM states,
Huh??? What in the world are you going on about??? Imagining a reality that exists outside my mind is certainly not a logical contradiction as you are trying to imply. Whereas claiming that reality is dependent on my, or any other, human mind clearly entails a large measure of solipsism.
If you are merely claiming that reality would not exist for us personally if we were not first conscious of it, that is another claim entirely than what you are currently trying to claim. i.e. “You cannot even imagine a world that exists outside of mind. No one can. It’s literally impossible.”
That I can imagine a world that exists outside of my mind is easy to demonstrate.
As the joke that I referenced from Planting makes clear, ““We take good care of the professor because when he goes we all go”, the professor’s mind is gone and yet the reality that the professor existed in still persists.
Thus, clearly, I can easily imagine a reality that is not dependent on my, or on any other, human mind for its existence.
It ain’t rocket science. And it certainly is NOT a logical contradiction as you are falsely trying to imply.
And as I stated previously, it is another question entirely if the reality that exists outside of my, or any other human mind, is ultimately dependent on the Mind of God for its existence, and is where ‘mental reality theory’ could gain far more traction.
In fact, I believe this line of thought was first elucidated in the ‘Idealism’ of George Berkeley, an 18th-century Anglo-Irish bishop
Perhaps ‘idealism’ is what you are really trying to get at with your ‘mental reality theory’ WJM?
WilliamJMurray
Fascinating stuff. So would you consider the following to be true or false or undecided:
The Pythagorean theorem
Fermat’s Last Theorem
The Axiom of Choice
The Continuum hypothesis
The Four Colour Theorem
Goldbach’s Conjecture
Is there a difference between those statements regarding their truth, i.e. do they share a common burden of proof?
If any of your answers to their truthfulness are NO or UNABLE TO DECIDE then what would it take for those statements to be determined as true or false or are some always indeterminate? And how do you distinguish between them?
Hi Q, re 43
Actually, so does Euclidean geometry! One of my favorites is Morley’s theorem: the three angle trisectors of any triangle intersect to form an equilateral triangle.
I also think the whole story of the non-Euclidean geometries is an instructive example about the nature of math.
You write,
There’s an important difference between applied and pure math. The fact that one drop of mercury added to one drop on mercury does not equal two drops of mercury does not negate the fact that 1 + 1 = 2. It just shows that some of the math concepts in 1 + 1 = 2 don’t apply to that particular situation. Same with your example: the objects represented by “1” and the operation represent by “+” have to be accurately modelled in the real world for 1 + 1 = 2 to be applicable.
And last, your example about the rotating table is neat.
Q, Coriolis forces and similar virtual forces tied to non inertial frames of reference are always interesting. And yes, one of Einstein’s points is that physical laws take their simplest forms in IFR’s. KF
WJM,
I too write, but not professionally (yet). Ideas do sometimes surprise me, but after I have written them down and let them marinate for a few months, I am reminded from other reading that I do, that my ideas were more like syntheses of many things learned before. (Then I have to quickly write down where the ideas came from, so I don’t look like a thief later on.)
I’m almost always able to eventually trace my “realizations” back to their origins, so any surprise I feel at first often fades as I realize where I got the seeds of the idea.
Viola Lee,
Cool—I didn’t know that! And from there, it’s equilateral triangles all the way down.
Yes, indeed.
You choose the math that seems applicable. You admire the simplicity, symmetry, and purity of the solution. Then some vandal has to come along and measure an experiment at a higher precision resulting in a small but reproducible deviation . . .
By analogy, if physicists are driven mad by such complications, how much easier is it to be misled by theological complications?
As one of my chemistry profs once warned her students (paraphrasing H.L. Mencken), “For every problem, there’s a solution. Neat. Plausible. And wrong.”
Same with theology.
-Q
I haven’t been involved in the theology discussion, but I imagine you’re right about that.
And speaking of “equilateral triangles all the way down”, are you familiar with Sierpinski’s Triangle? I read about this in my Chaos and Fractals book. See here if your interested.
And I think I remember it was you that mentioned Conway’s Life simulation. I just read this on the Wikipedia article:
I have no idea what this means, though. 🙂
Hi Querius
At #42, you posted the following to William, but I hope you won’t mind if I respond, as infinity is one of the subjects I’m interested in.
I believe you were offering this as a “proof by contradiction” of William’s claim that all things exist eternally. I am not following William’s mental reality theory, so my response is not really in regards to his ideas, nor to your argument as a whole, but rather to the ideas about infinity in sentences 2, 3, and the first part of 4.
You wrote,
First, I’d like to separate two topics: the physical universe we live in and the broader sense of referring to the existence of all of reality, assuming it is eternal, and thus represented by the positive and negative integers on a number line.
I think the consensus view is that our physical universe had a beginning of unknown origin about 15 billion years ago, and due to entropy will suffer a heat death sometime in the future. It had a beginning, and is thus not eternal. This is not the part that interests me, so I’ll limit my remarks to the parts about the nature of infinity.
Let’s assume reality of some sort is eternal, so that the past and the future are infinite, as stated in sentence 2.
I think sentence 3 is wrong. It seems to be implying that having an “infinite past” means that there is some point that is an infinite distance from now, but that is not true. Infinity is not a place on the number line: it is a shorthand way of saying that for any point there is a successor (as you move forward) and a predecessor (as you move backwards). Saying there is an infinite past is saying that there is no “first point” in time, because any candidate for the first point has a predecessor, so the candidate is not the first point. So, by proof by contradiction, there is no first point. Q.E.D.
That’s what an infinite past means. It means that there is no first point in the past. And yet, since all points are a finite amount of time, there is no “infinite distance” to traverse.
It makes no sense to say time “started at infinity”, because that implies it started an infinite amount of time from now, and there is no place that was an infinite time from now.
I know this is hard to wrap one’s head around, because infinity is such a slippery concept, but I think I’m right about this. YMMV
Viola Lee & Querius,
Pardon my interrupting, but this argument about infinity is very intriguing to me. I think I get the part about infinite time being such that, for any point in either the forward or backward direction, there is always another point farther in that direction. So can the argument be restated as the following:
1. In our experience, time is a finite succession of moments/increments/etc.
2. Adding more finite increments still results in a finite total.
3. Therefore, the infinite (as defined above) cannot be reached in the future direction.
4. Correspondingly, the infinite past was not ever reached.
Now, one might say, “Well, don’t stop the process of adding finite increments. Let that go on indefinitely. Then you DO reach the definition of infinite.” But that presumes that infinity can be reached, which is what the argument is about. So we can’t say that, or we’re guilty of reasoning circularly.
Does that work?
Yes, I agree with your 1 through 4. You can proceed indefinitely, but you never “reach infinity” because infinity is not a “place”. All you can every reach is just another moment just a little bit farther in the past.
Viola Lee and EDTA,
Hmmm. I’m really not that familiar with the mathematics of infinities such as Cantor’s and serious mathematicians would have my thoughts on the subject for a light breakfast . . .
First of all, some people assert that infinities exist only as mathematical concepts and not in reality. Also included in mathematical space are perfect spheres and exact integer lengths.
You’re right in your perspective that mathematically a point on a number line doesn’t require traversal in all points “to get there” and that infinities aren’t a place, but they do have comparative sizes and ratios as in L’Hospital’s Rule. So let’s do this.
Let’s move backward in time step by step. Entropy is decreasing at every step. Eventually, one cannot decrease the entropy of the now Perfectly Ordered universe anymore and we’re not able to continue after a finite regression of time.
But I suppose you might argue that the progress toward Perfectly Ordered is asymptotic (as it’s believed to be close to Heat Death). The problem I have with that scenario is that if we reverse course to move forward in time, the rate of entropy increase is much faster and is not symmetrical with moving backward in time. This leads me to conclude that only a finite amount of time has passed.
Good points, though.
-Q
EDTA,
I think your approach in your point 2 is interesting.
-Q
VL,
actually, no. The issue was hammered out here over several years, it’s the curvy ball again. In this case, the relevant domain is the hyperreals, not the reals. This allows us room to see why a transfinite causal-temporal past of cumulative finite stages cannot be traversed, whether the transfinite was explicit or implicit. The hyperreals turn out to be more relevant than the reals, allowing us to have elbow room to think with.
The underlying issue in logic of being is that a true nothing is non-being, which can have no causal powers. Were there ever utter non-being, such would forever obtain, i.e. an actual world implies an adequate root of reality always was, circular causation being something from the not yet. That root is finitely remote in a temporal-causal world, which of course may be potentially transfinite going forward, pending an organising factor able to resolve the clock running down problem.
In such contexts, eternity looms as a different order of being, not simply another causal-temporal successive stage timeline.
Where, we can identify that a causally independent, non-contingent being is a necessary being that must be part of the framework for any world to exist, i.e. it is or is connected to the reality root and has that eternal character.
Conceptually, try to imagine a world where twoness does not yet obtain (including, distinct identity); impossible, it is a necessary world framework entity. Serious candidate necessary beings either are or are impossible of being due to contradictory core characteristics like a square circle.
Reality root candidacy is constrained by adequacy, where we are inescapably morally governed creatures. That demands an adequate reality root capable of grounding it, thus bridging the is-ought gap. There is just one serious candidate — if you doubt, try to put up another _____ . The candidate: the inherently good, utterly wise creator-God, a necessary and maximally great being. One, worthy of our loyalty and the responsible, reasonable service of doing the good that accords with our evident nature.
As a bonus, such an eternal being is essentially different from a causal-temporal, contingent entity up to and including possible and actualised worlds. Though obviously, such have been eternally contemplated. The issue of actualisation is the matter of creation. Where, after Plantinga we see that a morally governed, free creature can open up worlds of virtues pivoting on love. Similarly, that freedom includes freedom to genuinely think and freely infer not merely carry out a causal-temporal, dynamic-stochastic computational process on a gigo-limited substrate with further questions of its architecture. Such is consistent with a world in which sometimes choice is abused.
Further to such, the idea of God as just outlined, thanks to the microcosm/holographic principle, leads to deeply coherent, highly familiar frameworks of the divine attributes or facets of being. That is the whole is reflected in each facet and each facet contributes to the others, so that strong coherence obtains. God’s attributes are not an arbitrarily dreamed up chaotic wish list.
More can be said.
KF
Viola Lee: I know this is hard to wrap one’s head around, because infinity is such a slippery concept, but I think I’m right about this. YMMV
I think you are correct as well.
Just wait ’til ET. and Kairosfocus get involved in a discussion about infinity. You will be very ‘amused’.
PS: I spoke too soon, I see Kairosfocus has already joined the fray.
Querius @42 asks,
Sorry if that was unclear. MRT = Mental Reality Theory.
BA77 @
This is really, really good. Is the statement “A world exists entirely outside of mind” a logical contradiction? I love this. Thank you so much for crystallizing this for me. I’m going to think about this a while.
The only reality the professor still be said to exist “in,” with any capacity to verify, is in the minds of the observers. They have no way to reach any world external of their mind.
Understanding whether or not a statement is self-evidently true, a logical contradiction, or something else depends on understanding the terms used in the statement and how they relate to each other. I think part of tackling this properly is understanding what it means to say something “exists.” But, I’m still working on it.
Saying that the Professor “still exists” in an external world is circular reasoning. It assumes we’re experiencing an external world to reach that conclusion. The problem with those that assert this is that they are assuming something that can never actually be directly experienced or verified: an external world. It assumes that what the other people are experiencing is world external of mind.
JVL, you don’t understand infinity. So perhaps you should just shut up, already.
KF,
Heh. This is so transparently revisionist. The debate devolved into two (more or less) sides talking past each other.
It started with a post claiming that some scenario having to do with time was mathematically or logically impossible. I think the OP was by that philosopher/wedding singer guy, but I can’t remember his name.
The OP said that “X is impossible” because of $argument. Others, including myself responded by saying that $argument was faulty, so whether X is impossible is still up for debate.
KF enters at some point, at first reiterating that X is impossible, but his position gradually evolved into “Y is impossible”. Which is fine, but no one else is talking about Y. To avoid confusion, we just have to be clear that two different proposals, X and Y, are being debated.
Thanks, Dave and JVL, for pointing out that this topic about infinity has been discussed here before. And, even though your description is generic, Dave, I know the kind of thing you’re taking about. I looked at KF’s post and it didn’t seem relevant to the mathematical argument X that I made, but instead seemed to be addressing a whole bunch of other topics that maybe were part of those past discussions, Y1, Y2, Y3 etc.
WJM,
if you are going to try to argue against my points at least state my points correctly. I did not say that the “Professor “still exists” in an external world” as you are trying to claim but I instead stated that “the professor’s mind is gone and yet the reality that the professor existed in still persists.”
And then I further clarified, “Thus, clearly, I can easily imagine a reality that is not dependent on my, or on any other, human mind for its existence.”
And as I also further clarified, repeatedly now, that arguing that the ‘external’ reality we are perceiving is dependent on the Mind of God is an entirely different question than what you are currently trying to argue. i.e. “You cannot even imagine a world that exists outside of mind. No one can. It’s literally impossible.”
I was clear to state that I can easily Imagine a world that is not dependent on MY, OR ANY OTHER HUMAN, MIND, for its existence.
Now, of course, I hold that the external reality we are perceiving is ultimately dependent on the Mind of God for its existence.
I even pointed out that George Berkley elucidated this line of logic, long before quantum mechanics came along, with ‘Idealism”.
Thus, I hold that what you are currently trying to get at with your ‘mental reality theory’ has, essentially, already been worked out with ‘Idealism”
I believe that Plantinga may also have (lightly) touched upon this line of logic in his book ‘God and other Minds”
WJM, did you notice the remark above on incomprehensible, i.e. immensus meaning unlimited or infinite, beyond any particular finite bound? KF
DS, no. I started with the hyperreals, inchoately put. There was a long needless detour through the reals (which turn out to be inadequate and by characteristics not what is implicit in many a number line we meet starting in schools . . . hence my note that the true model of quantity we want in general is hyperreal, with infinitesimals and an intuitive route into Calculus as a bonus) but by reference to model theory we were able to put it back in those terms more firmly established. Once that was on the table, we were able to readily see the challenge of spanning the transfinite as a finite stage cumulative step by step succession. Just as was originally symbolised in 2016, once we realise that every stage of the actual past had to have once been the present and had to have been succeeded by an immediate causally bound successor, then we see that a claimed infinite past — implicitly or explicitly — requires actually transfinitely remote past stages BEYOND ANY FINITE COUNT. And vague comments over well we have further finite values beyond any specific symbolised or counted to finite past point say k’ i.e. k’-1, k’-2 etc does not answer. It just shows that once we get specific and traffick in steps, we are stuck this side of the transfinite. Once we use R* to symbolise such a transfinite, say H’, then go forward H’+1, H’+2 etc, , we readily and clearly see the unbridgeable gap from such to now as we cannot in steps bridge to -2,-1, 0 etc. We are only warranted to discuss a finite past though we may point to a potentially infinite future that keeps adding up once we have a factor that can inject organisation to break through heat death. Such a factor is readily available. KF
KF @63,
Yep. Is there a point there I need to respond to?
KF,
Nonsense. 🙂
The proposal being debated (which I called X above) is modeled using the real numbers only. When you introduce the hyperreals, you are changing the subject to Y.
If by this, you mean that “X” implicitly assumes the existence of a particular point T in time such that the interval between T and the present is infinite, that is clearly false.
All the infinite past proponents arguing in earnest for that position assume that any two points in time are separated by a finite interval. And that the real numbers (or some subset thereof) is adequate to model time coordinates.
I see, Dave: My argument is about the real number line: that is X. KF thinks the hyperreals are relevant: that is Y1. I doubt that Querius, or anyone else that makes the argument Querius references, is talking about the hyperreals.
I see also that KF mentions the heat death factor, which applies to our physical universe only, not the general mathematics of infinity. I pointed out why I though that was a separate subject not relevant to my argument, so that would be Y2. And in his first post, KF brings up God, which would be Y3.
No wonder you had two sides talking past each other.
BA77 said: I was clear to state that I can easily Imagine a world that is not dependent on MY, OR ANY OTHER HUMAN, MIND, for its existence.
If you notice, I don’t use (or at least try to avoid using) personal identifiers when I talk about mind. I’m talking about mind, not “your” mind or “my” mind. “Universal” mind is the superset of all possible mental experiences. What we call “individual mind” would be “universal” mind “looking through” a particular information structure producing an individualized perspective and set of experiences.
Viola Lee,
Yes, in any argument concerning the real numbers here, the hyperreals will no doubt appear. And anyone who resists this will be accused of “locking them out”.
WJM, just a clarification, comprehensible has a peculiar older meaning. KF
DS, for cause I stand by my summary. I have drawn the conclusion that the hyperreals better answer to the issue and help us see the point. There is a way to see why a transfinite span to now cannot be our actual past. Recall, every “year” of the past had to once be the present even as 2020 is a present we all wish were not real. And CV19 is telling testimony to causal connexions year to successor. KF
Time for a Fisking!
Disagree with the “most theologies” paintbrush, but this is a fair description of the fundamentalist Judeo-Christian belief. The rebuttals below will take this perspective when pointing out logical flaws.
Logic FAIL #1: TIME DOES NOT CONSTRAIN GOD – THERE MAY BE NO “NOW” FOR GOD.
What was “created” is our universe, consisting of REAL things both limited to the universe (e.g. matter, energy, time, space, forces, etc.) and not limited (e.g. information, logic, math, etc.). God MUST exist outside the universe in order to “create” it, and therefore is NOT bound by the reality limited within the universe – more specifically to your argument, LINEAR TIME. Because you were created within a universe bound by time, matter, energy, etc., you are incapable of even conceiving what a timeless reality would look like, let alone accurately represent logical restrictions on such a reality. God can NOT be “subject to linear time”, or else He would not have been able to create it. YOUR inability to comprehend timelessness is NOT a logical restriction on its characteristics.
Logic FAIL #2: MATTER DOES NOT CONSTRAIN GOD.
The claim that God “is” everything from a theological perspective is false. Your inability, again, to comprehend how God can be everywhere (theologically true) without being everything (theologically false) is not a restriction on God’s attributes (which, by the way, NO theology claims to understand completely). Judeo-Christian theology clearly states that God “created” everything, and that in Him all things hold together – God is not, therefore, everything. Your logic is sound IF God IS everything – but that is pantheistic in nature, and not a major belief of “most theologies”. You are arguing a strawman.
Logic FAIL #3: YOUR CONCEPTION OF GOD/NOT-GOD IS CLEARLY NOT THE SAME AS “MOST THEOLOGIES”.
Your statement here is mere assertion, and depends on your definition of God’s attributes. Which, as we have seen in FAIL #2 above, are a strawman not representative of most theologies.
Logic FAIL #4: ASSERTION WITHOUT BACKING.
Of course God has a perspective, or point of view. It’s called Perfection, Holiness, etc. And He can make a decision. Again, your logic depends on limiting God to the “realities” of a time/space bound universe, and an inability to comprehend a timeless perfect existence. Your attempt to shoebox timelessness into the constraints of universal time limit your understanding, not God’s attributes.
Logic FAIL #5: KNOWING =/= EXPERIENCING
Self-explanatory and “self-evident”. You can know something without experiencing it, so can God. Compounded with a repeat of Fail #2 above, the assertion that no reality can exist that isn’t some pantheistic piece of God (or God’s mind, however you want to look at it). You’ve created a fourth characteristic for God that no major theology would agree with – “omniexperience”.
[Edit] It is also important to point out that “Knowing” is not restricted to knowing what IS – it is also possible to know what IS NOT. Therefore, God can be omniscient and know what IS NOT a possible reality – basically any reality that God chooses NOT to create. QED.
Logic FAIL #6: ONCE AGAIN CONFLATING KNOWING WITH EXPERIENCING
The issue with WJM’s argument is not the logical conclusions, it’s what he takes as being axiomatic. IF you accept that omniscience = omni-experiencing, or that a timeless extra-universe reality must follow the rules of time/physics within the universe, or that omnipresence = pantheistic, then sure, his logic makes sense. Fortunately, none of those are true.
Logic FAIL #7: THE LIMITATIONS OF OUR UNIVERSE WERE DEFINED TO BE MUCH GREATER THAN “WHAT IS POSSIBLE IN THE MIND OF GOD”
Again, the “all knowing = all experiencing, therefore all experiences exist” falls apart rather clunkily in step 1.
Logic FAIL #8: CITING LIMITATIONS THEN CLAIMING LIMITATIONS ARE ESSENTIALLY NON-EXISTENT.
With very little effort, “four-sided triangles” and “1+1=3” experiences quickly becomes a never-ending list of limitations. You can’t play basketball in the NBA. You can’t move objects with your mind. You can’t live forever. You can’t accurately imagine a reality not bounded by our universes created rules. You can’t know my experience. Etc.
While I appreciate WJM’s enthusiasm for his “new idea”, it smacks to me (as BA77 alludes to with his rebuttals) as a regression to the pre-Western civilization ideas that science was the realm of logic and analysis, rather than the scientific method and experimentation. Mental Reality Theory seems to sprout from the same root as solipsism, even if it (as WJM argues) isn’t the same thing.
So here’s a couple questions for WJM:
1) What practical experiment could be performed that would tell us whether your MRT theory is correct, or the view that objective reality exists (which we experience through our mind and senses)?
– If, as I suspect, the answer is “none”, then WJM’s argument is merely semantic – what we call an object, he calls a mental experience. To-MAY-to, To-MAH-to.
2) Applying Occam’s Razor, which theory below is the more likely and useful?
a) Objective Reality Exists, which we humans experience simultaneously through our senses and mind.
b) All reality is Mental, which we humans experience through our sense and mind. The fact that we all experience the same “mental” reality, and can create an entire discipline called “science” that defines “laws” of how Mental Reality behaves, is merely coincidental, as there is absolutely no reason why (if reality is not objective) we should all experience a consistent reality that abides by such laws.
Personally, I find MRT to be sophistry, and quite likely a philosophy that has been considered and discarded multiple times throughout history (see Descartes, Hume, etc.) Additionally, if the only response one can offer to people pointing out flaws in a theory is “oh, you just don’t understand the theory because it is too complex for you”, then it isn’t worth wasting brain cycles on, since the advocate won’t engage in a productive manner.
KF,
But it’s not your choice to make—the infinite past proponents have already chosen their model.
You are entitled to propose your own model (if only to immediately knock it over), but then you are talking about Y, not X.
Drc466 said:
I’ll take this to mean, “what experiment could be performed to determine whether or not an external physical world exists that is causing our mental experiences.” There is no experiment that can be conducted (even in principle) to verify the existence of an external, physical world. There is no experiment that needs to be conducted to know that all experiences occur in mind. Unless the existence of an external world can be first verified, which it cannot there is no reason to consider it as a serious contender.
Occam’s Razor means that one insert no more entities into a theory than are necessary to explain the phenomena. MRT has one categorical domain of entities: mind. External physical world theory has two – mind and an external physical world. External reality theory also requires a process by which the external world is translated and processed into a successfully corresponding mental version of that physical world. MRT doesn’t require that.
As far as “Most Useful,” External Reality theory is a theory held in mind about experiences one has in mind, but which adds to the theory an additional, hypothetical “external physical world..” As with any succession of theories, the latter must take into account the evidence of the former AND new evidence that calls into question the former, and provide more or better explanatory and predictive capacity, which MRT does IMO.
If you know of any evidence that supports the theory that an external, physical world exists, feel free to provide it.
@Drc466
Congratulation for your pacience. I also intended to debunk this article but were so many fallacies that my brain overheated. Another problem is that WJM didn’t use logic with this pseudo-theory ,he just got an “inspiration” ( as he admited in a comment) .
🙂 You imagine that inspiration wasn’t sent by God because was entirely anti-God.
WJM,
Your argument basically summarizes down into MRT is a better descriptor than Objective Reality because both theories acknowledge that our experiences are dependent on what we perceive through our sense and mind. Yet you don’t really distinguish any characteristics that differentiate between a “mental phenomena” and an objective reality (hence my “semantics” objection). So I’m not ready to agree that MRT is simpler by not requiring objective reality – whether you consider a car a “real” object or a “shared mental experience”, it is a +1 to your Reality theory. You’re just quibbling about its nature, not its existence (as matter or experience). However, for the sake of argument, I’ll let you have this, and take as given that MRT is simpler by not requiring objective reality.
So that leaves this:
I’ve already provided this (as has BA77 in a slightly different form): the continuity and accordance of our mental experiences that allow us to practice what we call “science”, and discover foundational traits of our environment, the universe:
If MRT is correct, there is simply no reason why billions of people all experience a consistent, discoverable universe that follows a definable set of “laws”. As you yourself have stated before, MRT is perfectly comfortable with both a “brain in a vat” and “dream state” version of “reality” that have equal footing (in your mind) with what the rest of us refer to as “objective reality”. If we are, in fact, simply experiencing a non-objective reality, there isn’t any reason why F=ma in both our worlds. Or why the color of “GO” on a street light matches the general color of grass for both of us. Or why scientific experiments provide consistent results for different people.
In fact, that only way for MRT to justify the consistency of our results is:
1) We live in a shared mental experience where mental phenomena are consistent, even mental phenomena that are after-effects of prior mental phenomena not personally experienced (e.g. if a tree falls in the forest and there is no one there to hear it, do I still trip over the trunk while hiking?). The problem with this justification is that a) it offers no discernable difference with an objective reality, and therefore provides no value as a theory, and b) there isn’t any particular reason why this should be true, as I explained above.
2) Solipsism – we don’t really share a mental reality, I’m just creating (unreal) persons who appear to share my reality.
Sure there is – the rational, logical conclusion of [almost] every person in the world that objective reality exists, and the practical effects of operating based on that assumption. If it were not true, there should be some practical consequence contradicting the assumption.
Thought Experiment #1: If I see a train rushing at me, using your logic, I cannot “prove” that the train is a real object in “an external, physical world [that] exists”, and not just an imperfect representation of a mental experience being perceived by my mind. However, the only sane response to my upcoming mental experience is move out of way of the [not real] onrushing train, so I don’t transition from my “living” mental experience to my “dead” mental experience. So which approach is more logical – external, objective reality or MRT? And, again, if your reply is that the mental phenomena called “train” will kill me just as dead as the external objective reality called “train”, we’re just arguing semantics, aren’t we?
Addendum: I’d like to also provide one additional response to your assertion that God must be somehow stuck in an eternal “now”, unable to act or create due to His omnipresence and timeless/unchanging attributes:
Thought Experiment #2: Imagine you are a person who suddenly popped into existence in 1970, as a fully mature 40yo, and pops out of existence in 2030. Furthermore, you possess the unique attribute of timelessness and unchanging-ness – your body does not age, you experience your entire life simultaneously, and you know exactly what happens throughout your entire lifespan. Do these properties in any way prevent you from acting during the lifespan? You may simultaneously “know” and “experience” the act of making dinner in 1993 and “know” and “experience” the act of buying a new car in 2020. Your actions are not in any way limited by the fact that you know and experience these actions simultaneously, nor do the actions change you, although they may change the world around you. Now simply imagine having these same attributes extrapolated out to eternity.
(Note that I am NOT saying that this in any way represents an accurate description on how God can be timeless and unchanging while also having the capability of creating, acting, and deciding – I’m just trying to provoke a consideration of whether timelessness does in fact prevent action, and whether we possess the mental capacity to comprehend/describe such extra-universe attributes).
Drc466 @72,
Nicely explained! I strongly feel that any attempt on the part of a human to trap God by seemly logical statements and conclusions is doomed to failure for the reasons you provided. That we can hardly escape from our temporal perspective isn’t a limitation on God. It’s as if a point on a line tries to logically construct a human in 3D.
Kairosfocus,
I appreciate your answer, but frankly admit that I don’t understand the concepts previously argued over. Personally, I think there’s a significant difference that should be carefully maintained between mathematical concepts and observed physical reality.
For example, I can easily imagine an integer, but as a real-world measurement, I’d suggest that integers are never encountered (i.e. a decimal integer with an infinite number of zeros after the decimal point).
William J Murray,
How are your beliefs different from solipsism?
I suppose that you might assert that our shared human experiences are also solo mental constructs. If so, how many independent minds are there?
Many physicists believe in the possibility of a holographic universe and that our external world is not actually physical but rather a simulation. How does that conflict with your beliefs? In other words, could we be living in a simulated world while a different world, an external physical world, also exists?
Viola Lee,
You’re right, I wasn’t thinking about hyperreals.
Yes, I have a passing familiarity with a variety of cellular automata, having played with software generating them, including Sierpinski triangles.
It’s possible to create a “square circle,” that is an object that can appear as a circle or a square, namely the projection of a cylinder (height = diameter). This is to your point about even Euclidean geometry yielding strange results.
Regarding infinitesimals, you might enjoy this if you’ve not already seen it:
n = 0.999 . . .
Most people would say that this number is infinitesimally smaller than 1. But
10n = 9.999 . . .
10n – n = 9.999 . . . – 0.999 . . .
9n = 9
n = 1 🙂
– Q
Hi Q. Here are a few comments about your post at 77. (I’m interested in some of the topics and not others.)
I like your answer to Kairosfocus:
I’ve taught both pure and applied math, and built a lot of stuff, so I appreciate the distinctions you made.
Cellular automata and interative functions are a favorite topic of mine. Not many people have heard of Sierpinski triangles, so it’s neat you worked on programming related to them.
I teach about infinite geometric series in pre-calculus, of which 0.999999… = 1 is an example. The whole business about “infinitesimally small” is of course one of the central issues in calculus.
I enjoy talking and thinking about math, so thanks for the feedback.
Viola Lee,
Actually, I just experimented with the program, I’m not a programmer. But I know of some resources that I think you might really enjoy:
There’s an old DOS program named CA LAB that was briefly sold by Autodesk. Check this out:
http://www.rudyrucker.com/oldhomepage/cellab.htm
Also check out the following program named Chaos (Mandelbrot set, strange attractors, etc.)
http://www.rudyrucker.com/oldhomepage/chaos.htm
And for students who want a humorous cartoon introduction to functions, calculus, and sets
https://www.amazon.com/Prof-McSquareds-Calculus-Primer-Intergalactic/dp/0486789705
Enjoy!
-Q
Drc466 said:
Nope, that’s not even close.
A few things here. First, to be explicit, I’m talking about mental reality theory vs the theory that a physical world external of mind exists that is causing mental experience. You keep using the term “objective reality,” but I’m going to assume you mean “external physical world” when you say that.
Second, you say that under mental reality theory, there is no reason we should have shared mental experiences that largely conform to what we call the laws of physics. I’m assuming you’ve read the reasons offered here and/or by other authors on the subject of mental reality theory Why do you say, then, that there is “no reason?”
Third, you haven’t actually provided evidence for the existence of an external, physical world. You only made a circular argument – that if there was “no reason” for mental reality experiences to behave this way, what we are left with is external physical world theory. But, that assumes physical reality theory is the best “other” option. You haven’t provided evidence that it even exists, much less that it would or should behave as it does in our experience.
Could you please begin by first providing evidence that an external physical world exists?
Drc466 said:
Every aspect of your thought experience would be solely experienced in mind regardless of whether or not there is an external physical world. If the mind was not capable of producing these experiences, even if caused by an external world, we would not be able to experience them.
So, we know for an empirical, experiential fact everything in your thought experiment is experienced in mind and can be produced by mind. All the physicality. All the consistency of laws, cause and effect, etc. Otherwise, we couldn’t experience those things.
This means the burden is on those who assert an external, physical world cause for those experiences to provide evidence that such a world exists. “What everyone else believes” or characterizing it as what “sane” people think is not evidence.
IF you have evidence an external, physical world exists, feel free to provide it.
I’ll open that up to everyone:
If anyone has evidence an external, physical world exists, lay it on me.
You mean any one of us in the external, physical world?
-Q
How about the observation that we have nerves that connect to our spinal cord rather than just our brain?
-Q
How is referring to a mental experience (the observation you described) evidence of an external physical world?
The question is if some mental experiences are caused by an external physical world. You can’t point at a mental experience and say it is evidence of an external physical world because mental experiences are the very thing we’re debating the cause of.
It’s like saying that we’re looking for evidence that Bob dropped the gun found at a crime, then pointing at the gun and saying that the gun is evidence that Bob dropped it there.
DS, that narrowing of perspective inadvertently erects a strawman that distorts ability to see what an infinite past implies. You will particularly note that for something to be the actual past as a stage, it had to have once been the present and then have been succeeded in causally connected cumulative stages to the now stage, 2020 AD in particular. That requires stepwise cumulative succession of finite stages. We are only warranted to account for a finite traverse on those terms, arguments we have seen since 2016 boil down to perpetually begging the question of prior traverse. To assert that at any particular stage that is finitely remote from now the onward past infinity has already been traversed does not answer as to feasibility of such a supertask. The use of the wider frame R* mileposted by Z* allows us to have conceptual tools to address that traverse more clearly and the result is almost trivial, given that the negatives are in effect the additive inverses of the positives. That is, if forward traverse from a given point in N* on in stages cannot be actually transfinite by accumulation, neither can that be so for the prior traverse enumerated by using the negatives. We cannot exhaustively count N, yes, and any k in N is exceeded by k+1 etc, but that simply means the ellipsis of onward succession highlights that the process points to the transfinite and that successive stepwise cumulation cannot traverse such; which is the core point. N*, Z* and R* allow us to clearly represent such and in so doing the challenge of supertask traverse rapidly becomes patent. KF
PS: for onlookers, the idea per model theory is, accept some H such that it exceeds any such k in N, and such that 1/H = h, a number closer to 0 than 1/k for any k in N. this gives us transfinite and infinitesimal hyperreals and a catapult function which connects the two. H has relevant numerical properties, e.g. it can be even or odd and we can get to a grand continuum, we can even get to C*. This wider frame also allows us to reduce Calculus to an extension of Algebra, using infinitesimally augmented numbers. And much more.
You may want to discuss your theory with a psychiatrist or an exorcist. Don’t worry they are part of your inner self ,they are just different masks of yourself,pigments of your imagination.
Kairosfocus: To assert that at any particular stage that is finitely remote from now the onward past infinity has already been traversed does not answer as to feasibility of such a supertask.
No one who is mathematically aware is saying that.
William J Murray: If anyone has evidence an external, physical world exists, lay it on me.
The bundle of perceptions you identify as being yours . . . where are those happening? How are they stored? You know they’re stored because you have memories of past perceptions (unless you want to think that those memories are being created instantaneously as your ‘universe’ is recreated over and over and over again) so where are those memories collected? How are you able to recall them, frequently on command? What is the mechanism?
KF,
This can only lead to a trivial semantic debate—“What they are proposing is not a truly infinite past, rather quasi-infinite” or some such.
I planned to respond further, but I don’t think I will, for the sake of my sanity.
Except for this point:
I don’t think I’d read this before (about the evenness or oddness)—do you have a source?
JVL @ 89, anyone who says there was/is an infinite past is saying that
JVL @90 asks:
In mind, by mind.
By placing my attention on them.
Do you have evidence for an external, physical world you’d like to share?
Let me give you a little more meat to chew on, JVL. Apparently you missed where I more fully fleshed out the MRT model.
The base of existence is infinite (or “universal”) mind. Mind is all that exists. Mind can be characterized this way: infinite consciousness of infinite available information. That state would be what some would call the “God” state. I prefer infinite or universal mind, but whatever.
Infinite consciousness has its attention on every possible informational subset. An “individual” exists as the experience of consciousness’ attention on any particular subset of information. Individual perspective is generated by this conscious attention on an informational subset. This means there are infinite individuals representing every possible attention/informational subset relationship.
Everything an individual experiences might be characterized as an algorithmic, or “most efficient” expression of this informational structure.
If we have “every possible” perspective, then there will be large numbers of individual perspectives that share large amounts of base information, but just different enough in some ways that would distinguish one “person” from another. This means that we can have an enormous amount of shared, consistent, mutually verifiable experiences, as long those experiences reflect shared information the “algorithmic” process is accessing. Our experiences will diverge inasmuch as (1) the information being processed is the same, (2) other aspects of individual information sets don’t cause the algorithm to generate divergent experiences, and (3) individuals in a shared experiential set don’t turn their attention to other available information that would cause experiential divergence.
Please note, what is being generated by the algorithmic expression of the information generates is ALL experience. Consciousness is not experience, it is what is observing, or having, the experience. Thoughts are not consciousness, they are experiences consciousness is having by having it’s attention on a particular informational structure or pattern.
Conscious attention is the 100% free variable in the algorithm. The variable is a referential variable; it represents what information the algorithm is referring to in the experience-generating process. The observer directs the path of experience as it moves its attention around. The observer directs it’s attention at information and then has the experience the algorithm produces from that information. The consciousness of the observer is not the experience it is having, although the process creates our “personality,” things we usually refer to as characteristics of who we are, or our “internal” experiences.
Remember, this is a model intended to better understand our existence and how it works. All the words and thoughts about it are representational from a perspective – mine. The only proper way to discuss or debate it is in principle and logically and not to think of the representational labels as an exact and full understanding of what they are “in principle” describing.
Dave, you quoted KF as saying, “that narrowing of perspective inadvertently erects a strawman that distorts ability to see what an infinite past implies.” You then replied, “I planned to respond further, but I don’t think I will, for the sake of my sanity.”
From what I’ve seen, that seems like a good idea. Discussing infinity in terms of the real number line, as I did, is not “narrowing the perspective”: it is accurately using the perspective that everyone else uses in discussing this topic. (I have done some google research and found no evidence that anything but the real number line meaning of infinity is being used in other conversations about this topic.) I think my argument in 51 is sound: KF’s wanting to talk about hyperreals doesn’t invalidate my argument about infinity on the real number line.
William J Murray @85,
What triggers a mental experience?
-Q
Further info on MRT: We don’t actually experience “free will choices,” or the decision to put one’s attention on something. That is our ineffable free will that is beyond individual experience. We can only experience the result of the choice. This can be understood by thinking, “I choose to think about ….” and then experiencing whatever you chose; you only know your choice after it has been made and expressed in the experience of what you chose. Give it a try.
Querius @96: I think I’ve already answered that question just above in my responses to JVL.
William J Murray:
Hmmmmm . . . what is “mind” made of? What holds it together? Why doesn’t it just dissipate. Thinking takes energy yes? Where does that energy come from?
Where and how is the information being processed? Where does the energy come to do the process? How is the ‘algorithm’ stored and read and implemented? How is the information stored and read?
‘Where’ is the observer relative to other observers? Where does the energy come from that enables the observer to direct its attention?
Fine, but what you describe still takes energy and storage and interpretation of perceptions. Where and how is all that done?
Viola Lee,
I basically agree, although I do know of one exception, a paper by Quentin Smith which considers models where time coordinates can be separated by infinite intervals. However, I’ve never seen work by infinite-past cosmologists (or anyone else) which seriously advocates such a thing.
The truth is that KF has dug in on this point and is using every tactic available to avoid discussion of the actual position that is being proposed.
William J Murray @98,
No. Thinking that you already answered the question is not the same as answering the question.
I bet you’ll say choosing to focus our consciousness on a piece of information, to which I’ll ask what triggers our choice to focus on a piece of information, to which you might respond by saying by choosing to focus on a prior piece of information, to which I’ll ask what triggers our choice to focus on that prior piece of information and so on into a sort of mental perpetual-motion von Neumann chain without any external reality to initiate it.
How do you know that you’re not the only conscious agent as in solipsism? Do you take it on faith?
-Q
Thanks. Looks like that paper agrees with me, but it’s behind a paywall so I can’t read it. However, it is probably more extensive than I would study anyway. The intro is clear:
Viola Lee,
Yes, that paragraph states the point very nicely.
Watch your comments, people. Keep it friendly and civil. Some comments have been removed and future comments that contain personal attacks or derision will be removed. I’m being entirely civil, respectful and friendly. I expect others to exhibit the same civility.
JVL said:
Those things are only relevant and meaningful in the external, physical-world model. Which is part of the reason why I said the logic and principles involved are the best way forward in a discussion about MRT
I’m still waiting for someone to produce evidence that an external physical world exists. No takers?
DS (attn VL), first, see Dr Carol Woods, on Model theory as discussed; in for example a video shared here some time ago she discussed even and odd hyperintegers briefly; which makes sense, H and H+1 in Z* will “naturally” have one being odd, one even. Second, I am not suggesting any idiosyncratic oddity but simply identifying what is embedded in the ellipses of transfinite extension in say . . . -2, -1, 0, 1, 2 . . . These indicate that beyond any particular k we have k+1 etc, and the additive inverses, i.e. for k’ additive inverse to k, we have had past stages k’-1, k’-2 etc without limit, implying precisely transfinite succession to k’. Of course this implies too that there is no specifically identifiable maximal finite integer z so z+1 is transfinite. The Hyperreals embrace the Reals and allow us to see what is implied in a descent of stepwise finite stage causal temporal succession to now where any past value k’ is transfinitely preceded L-wards. The point is, not abstract sets but actual past. That is where the transfinite traverse enters. KF
WJM, what does a physical world mean to you? KF
KF, are you willing to talk about this topic in reference to the real number line only? Or will you only discuss this topic when it includes the hyperreals?
My friend,I’m shocked I thought you really belive in your model of mental reality. In your model don’t exist things like “personal attacks ,derision” only algorithms and shared experiences. Are you refusing to accept realities of your model? Live what you preach:
William J Murray:
But how can those things occur without expending energy, without information being encoded and stored and then read?
Is that not just logical and, in fact, necessary for the phenomena you describe? If not then can you support an assertion that they are not required?
IF you choose to ignore some clear requirements then your model is flawed from the start and insisting that we stick with it is just begging the question. You have to consider the data and logic which runs counter to your model or you’re not really seriously trying to have a logical discussion about its merits.
KF,
Thanks, I do see references to even hyperintegers etc.
If I understand correctly, yes, these are just elementary facts about the integers. And I guess “implying precisely transfinite succession to k’” just means that if we assume an infinite past from the POV of the present, then the past from _any_ POV among the stages …-2, -1, 0, 1, 2, … would also be infinite. That’s what the “standard” infinite past model supposes.
Once again, the hypothesis under discussion (X) is that there are no stages or points in time at infinite remove from the present. As Q. Smith states:
Cosmologists etc. working on “infinite past theory” have wisely taken Smith up on this. Their model is based on R only, and they can “see” fine without bringing the hyperreals into the picture. Again, it’s their model, their choice.
Yes, we do aim to talk about the actual past. With the aid of “the logic of structure and quantity”, of course, which is necessarily abstract.
JVL asks:
What we call “energetic interactions” are behavioral patterns of phenomena we experience that can be described in mathematical terms. “Energy” and “forces” and “physical laws” is a label for the models of these patterned behaviors. Nothing more.
For instance, “gravity” is a model of behavior of phenomena, phenomena we experience entirely in mind. There is no actual “thing” we are talking about when we use these words other than referring to the behavioral model. We have fallen into the bad habit of referring to the name of the model of behavior, like “gravity,” as if that word represents the cause of the behavior the model describes.
There is no such thing as “energy” per se. There are only behavioral patterns of various mental experiences.
As for “where information exists” and “how is that information accessed and processed,” I’ve answered those questions; the problem is that you want them expressed in terms of an external, physical reality, and reject it when I express it in terms of mental reality.
I can instantaneously create absolutely anything in the set of mental experiences we categorize as imagination. Where was that information “located?” How did I access that information? Where is that experience located? How much room in mind does it take up? How much energy did it take?
Now you might say, “but imagination is different from the category of experience we label as the external physical world.” Yes, it is, but under MRT, they are both mental experiences. Neither requires what we commonly refer to as energy or space.
Those are only requirements in external, physical world theory, not MRT.
I’ve answered many questions here. Anyone want to take a shot at providing evidence of an external (of mind), physical world?
KF asks:
Not enough context in that question to begin to know how to answer it.
Querius asks:
Nobody knows that regardless of what theory they operate under.
Yep, just like everyone else – except solipsists.
“Yes, we do aim to talk about the actual past. With the aid of “the logic of structure and quantity”, of course, which is necessarily abstract.”
Nice line, Dave.
@WJM
🙂 Explain behavioral patterns of phenomena . What it is , how and why appear, where ,when, etc. After you explain that probably you will introduce in definition a new term . Well you have to explain also that term…and so on.
William J Murray:
Yes, I get that. But you can’t explain how all these ‘energetic interactions’ can occur without using some energy and having a storage system and an interpretation protocol. It’s all just ‘magic’ for you it seems. But what good is a model which doesn’t accommodate digging down into the infrastructure? Why put a limit on what questions can be asked? Why is it that certain queries just end with: because?
Fine. An interesting choice of topics for you I think since ‘gravity’ has gone through some progressive model changes which more closely mirror the repeated and observer independent data we have. But you don’t believe in repeated and observer independent data because your world is the only one that counts.
You keep avoiding the issue: how is it those mental experiences occur, are fuelled and are recorded for later playback? What is the mechanism that enables these things?
Your mental reality is limited and clearly dependent on some infrastructure you refuse to consider important. You propose some ‘system’ of thought which has no basis in logical and rational states. It’s just a pipe dream. You ask for evidence of external reality and then when someone brings up a point which supports external reality you dismiss it as off topic.
Questions you sidestep because you have no answer. You cannot ‘create’ things which impinge on me aside from your replies on these blog threads. You can’t. You can imagine you have but I will not share your experience or reality.
Well, how do these experiences have an actual existence then? How is it possible to store them and recall them or to relate them? You keep dodging the issue. Where and how are your experiences recorded? Please answer that.
MRT is beginning to sound like an ideological dead end. It gets you nowhere. It answers nothing. It’s a science stopper in that it just pretends that nothing aside from your own ideas have meaning.
Worst of all, it means you can deny and deny and deny that other people with feelings and pains and problems exists and are worthy of consideration. You can remove yourself from the world, including your own body. And when you die and your brain stops then the reality you bought into will cease without having helped anyone else or alleviated their pain.
Well done.
JVL,
As I’ve already pointed out, you’re asking me to describe MRT in terms of ERT. If that appears to you to be me “sidestepping” your questions, there’s nothing I can do about that.
Sure it is – let me quote YOU from the post I was responding to:
I didn’t explicitly add the part about “[ERT] also requires…”, but the summary is accurate.
External, objective, whatever. You do love semantics, don’t you? Yes, I’m referring to an external, physical world.
Yep – you! Allow me to quote your exact words on how MRT accepts as real “all” mental experiences, from the comments on another post of yours:
So, yes, I have read the reasons offered here, and that is why I say then that there is “no reason”!
I have provided evidence for the existence of an external physical world – the commonality of our experience and the efficacy of science in the “real” world versus the non-commonality of our experiences and the lack of efficacy of science in other worlds (e.g. imagination) that MRT would accept as “all completely, totally real” (again, YOUR words). Circumstantial evidence and logical conclusions ARE evidence (accepted in courts of law everywhere, see yours today!)
Additionally, allow me to turn the question around on you – Could you please begin by first providing evidence that MIND exists? After all, we only have YOUR testimony of YOUR personal experience with mind. Why should we accept your testimony, or as an example, your 12 successful predictions of MRT, as evidence for MRT, if we only have “your experiential algorithm” to go on, and none of it is an actual external physical reality? It strikes me that, like the argument that “our minds are not designed, they are just the result of random chance”, MRT is a self-defeating point of view. By denying the existence of external reality, it denies the possibility of external evidence for the reality of a self-focused theory. By denying external reality, solipsism is indeed the only logical valid conclusion. Extrapolating a “shared” mind that we are all a part of is an unwarranted and unprovable assumption, as you claim external reality to be.
The fact is, you are asking a stacked, loaded question when you ask “Could you please begin by first providing evidence that an external physical world exists?” by arbitrarily ruling out “the evidence of my senses, mind and logic” by fiat. “If I get hit by a car I die and my mental experience as it is currently experienced ends” should be more than enough evidence for an external, physical reality of a car (since, in my dreams and imagination getting hit by a car does NOT end my mental experience, even though MRT accepts them as “completely, totally real”). Your only way out for MRT is to essentially declare that your mental experience of being hit by a mental phenomenon known as “car” somehow “transitions” your mind (unproven and unprovable – the irretrievably dead can’t tell us). Just say no to epicycles, dude.
[Edited for spelling/grammar]
William J Murray:
You could acknowledge that even MRT must exist in some kind of supporting infrastructure but you won’t do that. For you your own conscience is fundamental and any questions as to how that works or how it is sustainable is beyond the scope of your interest.
Please answer me this then: there are chronological gaps on this blog wherein you do not respond to queries put to you. Why is that? Why do you not respond immediately to the queries you deem worthy?
William J Murray @119,
Haha, funny!
But, I do think my (persistent) response to your stated challenge is valid.
I can anticipate your response, but it would imply that all people in reality do not share the same experiences–in one person’s mind (mine), nerves connect to our spinal cord exist and I (erroneously) perceive them to exist in everyone else’s reality in books, lectures, and conversations. In someone else’s personal solipsistic world, they are highly intelligent tree-dwelling octopuses and they think everyone else perceives this, too. Yet another person thinks they’re a moonbat on planet X and so is everyone else. And so on.
Is your mind basically talking to itself by feeding it amazingly creative input, being stumped by bizarre physics, and arguing with other imaginary beings?
-Q
Viola Lee,
Did you miss my post @79?
I think the links would be interesting to you.
-Q
1)
2)ERT is a mental phenomena.
3)Therefore ERT is a completely,totally real.
1A) 1) assert that in MRT all mental phenomena are real
2A)ERT is a mental phenomena and contradict MRT
3A)MRT definition is self-contradictory
No, I saw your post, Q, and looked at the links. Sorry I didn’t acknowledge that. The programs were old DOS material that wouldn’t help me much, being a Mac guy, but I know of a number of Life, Mandlebrot, and other fractal simulations that run in a browser that are very cool, and that I have played with before. And, as a calculus teacher, I’m always interested in the idea of teaching the concepts in an engaging way that adds some life to learning the necessary mechanics. Thanks.
VL, are you aware of non-standard analysis? KF
WJM, what would a world that is physical, independent of our consciousness and yet allowing us to be rational, responsible, significantly free and even morally governed creatures look like? What would to you count as evidence of such a world? KF
Querius,
Your evidence is logically unsound as I’ve already explained. You’re pointing at something that occurs entirely in mind and claiming it is evidence of something that occurs external of mind.
The funny part of this is that originally external mind theorists claimed there was a world made of matter. Then we couldn’t actually find matter, so they claimed it was made of “energy” (which is really just patterns of behavior; but of what?) Now they have come to the external world theory that it’s all really about information – probability waves. Not waves of energy, but waves of probabilities that only collapse into specific characteristics in the presence of an observer.
Where is this probabilistic information stored? What is it stored “on” if there is no such thing as “matter” and “energy” isn’t even a “thing”?
There is only one place patterns of information can be stored, accessed and turned into experiences without any matter to store it on or energy to retrieve it: mind.
I’m really only stating the obvious here, especially in light of current quantum physics research.
DS, recall, we are counting cumulative, causal-temporal successive cumulative stages to the present. Years is partly convenient but runs into trouble before the big bang for our cosmos, i.e. I am not ruling out a multiverse in the common fluctuations model. If that is off the table we already have a credible beginning c 14 BYA and the debate is moot. That said, we count stages in their successive order. For there to have been a transfinite actual past, every countable in principle stage . . . k’-1, k’, k’+1, . . . -1,0,1 . . . n for now has to have once been the present. That means for EVERY finitely remote k’ there are transfinitely remote/many onward stages of the actual past traversed in succession to k’ as is seen by simply redefining the 0-point to what was k’. Yes, every k’ we can count to or represent has transfinitely many antecedent stages traversed to reach it on such a model. Which is where the trouble lurks, as the ellipsis of transfinitely many prior stages is a structural feature. Embracing the span in a hyperreal envelope simply makes it clearer, that there is an implicit transfinite span of antecedent stages for every finitely remote k’ in the model. The model fails through the need to traverse such a transfinite succession in stages. We are only warranted to discuss a finite temporal-causal past of cumulative successive stages to now, including if one goes beyond the big bang for our sub-cosmos. Begging the question by asserting or implying the traverse as already completed simply fails to address the issue. The issue of successive, finite cumulative causal-temporal but transfinite traverse is not going away. KF
KF, you ask, “VL, are you aware of non-standard analysis?”
Yes.
Here are my questions to you. Can you answer with Yes or No?
KF asks:
I don’t know, KF. And that’s the point. Neither do you. Nor does anyone. There’s no way to know.
WJM
I think I pointed out the basic problem above. God has created a world where if you are seeking God you will find Him, if not seeking you are never forced to find Him.
Myself, and apparently others on this string, have no problem coming to a clear understanding that there is a physical world here and that world reflects its creator.
An interesting thing happened as I headed toward baptism at age 49.5. The world suddenly changed. Actually the world did not change 1 iota, I changed in how I saw it. Basically everything made sense, even your stubbornly holding on to your idea.
I recognize that I can never change your ideas, only you can do it. I can offer you an experiment to do. Honestly ask God to reveal Himself to you. You will be surprised how quickly you will get an answer.
Of course the answer will not be a booming voice or writing in the sky. I suspect it will be an unexpected situation in which you will know you have to make a choice. You will know that this is a totally free choice. You will know that it will affect the rest of your life.
Go for it!
GCS,
I fully and completely believe that what you have written, you experienced.
Long ago I did exactly as you asked – not once, but continuously over time, with an open mind and heart. I had a complete change of perspective. Everything in my life changed for the better. My life became an ongoing series of miraculous events, many of which would be unbelievable to most people. Tragedies turned into triumphs. The design of my life was – and is – clear to me. I didn’t know such love, joy, and happiness existed. It can only be described as divine. This has been my life for decades now. I marvel at and enjoy every aspect of my life. I feel completely fulfilled, yet still excited and enthusiastic for what is yet to come.
I am happy you found this in whatever way you are experiencing it, brother (or sister).
Viola Lee,
Are you also familiar with Professor E. McSquared’s Calculus Primer?
-Q
I looked at the link you sent, but no, I’ve never seen the actual book. I hadn’t heard about it until I followed your link. As I said above, I feel strongly that we need to make the concepts of calculus engaging, and not just fill a course up with mechanics without a sense of human importance.
William J Murray,
Yep. And glad you asked!
Here’s what the Bible describes at the start of the Gospel of John:
“In the beginning was the Word [the Greek word here is Logos, which includes a word, communication, perhaps a concept, and our word logic is derived from logos–in other words information], and the Word was with God, and the Word was God. He was in the beginning with God. All things came into being through Him, and apart from Him nothing came into being that has come into being. In Him was life, and the life was the Light of men. The Light shines in the darkness, and the darkness did not comprehend it.”
Jesus is described as the living Word of God. Imagine that!
-Q
Viola Lee,
Just trust me and order the book from Amazon (use the link I provided). You might be able to use at least part of it in your classes and your students will love it!
Incidentally, I once met the author, Professor Swann. He was as funny and delightful as his books.
-Q
VL,
why do you wish to impose as a prior, that we confine discussion of what an infinite actual past means, to a particular structured set R mileposted by its subset Z that — per 4 years of discussion now — is likely to be conducive to misunderstanding?
My eventual recognition of the import of R* in general
. . . starts from discomfort with how we treated what turns out to be a subtle but pivotal structure, the ellipsis of limitless or transfinite or immeasurable or unbounded extension, . . . etc.
There is nothing wrong, suspicious, deceptive, misleading or confused and dubious with considering a set in its wider, acknowledged, reasonable, wider context, here, the hyperreals.
My point has been that there is a lot hiding in the ellipses or arrow points on axes etc, which turn out to be a key part of the filling in the details on the import of R mileposted by Z. And in particular, the result of counting up to some k then going on k–> k+0 [to see its import], k+1, k+2 . . . such that this clear subset can be placed in one to one match with 0,1,2 . . . implies the inherently transfinite span lying in both ellipses so that we cannot specify a final positive integer or natural counting number. Where, the use of additive inverses immediately extends to Z, with k’ + k = 0 defining k’ as -1 * k. In that light, . . . , k’-1, k’, k’+1 . . . -1, 0, 1, 2 . . . will draw in the same structure of transfinite extension as we saw for k. Every particular integer we count to, construct or symbolise, k or k’ is bound by onward values R-ward or L-ward as appropriate, values that extend beyond any onward finite case we similarly put up.
By referring to R* (or more or less isomorphically the surreals, let’s label S*) we can draw on wider thought so we can think more clearly. There is nothing pernicious in that, so I have no reason to take your stipulation as reasonable. What that span allows is then thinking of H’, additive inverse duly extended to the transfinite hyperreal, H. So, we go (with n for now) in a model timeline counted by causal-temporal, successive, cumulative stages:
. . . H’-1, H’, H’+1 . . . [ –//– ] . . . k’-1, k’, k’+1 . . . -1, 0, 1, 2 . . . n . . . –>
Notice, I added a structure showing a transfinite span, showing that from H’ we cannot count up in steps to k’. 1/H’ of course is h’, a number closer to 0 than any 1/k’ on the L-ward side. That reverts to the full structure R*. As well, say H is even, H’/2 is in the ellipsis after H’+1 but still we cannot bridge into a stepwise count up to k’. Transfinite traverse, explicitly shown, is impossible.
The problem is subtler, the ellipsis L-ward from k’-1 is standing in for the transfinite span also. That it is implicit does not make it any less real. And that is my core objection to the idea of transfinitely many stages antecedent to k’, all only finitely remote from 0. The insertion of finitely remote, for any k’ whatsoever, implies the onward structure, which is transfinite in span.
Where no causal temporal stepwise succession will span the transfinite.
Thus, my conclusion that we can only properly discuss a finite causal-temporal past of finite stages, years for convenience.
The observed causal-temporal order and its quasi-temporal antecedents if any are inherently finite in the past, per the logic and quantitative structure of such succession of stages.
This of course embeds the temporal in the eternal, whatever such turns out to be structurally.
KF
WJM, that’s strange, through the window of consciousness we experience a palpably independent world manifestly different from dream-worlds, day by day. We have good reason to accept it went on before we were born or even before there were any humans, and when we go to a funeral we accept that it goes on after we die. Not to mention, many of us acknowledge the distinction between our inner selves and our outer bodies that is severed at death, leading to the disintegration of the latter. It seems to me there is very good reason to see both minds and bodies, in a world that our bodies are definitely part of. Using distinct identity, required characteristics of mind are distinct from brains as computational substrates but the two interact; we are back at the Smith, two-tier controller cybernetic model, with perhaps a quantum influence interface. I think we come close to grand delusion if we try to deny one or the other; that which makes grand delusion probable so undermines credibility of reasoning that it becomes self-referentially absurd. The balanced middle way is to accept both, while using comparative difficulties to understand that in every view there will be difficulties. KF
WJM,
A few more meta-questions:
1. If MRT is correct, then why are the majority of its occupants (algorithms) misled by it’s very nature to accept a false (and more complex) picture of what MRT is?
2. Does #1 affect the probability that MRT is correct? (Does it at least lower it?)
3. In what other areas of philosophical inquiry has MRT misled the majority of its occupants?
KF’s answers, in shorter form:
“KF, are you willing to talk about this topic [the nature of the past] in reference to the real number line only?”
KF: “No”
“Or will you only discuss this topic when it includes the hyperreals?”
KF: “Yes”
When Querius asked the original question, he made it clear later that he was not talking about the hyperreals. I don’t think any of the traditional mainstream proponents of the “no infinite past” argument were talking about hyperreals, especially since hyperreals were just conceived about 60 years ago.
Therefore, I’ll move on and consider the discussion closed as far as I’m concerned.
KF,
I’ve addressed each of these points many times, so I don’t think there’s much point in going over it all again.
I’ll focus just on this:
If you have a critique of hypothesis X, then you must refer only to entities which exist in X. When you bring in infinite numbers, you are no longer talking about X, but Y.
Sometimes I wonder if you just think we’re exceptionally dim and won’t notice this chicanery. This is sort of like the dishonest mechanic who squirts oil on your shocks in order to convince you that you need new ones. Nothing personal, but I try not to engage in any underhanded debating tactics and would appreciate some reciprocity.
VL,
explicit address and implications of the context of discussion are quite different things.
What you clipped off in your attempted summary is the reason why I point to that issue.
DS
Yes, we have had exchanges.
I am not committing chicanery (that is an utterly unwarranted personality), but it is clear that absent major developments there will be no agreement.
I note that my very point is that there is the implicit transfinite in the discussion on reals, so it is reasonable to point to the wider context that allows us to see the issues more clearly.
On logic of dealing with issues and paradigms, can I point out that the rise of modern physics could never have happened if there was a constriction of discussion to terms used in C19 classical physics? this example should suffice to show that imposed datum lines can frustrate discussion.
KF
Hi Dave.
You quote KF as writing, “Embracing the span in a hyperreal envelope simply makes it clearer, that there is an implicit transfinite span of antecedent stages for every finitely remote k’ in the model.”
But there is nothing “clearer” or “implicit” about any this. The hyperreals, by definition are numbers that are larger than any real number. Therefore, they establish what KF wants to be true by, as you say, changing the conditions of the topics. All his long-winded explanations are unnecessary, and don’t establish anything. His argument is, “If you consider the hyperreals, I am right.” My response is, “And if you don’t, you are wrong.” KF can only be right if he includes the hyperreals, so that is what he must do.
This has been instructive: Thanks for cluing me in on how what I thought might be an interesting discussion was likely to go, as it did.
Viola Lee,
Yes, that’s about the size of it.
VL, ponder, please, the ellipsis as a structural feature of the reals mileposted by Z, as was already pointed out. What is that telling us on what goes on beyond some large k or its additive inverse k’. That is where the problem is, there is no k that is not exceeded by transfinitely many further naturals mileposting R+. The hyperreals frame all of this allowing us to zoom back and see that wider context; if you want the surreals also allow this, and are in effect isomorphic to the hyperreals in relevant form. What comes out is the reals inherently point beyond themselves. It seems to me that you are seeing R* as radically different and a needless imposition, rather than a highly relevant wider context within which R is embraced. In some ways this reminds me of debated over C. My point is once we face the import of the ellipsis, a claimed infinite past of successive stages that are causally-temporally connected requires spanning the full import of the ellipsis. That is, implicit transfinite traversal, stepwise, which is a futile supertask. KF
In reference to the reals (the integers, really), the ellipsis is just a piece of notation to represent the basic postulate that every number has a successor and a predecessor. That’s all.
Back to the magical ellipses, eh? 🙂
KF, all three of us understand the set of integers well enough, including standard notation such as ellipses.
Here’s an example to illustrate what’s going on.
I’m sure all three of us are familiar with the development and structure of imaginary and complex numbers.
Statement 1: In the real number system, every positive number has two square roots and every negative number has no square roots. This is a basic fact taught in Algebra I, and earlier.
Statement 2: In the complex number system, every number has two square roots (except zero).
Suppose person A make statement 1. Person B says no, that’s wrong, and offers statement 2.
Person A says, “But I’m not talking about complex numbers.”
Person B says, “But if you were“, you would be wrong!
Person A: “OK, if I were talking about something that I am not in fact talking about, I would be wrong.”
🙂 Seems pretty silly to me.
VL, what does succession of mileposts WITHOUT ANY FINITE LIMIT mean? KF
Good. I think taking arguments one proposition or concept at a time is good.
It means, as I have stated above, that in the set of real numbers, every integer has a successor and a predecessor.
Or a bit more formally, if k is an integer, both the integers k + 1 and k – 1 exist.
Does that seem accurate to you?
KF,
I suppose the sequence a_n = (-1)^n for n in N defines a sequence with no finite limit.
But you might be talking about sequences which are unbounded, for example a_n = n^2 for n in N. This one has the property that given any integer M, no matter how large, there exists n in N such than a_n > M. Of course a_n = n for all n in N has the same property.
Edit: I’m not sure what the point of these elementary questions is. Clearly we are all familiar with sequences with no finite limit?
Kairosfocus: ponder, please, the ellipsis as a structural feature of the reals mileposted by Z, as was already pointed out.
The ellipsis is NOT a structural feature. The ellipsis just means ‘and so on in the same pattern’.
What is that telling us on what goes on beyond some large k or its additive inverse k’.
The ellipsis is not telling us anything. It’s just shorthand for continuing on in the same pattern.
That is where the problem is, there is no k that is not exceeded by transfinitely many further naturals mileposting R+.
So? There are infinitely many reals between any two integers. In fact, there are infinitely many reals between any two given reals. You keep flinging jargon around as if you are saying something profound when you are just restating the obvious.
What comes out is the reals inherently point beyond themselves.
That is nonsensical.
It seems to me that you are seeing R* as radically different and a needless imposition, rather than a highly relevant wider context within which R is embraced.
No, that is NOT what anyone is saying. You should stop trying to ascribe greater meaning or weight to very small or very large numbers. You don’t want to consider the possibility of there being an infinite past. Fine, you do that. But don’t try and create a could of mathematical jargon in some attempt to justify your belief.
My point is once we face the import of the ellipsis, a claimed infinite past of successive stages that are causally-temporally connected requires spanning the full import of the ellipsis. That is, implicit transfinite traversal, stepwise, which is a futile supertask.
This has everything to do with your beliefs and nothing to do with mathematics. I don’t know if there was anything before the Big Bang. But whether there was or not has nothing to do with mathematics. Stop trying to pretend it does.
Dave, I appreciate it that KF asked a basic question. Sometimes it’s good to establish what people agree on first. I’m hoping KF comes back and tells me whether what I wrote at 150 is accurate.
JVL, on the contrary, the ellipsis brings in the force of infinity. KF
VL, what is the implication of, that for every specific natural counting number we can count to or represent k and its additive inverse k’, we can recognise that there is onward extension WITHOUT LIMIT, one that can be matched 1 to 1 with 0, 1, 2 . . . again without limit? Symbolised, by the ellipsis? (Do you see the key factor that keeps getting skipped? The same in “succession of mileposts WITHOUT ANY FINITE LIMIT.”) KF
PS: It is fairly obvious that there is a paradigm gap here.
DS, you full well know what is being discussed in what context. Lay aside the tangents. KF
WJM,
In a sense, I regret that a seeming side issue has come up, though it is significant because it shows that a temporal causal successive finite stage domain is structurally limited in the past, establishing that a different, eternal order is root to reality. Which is of course very hard to swallow if you come from some fairly dominant current perspectives.
(That comes from recognising that true nothing, non-being, has no causal capability. So were there ever such, it would forever obtain; as a world is, something has always been, something of utterly independent, necessary being character. By contrast, circular retro-cause where the not yet somehow reaches back in order to become is again world out of non-being. And, infinite past chain runs into the implicit challenge of traversal of the transfinite in steps, the point that lurks in the secondary exchange.)
That said, I wish to again put on the table what appears at 138:
KF
Kairosfocus: JVL, on the contrary, the ellipsis brings in the force of infinity.
It depends on how they are used:
You can define the set of all positive integers less than 100 as {1, 2, 3 . . . 99}
The ellipsis only means: follow the pattern. Yes, they are frequent used to indicate continue on indefinitely but, again, the notation is strictly shorthand, a faster way of writing “continue on in the same fashion”.
Do not mistake notation for concept(s).
what is the implication of, that for every specific natural counting number we can count to or represent k and its additive inverse k’, we can recognise that there is onward extension WITHOUT LIMIT, one that can be matched 1 to 1 with 0, 1, 2 . . . again without limit? Symbolised, by the ellipsis? (Do you see the key factor that keeps getting skipped? The same in “succession of mileposts WITHOUT ANY FINITE LIMIT.”)
So? It’s just a countably infinite set. What is the big deal? It’s not mystical or symbolic or anything like that. It’s just a countably infinite set. The really interesting part is when you start realising that some infinite sets have more elements than some other infinite sets. That’s the real “WOW” moment.
This is all well established and non-controversial (dare I say) undergraduate level mathematics.
You want to use the mathematics to draw some other conclusion, you want to apply the mathematics to some situation, you’re saying the mathematics models (or should model) something else. Fine. You may or may not be right. But you’re not saying anything mathematically profound or note worthy.
JVL, the context of ellipses of transfinite extension as opposed to finite has been quite clear all along. At one point in the debate I used four dots to emphasise the contrast. That is not generally used but can be if it becomes necessary. KF
PS: JVL, the mathematics is telling us something about the structure of reality that then becomes highly significant in a causal-temporal, thermodynamic [energy dynamics constrained] world such as we inhabit. Physics is inextricably intertwined with such structural, quantitative aspects of the logic of being. A simple mathematical point can have most profound physical significance as say key conservation laws bring out. Laws of that order pivot on x1 +y1 . . . z1 = x2 + y2 . . . z2, utterly simple algebra but powerful physical import. And, you full well know or should know this.
Kairosfocus:
No, it does not UNLESS you choose to try and apply the math to that situation. Which I do not think is sound but I have to say I’m not sure exactly what physical state or situation you are trying to apply the math to.
Again, you may CHOOSE to try and apply the math but it doesn’t mean the model holds.
What does that even mean; “Laws of that order pivot on . . . “? You just set up an equation with six variables and some ellipsis on either side for some reason. If your pattern is x then y then z would follow and you should just write “x1 + y1 + z1 = x2 + y2 + z2”.
You are conflating math with an application of it. If you want to talk about your application of the math that’s fine but the math exists independent of its application.
Just state simply and clearly what physical situation or state or phenomena you want to model, what math you are using and how the math maps to your situation and then we’ll see. You can’t say: because the math says this reality must follow. That’s crazy.
All models are wrong but some are useful – generally attributed to George Box.
https://en.wikipedia.org/wiki/All_models_are_wrong
KF,
I’m going to paste your comment at 157 in the new thread I created and respond to it there. I’m going to police that thread better to stay on track. This thread is irretrievable. No worries.
KF and Viola Lee,
I guess Viola Lee was right, as I thought my post addressed exactly the issue you raised. The positive integers or “mileposts in R”, when read left to right, comprise a sequence that has no finite limit.
What additional points do you wish to make about sequences that have no finite limit? What is this “key factor that keeps getting skipped” you allude to in #155? I honestly don’t know where you’re going with that. It would be helpful if you simply posted the answers to these questions. 🙂
Unguided/ blind watchmaker evolution cannot be modelled. It must not be real…
DS, enough has already been pointed out. The general evasiveness tells us the real balance on merits. KF
KF, You didn’t actually answer my question at 150, but I gather you agree that the integers extend without limit in both directions, because there is also a next integer: that is what without limit means.
And since every such integer is finite, because it is just one more than the last integer, the sequence is without finite limit: there is no largest or smallest integer.
It seems that we agree about that.
However, you say, “Do you see the key factor that keeps getting skipped? … PS: It is fairly obvious that there is a paradigm gap here.”
No, I don’t see what key factor is getting skipped? I know you are mathematically literate: can you explain what is being skipped in mathematical terms.
Viola Lee,
Mathematics is an indispensable tool when matched with experimental results within specified limits, but extrapolation or interpolation based on math is not reliable. One can happily map the number line to time, but there are problems with doing so.
– The entropy problem is ignored (entropy must continually decrease infinitely as one moves back in time)
– The connection with space and space-time dilation disappears (and you must have an infinite number of unique time lines)
– Planck lengths are no barrier (there are an infinite number of distances between any two points)
– The Big Bang, cosmic expansion, and the red shift are discounted (time and space are infinite and static)
– Homogeneity is required to fit the math (stars spontaneously appear in an infinite universe)
– The peculiarities of gravity remain unaddressed and the inverse square law is enforced, even with the orbit of Mercury, for example
– Quantum mechanics is ignored, especially quantum erasure and the quantum Zeno effect
Will we will return to applying Platonic solids to orbits and concentric spheres for stars?
All of these might have mathematical beauty and symmetry, but so far, nature hasn’t been very cooperative. You might want to consider reading Sabine Hossenfelder’s book, Lost in Math: How Beauty Leads Physics Astray.
https://www.amazon.com/Lost-Math-Beauty-Physics-Astray/dp/1541646762
Also, I think Kurt Gödel’s incompleteness theorems apply here as well, since it’s very likely that more than one set of mathematical axioms will be required for describing the observed phenomena in the universe.
-Q
@Querius
You’ve been too brutal destroying all dreams and hopes about infinity.
I agree, Querius, that those are all relevant to the subject of time.
However, my interest in this topic is strictly about the nature of infinity in pure mathematics, not about the topic of what time might be “outside of” or “before” our universe, or about all the complexities about what time is inside our universe.
My interest is solely in the mathematical argument made by various philosophers, which you brought up in 51, that an infinite past is impossible. I am interested in explaining, from a purely mathematical point of view, why that argument is wrong.
@Viola Lee
I’m not into maths but if you take a point P on a line which is infinite and is considered that will never reach that infinite “end” then if you inverse notation point P will became infinite and infinite will became point P. If point P is present day and past is infinite then will have to pass a infinite time till reach point P because from infinite past “point of view” this point P is infinite but it’s obvious this point P is NOT infinite because we live/reach in point P( present) Therefore past is finite
If you consider that on a line between 1 and 2 are a infinity of integers i guess is not related to time and past infinite because is a false presupossition that you can have infinity between 2 limits, it’s a contradiction because infinity means NO LIMITS.
John, infinity is not a “place”, and a point P can’t be “at infinity”. That is the basic flaw in your argument.
Your second paragraph is confused. 1 and 2 are integers, and there are no other integers between them. This has nothing to do with our discussion, which is considering integers as representing equally spaced discrete intervals: what KF is calling mileposts.
🙂 Exactly that I said. that’s why there is no past infinite and if I understand corectly, you would like to exist at least in maths formulas .
I guess not integers but fractions or decimals .
JohnB:
None of this makes any sense.
None of this make any sense either.
Again, none of this makes sense.
Again, not even sure what you’re trying to say.
I can’t remember whether I have seen this before, but apparently Ed Feser also is not convinced by “anti infinite-past” arguments:
@JVL
Don’t worry. Read those comments you understand…
Viola Lee,
Ok. My mathematical argument would be that a number line is infinite in both positive and negative directions, but that it would simply be inappropriate to map the number line against space-time. Not all math is appropriate for all situations (such as my prior example of the $30 room being shared by three sales guys).
An analogous situation would be that for large distances from a large mass such as the sun, a 1/R function could be assigned and would have nearly the same change in gravitational gradient (!) as a 1/R^2 function. When R is close to the Sun (as is Mercury), that’s when the difference is most noticeable . . . and in fact, 1/R^2 at those distances also famously deviates due to relativistic effects.
Or to put it another way, why map a line to space-time when you can project y = tan x instead! Tangents have asymptotes that are way cooler than what boring lines have to offer.
-Q
Q, you write, ” it would simply be inappropriate to map the number line against space-time. Not all math is appropriate for all situations.”
I agree 100%.
I would love to hear how an infinite past, from a purely mathematical point of view, could be true.
On a number line if you start @ 0 then, yes, you can take the infinite journey in each direction. With an infinite past there isn’t a starting point. If you have, from a purely mathematical point of view, an argument against that, I would also love to hear it.
ET,
See @176. You could alternatively apply a circle instead of a number line to space-time. Or a tan x function. The question is, how would you choose between them?
In fact, the measured red-shift evidence points to the increasing, non-linear expansion of space-time.
Linear math simply doesn’t match the measured data.
-Q
To ET:
I offered an argument at 51. A short and slightly different version of the argument is this:
The confusion arises because what is meant by “infinite past” is unclear. It does not mean time started at “infinity”, because infinity is not a “place” from which you can start.
It seems to me that “infinite past” means there is no point at which the past started. Suppose you claim that point P is the first “moment” of the past. Since every point P has a predecessor P – 1, there would then be a moment before the start of time P, which contradicts the assumption that P is the first moment. Therefore there is no beginning to time – no first point: That is the sense in which the past is infinite.
Just thinking of the number line, this can be restated this way: every integer is a finite distance from zero, but there is no limit to how far away from zero an integer can be.
Viola Lee:
It seems to me that you can’t get here from there if you can’t get there from here.
That is a good way of stating the argument that I think is wrong.
The reason is that infinity is not a “there”: it’s not a place (that is, not a point on the number line). “Infinite past” doesn’t mean that the past started at “infinity”, which is not a meaningful phrase. “Infinite past” means that there is no starting point for time, and therefore no limit to how long time has been going on.
VL (& attn DS), more exactly, every particular integer or real for that matter as they interpolate between pairs of integers [ . . . j—j+1 . . . ], that we may count to or so bracket, k or k’ will ALWAYS have unlimited further values beyond, which by the ellipsis will be unspecified. It is that implicit transfinite span that poses the traverse supertask challenge. What keeps on being missed is that in indicating a set we have not established a means by which the relevant succession of stages in a causal-temporal, thermodynamically constrained world, can in stepwise succession span that implicit transfinite. What repeatedly occurred in the discussions is the repeated begging the question on prior transfinite traverse. That question is structural and will not go away. The “question” is actually settled in one aspect, a transfinite traverse is an inherently futile supertask, so the remaining question is whether a past countable succession of stages WITHOUT FINITE LIMIT constitutes such a transfinite. The answer is obviously yes, and thus regardless of how any particular k’ and k’-1 as well as the continuum between [ . . . k’-1 — k’ . . . ] may be exceeded onward L-ward by k’+2 . . . (so being finite), the structure exposed by the ellipsis indicates the transfinite span to be traversed. I therefore turn around the idea that any particular specific k’ in the past as label of a stage in the succession to now is manifestly finitely removed, to the point that once we discuss actual stages countably removed from now, they will all be at finite span from us — that is trying to tell us something. We are only warranted to speak of finitely removed actual past stages and a transfinite succession to now is an implicit traversal of the transfinite, leading to failed supertask. The actual past is limited, is finite. KF
F/N: The underlying significance of this lies in a context, which we need to briefly ponder.
It is patently indefensible to try to pull a world out of utter non-being as that has no causal capability. Circular retrocausation is the same. So, as a world is, SOMETHING of independent character always was, there is a reality root. The issue is the nature of that necessary being.
As is now commonly touted, there is a sub-cosmos fluctuating up from an underlying quasi-physical substrate model that has been promoted in part to evade the import of the indications of a beginning at a singularity usually estimated at 14 BYA roughly. Yes, there are other reasons, but this aspect is definitely there, just look at discussions of “nothing” recently made by Physicists and those who picked up on their remarks, publicly embarrassing themselves.
The key issue is, such a subworld is quasi-physical and has causal-temporal succession of stages of finite duration; which can be counted bringing to bear the structure of the number line and sets tied to it.
Notice, the numberline and its extension are antecedent to the sets we frame on it, it is the underlying observed mathematical fact we try to model.
The integers and reals model it, in part as we know from surreals and hyperreals that there are transfinitely large and infinitesimally small numbers. Notice, the resistance above to that simple well established fact.
But the hyperreals H and h, connected by H –> 1/h = h, closer to 0 than 1/n for any specified counting number, unifies. In fact 0 is surrounded by an infinitesimal cloud, *0* and any real can be vector added with that cloud to yield r –> r “+” *0* –> *r* (and by direct extension we similarly get *H*). Similarly, [0–1) as a continuum interval can be interpolated between any successive integers, there is a pervasive continuum. Bring in additive inverses and the L/R directionality is clear. The number line as antecedent fact is rich, richer than we can fathom.
There is no good reason to truncate our view of the number line at the level of the reals. It may be helpful to use that frame for some things but it is not an ultimate structure beyond which all is forbidden or frightful and it is equally plain that R is fuzzily bordered, as is Z which mileposts it. In many ways, insert a Schnitt to identify continuum and there is no definable nearest neighbour. Any r has a fuzz of infinitesimally altered values closer than we can get on using reals, *r*, and beyond any particular k we find k+1 . . . where the ellipsis is seen as structural, telling us extension beyond any definable value symbolised by k.
The reals, integers and naturals inherently point beyond themselves, they scream; we are only part of the big picture lurking in that seemingly simple number line.
The problem is, this is terra incognita for many. As a matter of course, our education invited us to conflate R and the number line. But, manifestly, the line is the antecedent fact and has much more than R in it.
That is the paradigm-shift incommensurate leap that has to be spanned. Which is admittedly hard.
One of the consequences is, once we see this picture we recognise that R and its mileposts Z, have indefinite extensions pointing to the transfinite hyperreals. Whenever we put up a specific milepost pair k/k’ we see beyond k+1 and its complement k’-1. Then more beyond these. The transfinite fuzzy border emerges. Likewise counting inwards to 0 from H’ we see a similar transfinite count, due to the structure of the naturals. So, we are back to:
. . . H’-1, H’, H’+1 . . . [–//–] . . . k’-1, k’, k’+1 . . . -2,-1,0,1, 2 . . . n —> . . . k,k+1 . . . [–//–] . . . H, H+1 . . .
The bolded is what we have been talking around, and the point is that we can label stages, reflecting the successive structure and causal dynamics of succession. The ellipsis immediately L-ward of k’-1 is inherently transfinite and CANNOT be traversed stepwise.
In short we now see that advocates of evolutionary materialism and fellow travellers are forced into the corner of defending an implicit transfinite, already completed succession of stages connected causally-temporally, thus thermodynamically. The difficulties involved, though they will sidestep them, are plain.
All of this points instead to a different order of being for the required reality root, world zero we can suggest. One, that is eternal.
The Eternal — the I AM — beckons.
Which is the root worldview, plausibility structure issue.
KF
KF,
Like Ed Feser and David Snoke. 🤦
F/N: What I can find of Feser in his own voice http://edwardfeser.blogspot.co.....lam_2.html KF
DS, as you know from several years of discussion I spoke specifically to an identifiable cluster involving people like Krauss and Dawkins etc. as well as those who tend to go along though they may nominally be theists, pantheists etc. Feser is a Thomist, Thomas Aquinas set aside the problem of transfinite causal succession in part as the issue then becomes trivial. Snoke, I hardly know about, but it would not surprise me that the issue of the wider number line and the in context import of the transfinite ellipses has not been thoroughly addressed by him; if I am wrong, kindly provide details and/or links. My concerns on the number line — notice, an antecedent fact of mathematical experience . . . have independent standing, the line is clearly antecedent to R as we have modelled, and R inherently points beyond itself, where Robinson’s rehabilitation of infinitesimals brings back the millennia of cases where they kept popping up even in classical geometric thought, much less the emergence of Calculus in the 1600’s. With Newton’s famous h structurally and logically comes H = 1/h, that matter is settled and R’s mileposts Z then enter as showing us that R is a fuzzy-bordered set built up from finites but structurally embedding transfiniteness (shown by the ellipses) thus pointing beyond itself. We face h smaller than 1/n for any n in N, and so too H greater than any specific n in N. This is antecedent to going N –> Z –> Q –> R. R is part of the wider number framework since what, Archimedes and his bouncing around edges of Calculus, among others. In that context, the futility of transfinite traverse in stepwise cumulative . . . thus, causal . . . succession is readily manifest. As for how heat death is to be evaded on such models, it is looking a lot like there is an implicit appeal to infinite material scale for at least the wider sub universe. Where are the observable signs of such? KF
@ViolaLee
When we talk about past time (like yesterday, last year, 500 BC) we connect at least 2 dimension together :time+space. Could exist a past time without involving space?
You are right, the infinite is not a space because cannot exist inside a spatial system.
The infinite don’t have a quantitative but a qualitative significance.
You said : infinite don’t have a spatial dimension
Psysics said: spatial dimension is always welded together with time dimension.
I said: the infinite cannot be related to time so infinite past is a mish mash,hotchpotch,gallimaufry.
KF,
Apparently the infinite-past-proponents haven’t heard their screams and have chosen to stick with models in which time-points or “stages” are separated by finite intervals.
I mean, just because the hyperreal (and surreal) numbers exist doesn’t mean we need to use them in every application. Can you imagine what would happen if I walked into a 7-11 and tried to pass an ω-dollar bill?
F/N: FWIW, Wiki, speaking inadvertently against ideological inclinations:
In the article, there is a sketch (using the arrow-tip not the ellipsis) with a telling caption:
Put that with the already highlighted:
In this context first the transfiniteness of Z mileposting R is clearly implied and we need to see that R does not exhaust the number line considered as a fact of mathematical experience once we realise that infinitesimals have been knocking on the door for thousands of years. With them come the transfinites.
Further to such, notice the real vs imaginary contrast.
Not, no there are no infinitesimals — thus transfinites — but that the sqrt – 1 and two successive 1/4 turns A/C turns x into – x implies a second dimension (opening up a world of multidimensional vectors and onward structures such as quaternions that are now popping up in computing).
Once infinitesimals are back on the table, a much wider world follows with them.
KF
PS: Wiki on infinitesimals:
Probably the infinite past proponents realize that using infinite numbers in their models leads immediately to serious problems, as you have argued for several years here at UD.
Viola Lee:
True, but the past did start @ a certain place and time.
True, but the past did start @ a certain place and time.
That sounds incoherent.
Wow, what a lot of stuff that doesn’t address the actual nature of the integers. The heart of the matter, as best I can tell, is that KF thinks that the ellipsis doesn’t just mean “there is always a next integer”, but that it represents an “implicit transfinite span”.
I think “implicit” is in the eye of the beholder. For something to be mathematically well-defined it needs to be explicit.
Back at 166, I wrote,
It doesn’t seem like KF can do this.
His solution is to turn to the hyperreals, but as has been repeatedly pointed out to him, this is not the context in which all other “no infinite past” proponents have argued.
Viola Lee:
So what? You say that as if it means something. It doesn’t.
People do NOT have to take up the same arguments as others. People are free to take up their own arguments if they think they have merit.
VL,
let’s go to basic concepts.
1500 years ago, in trying to clarify the nature of God, the Athanasian creed used a key term, IMMENSUS — not measurable, i.e. beyond finite value. This reflects, say, Isa 55 where God’s thoughts and ways were viewed as as high as the heavens are above the earth.
In Almagest, Ptolemy compares the distance of the fixed stars to the size of the earth; by comparison, a mathematical point . . . what we would now call infinitesimal scale.
The consistent concept is that of being beyond finite bound. Indeed, IN + FINITE is NOT+ BOUNDED, beyond finite scale. Am HD
In that context, let us observe the number facts line I have already put on the table above, but this time I will use FOUR DOT ELLIPSES to mark transfinite spans:
. . . . H’-1, H’, H’+1 . . . . [–//–] . . . . k’-1, k’, k’+1 . . . -2,-1,0,1, 2 . . . n —> . . . k,k+1 . . . . [–//–] . . . . H, H+1 . . . .
That should long since have been specific enough. However, to draw out further the import of such, let me do a shift right comparison [originally, I said imagine a red and a blue tape like the old computer punched tapes]:
0 – 1 – 2 . . . k – k+1 -k+2 . . . . —>
k[+0] – k+1 -k+2 . . . . —>
As was long since discussed, we see a 1:1 match of endless succession between the natural counting numbers as a whole and a clear subset from k on. Indeed, this was one of the ways to define infinite in Mathematics.
We thus see the point that not only is the whole set of counting numbers transfinite but so too is a subset from any arbitrarily high but specific k on, both have cardinality aleph-null, as in effect we can do a 1:1 transformation from k on to from 0 on, similar to 0,1,2 . . . . with 0,2,4, . . . . or 1, 3, . . . . etc. The ellipsis and the every k in N we specify has successors that can be matched 1:1 with N from 0 on, are indeed showing that infinity, more specifically transfiniteness lurks in the ellipsis.
As we already saw, H and 1/H = h bring in transfinites and infinitesimals. Thus, we can fill out the line R-ward. To do so L-ward, just bring in additive inverses.
The issue of definiteness as to what infinite means and as to how it pops up in say the von Neumann construction:
. . . is NOT the problem.
The transfinite spans are real, are facts of quantity, and by the direct implication of the 1:1 match cannot be spanned in successive actual steps. They can be projected, but that is a matter of pointing not exhausting.
And recall, we are here seeing structures on quantity that are present in all possible worlds.
KF
PS: we can expand. Take H’, and for convenience say it is even so H’/2 is also a transfinite negative integer:
. . . . H’-1, H’, H’+1 . . . . H’/2 . . . . [–//–] . . . . k’-1, k’, k’+1 . . . -2,-1,0 . . . .
Yes, H and H’ are far out in the transfinite spans, cf how the surreals construction allows very interesting constructions far more elaborate than that.
PPS: Using the hyperreals, transfinite and infinitesimal is a way to bring on the table one unified quantitative facts line so we can see where the relevant transfinite ellipses fit in.
As Dave said long ago, I am discussing X and you want to discuss Y. No one else, here or elsewhere, wants to discuss Y. That is explicitly clear.
Kairosfocus: 1500 years ago, in trying to clarify the nature of God, the Athanasian creed used a key term, IMMENSUS — not measurable, i.e. beyond finite value. This reflects, say, Isa 55 where God’s thoughts and ways were viewed as as high as the heavens are above the earth.
Nothing to do with mathematics.
The consistent concept is that of being beyond finite bound. Indeed, IN + FINITE is NOT+ BOUNDED, beyond finite scale. Am HD
So . . . .
In that context, let us observe the number facts line I have already put on the table above, but this time I will use FOUR DOT ELLIPSES to mark transfinite spans:
Why? What does that get you? What is the physical reality you are trying to model with the mathematics?
. . . . H’-1, H’, H’+1 . . . . [–//–] . . . . k’-1, k’, k’+1 . . . -2,-1,0,1, 2 . . . n —> . . . k,k+1 . . . . [–//–] . . . . H, H+1 . . . .
What is H?
That should long since have been specific enough. However, to draw out further the import of such, let me do a shift right comparison [originally, I said imagine a red and a blue tape like the old computer punched tapes]:
0 – 1 – 2 . . . k – k+1 -k+2 . . . . —>
k[+0] – k+1 -k+2 . . . . —>
What is k and what point are you trying to make? Shifting the number line accomplishes what exactly?
As was long since discussed, we see a 1:1 match of endless succession between the natural counting numbers as a whole and a clear subset from k on. Indeed, this was one of the ways to define infinite in Mathematics.
Yeah, so?
We thus see the point that not only is the whole set of counting numbers transfinite but so too is a subset from any arbitrarily high but specific k on, both have cardinality aleph-null, as in effect we can do a 1:1 transformation from k on to from 0 on, similar to 0,1,2 . . . . with 0,2,4, . . . . or 1, 3, . . . . etc. The ellipsis and the every k in N we specify has successors that can be matched 1:1 with N from 0 on, are indeed showing that infinity, more specifically transfiniteness lurks in the ellipsis.
No, you are just mapping part of the real number line to another part. So what? Transfiniteness doesn’t ‘lurk’ anywhere. If it seems all mystical and magical to you that’s just you. It’s just standard set theory to me.
As we already saw, H and 1/H = h bring in transfinites and infinitesimals. Thus, we can fill out the line R-ward. To do so L-ward, just bring in additive inverses.
Again, so?
The transfinite spans are real, are facts of quantity, and by the direct implication of the 1:1 match cannot be spanned in successive actual steps. They can be projected, but that is a matter of pointing not exhausting.
I really don’t know what you are trying to get across. We know the cardinality of the reals is ‘greater’ than the cardinality of the integers. So what?
And recall, we are here seeing structures on quantity that are present in all possible worlds.
What physical situation are you claiming to model? Please be specific. Don’t just fling about vague mathematical statements, don’t use structures you don’t need to use, keep things as simple as possible. But be very, very clear.
we can expand. Take H’, and for convenience say it is even so H’/2 is also a transfinite negative integer:
Sigh.
Yes, H and H’ are far out in the transfinite spans, cf how the surreals construction allows very interesting constructions far more elaborate than that.
You aren’t really doing anything mathematical, you are just slinging lingo about.
Using the hyperreals, transfinite and infinitesimal is a way to bring on the table one unified quantitative facts line so we can see where the relevant transfinite ellipses fit in.
‘Facts’ line? What does that mean? Don’t make things up.
Again, what physical situation or phenomena are you trying to model?
Not to derail the discussion, but am I the only one here who didn’t know that Keith Jarrett wasn’t black? Turns out his parents were white Europeans.
Kairosfocus: In this context first the transfiniteness of Z mileposting R is clearly implied and we need to see that R does not exhaust the number line considered as a fact of mathematical experience once we realise that infinitesimals have been knocking on the door for thousands of years. With them come the transfinites.
So what? What is your point? That there are a lot of numbers out there, some really big and some really small, that there are uncountable? What is your point.
Not, no there are no infinitesimals — thus transfinites — but that the sqrt – 1 and two successive 1/4 turns A/C turns x into – x implies a second dimension (opening up a world of multidimensional vectors and onward structures such as quaternions that are now popping up in computing).
Basic, undergraduate complex analysis. So?
You sound like someone who is standing outside the mathematical tent and hears a few really odd things but are unable to use them or put them into a solid context.
DaveS: Not to derail the discussion, but am I the only one here who didn’t know that Keith Jarrett wasn’t black? Turns out his parents were white Europeans.
Are you trying to be part of the problem?
VL, on the contrary, it is clear that my remarks are in fact highly relevant. Simply put, the reals etc live in a wider context that has been around for thousands of years but was only put on a firm basis about 50 years ago. That wider context allows us to see where transfinite spans appear, including therefore the significance of the ellipses of endless continuation we commonly use in say the von Neumann construction etc. The 1:1 match of 0,1,2 . . . . with k[+0], k+1, k+2 . . . . where k is itself a finitely remote successor to 0,1,2 etc, brings out that the cardinality of N and that from k on is the same, aleph null, transfinite. The ellipses of transfinite extension do mean that every finite k has successors without limit, thus we see the transfinite scale of the set. Take in additive inverses, tag relevant stages of the actual past as modelled and the claim of an infinite, step by step finite stage past [years for convenience] does entail traversal of an implicitly transfinite span. Such a traverse is an infeasible supertask and cannot be completed stepwise to now. We have good warrant to hold the temporal-causal past finite, even were there a quasi-physical subuniverse behind our own common cosmos. The use of hyperreals — numbers that are just as there as the transcendental or irrational reals that require countably infinite, non repeating cycle decimal places [they are non-rational, sums of power series] — simply allows those willing to accept it, to see this more clearly. KF
PS: Yest, the transfinite lurks in things like sqrt 2, log 2 or pi or e. Where 0 = 1 + e^i*pi, showing infinitely precise fit.
JVL,
What problem?
KF,
Infinite past proponents have wisely eschewed models which feature stages separated by infinite intervals for the reasons you mention. The question is, why do you keep bringing them up?
Dave, I knew that! I saw the Keith Jarrett Trio once when they played at the school where my son was a composition major. (My son got to play once with Dave Brubeck there also!)
To ET at 194. Sure, KF, and anyone else, is free to talk about what interests them. My point is just that what he wants to talk about is not what I’m talking about, so there isn’t much profit in trying to have a conversation, because we are not talking about the same things. I’ve learned my lesson, maybe.
Viola Lee,
Wow, I’m envious. I’ve never seen geniuses of that caliber perform in person.
Edit: Re #208: I also saw the GD and Bruce Hornsby together a few years earlier. It was an incredible performance.
Maybe not in the same category, and a different style of music, but I saw Bruce Hornsby with the Grateful Dead in 1991 also.
DS, anything that implies an unlimited extension of the past beyond any arbitrarily L-ward but finite k’ simply makes the same problem appear by implication. It does not remove it. KF
KF,
So far no one has presented a proof of this implication. I’m not suggesting you attempt it, btw.
(edited)
PS to 210:
I originally posted this:
You might be talking about this property instead: There exists m such that for any k < 0, m < k. In that case, it is true that no such m exists in Z.
But this game could be played with the hyperreals as well. Suppose I'm working in *R and demand that there exist some M such that M < x for every x in *R. There is no such M (in *R), but I could construct a system with such an M. At what point do I stop?
I’ve been doing some reading on the philosophy of time, and the nature of the infinite, and specifically on the difference, which goes back to Aristotle, between actual infinity and potential infinity.
I’ve also been thing about what ET wrote last night: “It seems to me that you can’t get here from there if you can’t get there from here”, to which I replied that “infinity isn’t a ‘there'”.
I think I can make a distinction about two ways of thing of this that might help.
A potential infinity is a sequence that can go one forever, without bound, such as movings backwards along the negative integers: k, k-1, k-2, … Such a sequence never “gets to” infinity because infinity is not a “place” that you can get to. In this case, the word “infinity” just refers to this property by which every number has a predecessor, and thus the sequence has no end.
On the other hand, an actual infinity (sometimes called a completed infinity) is an entire whole infinite set. Cantor clarified this distinction over a 100 years ago, and Zermelo formalize it in the axiom of infinity, which states (this is a simple version), that the set of natural numbers is a completed infinity. (Note well: completed infinities exist as abstract, mathematical concepts: I don’t think anyone claims a completed infinity can exist in the real world.)
So:
1. The sequence 1, 2, 3, … is a potential infinity
2. The set {1, 2, 3, …} is a completed infinity.
You can’t make a completed infinity by just extending a potential infinity. A completed infinity exists in its entirety, all at one time. You don’t assemble it piece-by-piece by adding elements one at a time.
My arguments have all been about the integers as a potential infinity, thinking of modelling time as proceeding (or having proceeded) moment-by-moment. I think ET’s comment is thinking of the integers, representing time, as a actual, completed infinity. I agree that that is not reasonable, because a completed infinity is an abstract concept that can not be actualized in step-by-step fashion. Using the language of “getting” anyplace is not consistent with the idea of a completed infinity. A completed infinity just is: it doesn’t become.
Maybe this distinction is useful.
Kairosfocus,
I’m hesitant to play with infinities, but what do you think of these ideas:
1. We do in fact traverse time intervals of {-1 . . . 1} in real-number increments, which are infinite. Next, we ask a mathematician to invert this segment for us such that -1 and 1 overlap at zero, leaving the infinity that we already traversed on either side of 0.
2. Substitute “arbitrarily large number such as googolplex” for “infinite.” The physics and cosmology of the universe as currently understood has problems with this amount of space-time.
I already mentioned the problem of entropy with arbitrarily large past and the arbitrarily large future. In the finite future, we have the heat death of the universe. With an arbitrarily large past, we should already be observing this heat death.
With an arbitrarily large past, every point in the sky should have an arbitrarily large number of photons that shine brighter than the sun, a version of Olber’s Paradox.
Olber’s Paradox is addressed by cosmic expansion as also evidenced by the red-shift, but the red-shift itself cannot be arbitrarily large, otherwise all we would see is blackness after an arbitrarily large amount of time.
-Q
@ViolaLee
Could you explain why -while infinite is not a space(true!)-you relate infinite to time(???). I thought space and time are glued together. If the infinite is not related to space also has nothing to do with time .
re 211: Dave wrote, “At what point do I stop?”
I thought of this a few days ago. If you list the hyperreals, you use the ellipsis to indicate that they go on forever. What does that imply? The hyper-hyper reals! And of course they go on forever, so now we have the hyper-hyper-hyper reals!
Where does it stop! It doesn’t! Its hyper-numbers all the way down (maybe one set for each turtle!).
Sandy, if you read up above, you’ll see that my remarks have been about the purely mathematical nature of the real numbers, not about actual time and/or space. See remark 177.
Kairosfocus: DS, anything that implies an unlimited extension of the past beyond any arbitrarily L-ward but finite k’ simply makes the same problem appear by implication. It does not remove it.
It’s clear there is no point in trying to continue this conversation.
***************…R
Re 207 to Dave. Hornsby only played with them a few years, but I have lots of concerts of those years, and other, because the soundboards are available at archive.org. The GD was spotty then – not like their prime years, but Hornsby and Garcia have said that they rejuvenated each other.
DS & VL,
I first note as you DS, will recall, that R* suitably formulated is isomorphic with the Surreals, which is maximal in terms of embracing the span of the ultra-small to ultra large. In simple terms, remember H and h are representative not sole values and can be themselves manipulated to go to bigger or smaller values. They are yardstick cases, in short.
Next, it is quite clear that the problem of transfinite traverse stepwise is infeasible, for obvious reasons discussed four years ago and as was again outlined. You can deliver a transfinite set all at once, you can point to it with an iterative process, you cannot complete it stepwise successively.
The only question remaining is whether those who assert a transfinite scale or infinite actual past really mean that. The answer is obviously yes. And playing around with debates on how any particular integer (or real embraced by a pair of neighbouring integers) can be surpasses L/R ward as relevant only amounts to, the sets are indeed transfinite. Which is what the ellipses that were made so much weather of above mean.
Even so humble a source as Wikipedia concedes the point.
Yes, there is no definable highest natural, for the good reason that if we call it k, it can be exceeded as if it were 0 all over again, as was shown. This extends, suitably modified to additive inverse k’ a negative integer.
The claim that the past, counted by stages [which specifies the succession and distinctively labels each stage], was transfinite is thus a claim to have traversed the transfinite, and it is therefore an infeasible supertask. This, one may model on paper but cannot effect on the ground by successive, causal temporal succession of finite stages such as years.
Nor is it any help to imply or assert that at every k’, the traverse was already completed. That simply begs the question (which I pointed out when you DS did it years ago). The problem is such a traverse and it cannot be done the way time works, as measured by years etc.
The past was finite for our world and for any underlying quasi-physical sub universe from which it may have bubbled up by fluctuations etc.
That is different from a necessary being (so, eternal) reality root. Where I don’t need to go over again that we do not pop worlds up out of non existent hats, including both non being becomes a world and circular retro causation.
Transfinite quasi-physical past is similarly a failure but it will be stoutly defended because the alternative opens up possibilities that many find distasteful today.
As for oh you have failed to prove, I simply note that adequacy of warrant and acceptability of said warrant are categorically distinct subjects.
KF
PS: I trust that it is accepted that infinitesimals have lurked since Archimedes or more, and that their inverses will be transfinite. Thanks to Cantor et al and latterly Robinson et al, we know how to handle such; they are valid number scales and have every right to be present on a quantities facts line, i.e. the reals do not exhaust the span, and transfinite ellipses etc are legitimate representations for such. So, to set the wider context and point to the traverses of transfinite span involved do not constitute a question begging red herring. They allow us room to widen our thinking. That is how (having been taught the standard focus on R) I came to eventually realise R was only part of the number line story. But to see that is a paradigm shift.
Viola Lee,
Interesting. I only saw them twice, both times in the late 80’s. The combination of atmosphere and music was like nothing I’ve experienced elsewhere.
KF,
If by R* you mean the hyperreal numbers, this is not true. The surreals are much larger (they comprise a proper class, whereas the hyperreals comprise a set).
Among ordered fields, that is. Time/stage coordinates don’t have to be members of a field.
Not if the process has a beginning, which it doesn’t in the proposal under discussion. For some reason that keeps getting skipped. 🙂
It does not beg any question (which would be a logical fallacy). The hypothesis is that the collection of stages prior to the present stage S_0 is infinite, where all stages S are indexed by the integers. This hypothesis happens to be hold iff the collection of stages prior to S_(-1) is also infinite, which you attempted to reframe as question-begging.
Furthermore, the hypothesis:
“the collection of stages prior to S_0 is infinite”
is equivalent to:
“For any stage k, the collection of stages prior to S_k is infinite”
or even:
“For some stage k, the collection of stages prior to S_k is infinite”
in view of the fact that all k’s are integers.
The “conclusion” you claim was assumed is actually equivalent to the hypothesis. I did not claim to be proving Q and then cheat by assuming Q somehow.
kf writes
I believe that everyone agrees with this statement, unless by transfinite you mean something other than infinite. I summarized this from the point of view of actual and potential infinity at 212 above. You cannot complete an actual infinity by successfully adding more and more elements to it.
But you write,
This is where you don’t accurately state the claim that is being made. At 180 I summarized my claim that the past has no beginning, which Dave points out is a point you keep skipping over. In terms of actual and potential, my claim is that “the past”, as modelled by the integers, is a potential infinity in that it is unbounded because it has no beginning. Nevertheless, there is no infinite distance from any point in the past until now: no “traverse of the transfinite” is being claimed.
You are arguing that the past cannot be an actual, completed infinity, and to this I agree. Nothing can be an actual infinity, other than the abstract mathematical concepts which describe them. But that is not what I am arguing. I am claiming that the past, in this model, is a potential infinity that has no beginning, and is unbounded no matter how far back from now you look. It is in that sense that the past could be infinite.
To Dave: I saw the new Dead and Company, with John Mayer on guitar, twice in the last few years. The spectacular music and magic is still there.
There are lots of high quality videos on Youtube. If interested, check this out as a sample: Shakedown Street 2017
And here’s a complete concert from 1989, one you’ve might even been at: Foxboro 7/2/89
And, indulge me here, here is the original album version of Viola Lee Blues, from 1967, that first turned me on to the Dead and jam music: Viola Lee Blues
VL, re 199, I note that a description is not an invention of whole cloth, and should not be rhetorically dismissed as if it were such. The full number line involving infinitesimals and transfinite hyperreals (and for that matter infinitesimally altered numbers such as r –> r + dr) is a compilation of facts of quantity. I simply note for record on tone, and to point out that the full span of numbers is a widely recognised reality though obviously we most often speak of N, Z, Q, R and another extended range C. You will understand why I have in the main focused on the core issue as just above. KF
VL, to claim a no beginning causal-temporal past in which finite stages succeed one another up to now is to IMPLY a completed past infinite succession. We may tag stages with successive numbers as say 2019 –> 2020, here with implication of causal temporal succession. On the no beginning past any past stage k’ had before it an unlimited number of earlier ones thus again infinite past to be spanned stepwise. KF
PS: Handy online dictionary:
trans·fi·nite (tr?ns-f??n?t?)
adj.
Going beyond the finite.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
KF, you write, “to claim a no beginning causal-temporal past in which finite stages succeed one another up to now is to IMPLY a completed past infinite succession.”
No it doesn’t. I have made a clear distinction that shows that the one doesn’t imply the other, and this distinction has been acknowledged by many philosophers and mathematicians, starting with Aristotle.
In fact, the phrase “completed past infinite succession” is mathematically inaccurate and embodies the very confusion I am talking about: an actual, completed infinity isn’t produced by adding a succession of elements.
VL,
You actually admit the core issue:
I am not the one injecting such an error, it is those who propose a beginningless causal-temporal past. Without beginning means, that for every past “year” k’ there were unlimited prior stages leading up to k’. It is that unlimited prior succession of stages that — whether or not you accept it — directly implies an infinite past.
As for Aristotle, he rightly pointed out the difference between a potentially infinite but never completed succession of [finite!] steps and what states or implies such a succession has been completed. (We are not discussing limiting processes where as each next “step” becomes smaller and smaller and takes a smaller and smaller increment of time until in the end infinitesimal, so we have convergence in the limit of finite duration in finite time; which answers say Zeno.)
KF
A beginningless past extends in a unlimited, unbounded way into the past. It is a potential infinity. However, there is no point in the past that is an infinite distance from now, because all integers, no matter how far you extend the sequence, are finite.
VL,
Let’s take in reversed order as that will clarify:
>>there is no point in the past that is an infinite distance from now, because all integers, no matter how far you extend the sequence, are finite.>>
— all specific past integers k’ labelling past stages will be finitely remote from us indeed . . . do you see what this concedes?
— if for the duration d = n – k’, for every k’ is finite then d is always finite.
>>A beginningless past extends in a unlimited, unbounded way into the past. It is a potential infinity.>>
— to extend in the past in such an unbounded way implies that for every k’ we identify ONWARD there is a transfinite succession of prior stages.
— it is that which cannot be traversed. It is that which is the actually completed transfinite span.
KF
*twitch*
KF, you once again say something is implied without addressing the arguments that show that implication is false, and continued to conflate a potential infinity with an actual completed infinity.KF, you once again say something is implied without addressing the arguments that show that implication is false, and you continue to conflate a potential infinity with an actual completed infinity.
It is not the case that the existence of an potential infinity implies that an infinite number of element have been traversed because an actual infinity isn’t created by adding a succession of elements within a potential infinity.
[I wonder how long this can go on? I think it’s being hard on Dave, perhaps. :-)]
Let’s try a different perspective:
KF, you believe the claim that the past is (or could be) infinite is false.
1. Therefore you believe the past is finite.
2. Therefore you believe the past had a beginning.
Are statements 1 and 2 true statements about what you believe?
Which was first :chicken or egg ,infinite or maths? 🙂
What is very interesting :we have in mind 2 abstract concepts that are beyond this universe : God and infinity .
Thanks for those links, Viola Lee. I’ll be listening to them this week. Also glad to hear the magic is still there in the present incarnation.
VL (& attn DS),
kindly notice the difference between the [timeless] set of integers as a whole and the issue of temporal-causal succession to now. The latter implies that there is an asymmetry in time, a direction of flow, a succession from one “year” to the next. As a direct consequence, going forward from any given now, succession proceeds and may well ultimately continue without onward stopping-point. At each actual successor to the relevant now, there will have been a finite succession to whatever future point has been reached and is in process of giving rise to its own successor.
There is no problem here, we are never actually at a transfinitely remote future point and potential infinity simply means for all we know succession will continue without a limit. (Such would not be our actual world under present trends; one, which is subject to energy flow dynamics and eventual heat death.)
The problem lies in the implications of claiming that no past, once now in a causal-temporal, energy dynamics world was a first stage, a beginning. Those implications have been highlighted several times but evidently because of prior assumptions on your part have been missed.
For, in a no-beginning world, the pivotal focus is not duration since past stage k’ but the import of there having never been a first stage. That is, without past limit, beyond k’ are k’-1, before it k’-2 and so forth WITHOUT LIMIT. That is equivalent to the set of naturals in cardinality and as each stage, each unit can be deemed a “one” the onward past to k’ [k’ being a negative value] can be counted up and summed up:
SUM [1_0 +1_1 + 1_2 + . . . . ] = 1 + 1 + 1 + 1 . . . . –> an utterly, manifestly divergent value, with magnitude aleph_null.
And yes, I know Aquinas apparently tried to argue that such a divergent sum is altogether finite. I am also aware that some argue that only now actually exists and so there is no actual infinity. In reply I simply ask what is the limit of the sequence of partial sums for adding one unit at a time? It diverges to value w as that is equivalent in magnitude to aleph_null. That is, we are here taking the successive cardinalities of the von Neumann construction and asking where as a completed whole we end up.
I remind:
Of course, no physical, successive calculator can complete that summation in steps to give the total, but we know where it ends.
Now, next step, let us consider the facts of quantity, the naturals and kin comprising a grand number line. Where, to distinguish FINITE gaps or traverses and transfinite, I will use four-dot ellipses for the latter. In answer to your dismissive question, to make the point precisely clear. I will connect using dashes to make it clear we are speaking to a continuum, where *0* is used to represent h and other infinitesimals, h = 1/H:
. . . . H’-1 — H’ — H’+1 — . . . . H’/2 . . . . [–//–] . . . . k’-1 –k’ — k’+1 — . . . -1 — *0* — +1 — +2 . . . k-1 — k — k+1 . . . . [–//–] . . . . H/2 . . . . H-1 — H — H+1 . . . .
This “yardstick” of scales forming a wider number line would be constructed using the surreals approach, where for example R as a continuum emerges after w steps, and we keep going on from there. H is a very large transfinite value and h is its multiplicative inverse H*h = 1. As I noted, infinitesimals have lurked for a very long time, but until Cantor we were leery of transfinites. Robinson et al allowed us to tame the problems of infinitesimals.
KF
KF you write, “The problem lies in the implications of claiming that no past, once now in a causal-temporal, energy dynamics world was a first stage, a beginning.”
I have made it very clear that I am not talking about an “energy dynamics” world. I’m just talking about the integers as a model for time passing.
Do you have answers to my questions at 233?
Kairosfocus: The problem lies in the implications of claiming that no past, once now in a causal-temporal, energy dynamics world was a first stage, a beginning. Those implications have been highlighted several times but evidently because of prior assumptions on your part have been missed.
None of us are making that claim! You keep trying to shoot down some straw man. We are just talking about the mathematics. And what you think the mathematics MIGHT model.
You don’t think the maths models the real world scenario. Fine. I don’t have a problem with that. I’m nat saying abstract set theory is a model of the real world. But you keep banging on and on and on about types of numbers as if it adds something to your argument.
Just leave it. No one is actually arguing with you. The math is independent of the world.
VL & JVL:
First, once you refer to TIME, and temporal succession, you inescapably involve energy dynamics.
Beyond that, the flow of time from stage to stage involves a logical, structured, quantitative aspect such that once we involve finite stages in such succession, there are quantitative implications. In particular, once one refers to a claimed beginningless past, immediately, for any remote past, finitely remote k’ so that n – k’ is a finite value, n + k as k’ is negative of k, then immediately the claim of beginninglessness implies that you have not actually “covered” the full duration of the past.
I think this is likely the crucial issue.
Beginninglessness means there are onward stages k’-1, k’-2 and so forth beyond any further finite limit, for every k” we may specify, count back to or represent algebraically.
Were there a beginning at some b beyond k’, we would have only a finite further span as stages beyond b would be null, would have no existence as once now but now past stages.
So, to address the magnitude of the past, as a WHOLE, we have to reckon not with just the n+k value but with the past beyond k’. Where, the case being examined is not that of a very first stage b, but where there is no such stage, there are always going to be unlimited onward stages beyond any k’ or supposed b.
That is what I showed in further detail above, and of course the partial sums beyond k diverge, equivalent to counting without finite limit. From von Neumann’s construction as shown and uncontroversial the resulting scale is aleph_null in magnitude.
A past without a beginning is transfinite and traversing it to now would be a supertask that fails.
Where, JVL, there actually are people who have proposed a beginningless past and indeed an infinite one.
The problem I have perceived is a have the cake and eat it too attempt. Denial of a finitely remote beginning, while imagining that as once we specify a particular remote past stage k’ then the duration to k’ is finite. The next step is to fall into an error of omission and composition: to select a k’ is to imply an onward prior succession to k’ without past limit.
That fails, for reasons shown.
Shown, not merely believed and not merely tilting at an imaginary strawman.
Can you answer my questions in 233, KF?
Dave, my last input. If you are someplace where you can listen while you work, here’s a famous concert from 1991 with Hornsby: 6/17/91 at Giant’s Stadium
This is a high quality video and a great concert. Good shots of Hornsby playing at 1:25:50 for a while. I saw them just one week after this.
I know that I am totally indulging myself, but I had never watch the video of 6/17/91 above, but I am enjoying the heck out of it today. Start at 1:05:00 and watch a great 45 min sequence. Also, at 1:30 Hornsby switches to accordion!
Kairosfocus: Where, JVL, there actually are people who have proposed a beginningless past and indeed an infinite one.
Fine, whatever. You don’t agree with them. I’m not saying I agree with them. But that is a completely separate issue from the mathematics.
What we don’t understand is you continually and overwhelmingly trying to argue against something none of us on this forum are defending.
And, no matter what, none of that has anything to do with transfinites or hyperreals or any of that. Bringing all that up only obscures the point you are trying to make. I think.
IF the universe is not cyclical then there cannot be an infinite past.
IF the universe is cyclical then the question is trickier.
But we don’t know which of those scenarios is true so we cannot even begin to decide if there is an infinite past. End of.
But also, we cannot argue against an infinite past based on the mathematics because there is no reason to assume the mathematics of set theory can be accurately applied to the history of the universe. Set theory was not developed to answer any questions about the universe. So there is no reason to suppose it reflects reality whatsoever. So stop arguing about what the math says. Argue about the universe and its history. That’s fair.
KF,
Not true. A supertask is a countably infinite sequence of tasks occurring in a finite amount of time. (from Wikipedia and SEP)
Thanks for the link, Viola Lee, I’ll check it out.
Why? There is no diference between a non cyclical and a cyclical universe both are related to a certain finite past. If the phrase contain the word “universe” or “multiverse” that phrase must not contain “past infinite”.
Maths can have how many past infinite you want but that have nothing to do with the reality of our universe.
Good morning, KF. I’ll bump 233 down here:
KF, you believe the claim that the past is (or could be) infinite is false.
1. Therefore you believe the past is finite.
2. Therefore you believe the past had a beginning.
Are statements 1 and 2 true statements about what you believe?
Could you answer just yes or no first, and then explain if you wish?
@ViolaLee
🙂 you soon gonna reach 1/2 infinity with messages.
VL & JVL,
The focal issue has to do with the meaning of a past without a beginning, where every stage of the actual past has to have once been the now, succeeded down to the current now and continuing onward. Such a past means that for every k’ we specify that is finitely remote, d = n – k’ = n + k, WE HAVE AN ONWARD SPAN k’-1, k’-2 etc without limit, not reckoned with.
The claim that z is a potential infinity not an actual one meets the point that we can identify its overall magnitude, aleph_null. That is its order type is w, of magnitude as just noted. What we cannot do is traverse it by successive steps of counting from 0 then in effect taking also the symmetry of the negatives. (This is of course the precise challenge of traversal of the transfinite.)
Now, the point further is, that it can be easily shown that certain core quantities forming structured sets will be present in any possible world, thus this actualised one. In particular, N, Z, Q, R, R* and . by extension C and C*. So, JVL you err in your doubt regarding relevance to this world.
If a world W has a distinct identity from a close neighbour W’, we can partition W as {A|~A} and find quantities and onward structures inherently present, these are necessary, world framework entities. To see a point, try to imagine a world without two-ness, thus distinct units, so oneness; or one in which such has ceased from being. Such suggested worlds are impossible of holding distinct identity. See here.
So, I must reject your doubt regarding relevance. Wigner’s astonishment at applicability of Mathematics pivoting on such quantities has a fundamental, reality root level answer. There is excellent reason to expect these quantities and structures to be highly relevant to this and any other world.
In short, you have laid out a further breakdown.
The magnitude of a beginningless past of finite, causal-temporal stages, then leads to evaluating the scale of the beyond k’, which is equivalent to SUM from 1 to n as n rises without limit of x_x where this value is always 1. That summation has an identifiable magnitude, aleph_null. That is a past where for every specific k” there are unlimited onward earlier stages, the whole is a transfinite span.
Such cannot be traversed in steps, so there is some b, a finitely remote first stage.
KF
Kairosfocus: Wigner’s astonishment at applicability of Mathematics pivoting on such quantities has a fundamental, reality root level answer. There is excellent reason to expect these quantities and structures to be highly relevant to this and any other world.
That doesn’t mean that ALL mathematics has a physical manifestation or application. Do we see prime number sequences in nature? Do we see infinite series in nature? Do we see Zorn’s lemma in nature?
The magnitude of a beginningless past of finite, causal-temporal stages, then leads to evaluating the scale of the beyond k’, which is equivalent to SUM from 1 to n as n rises without limit of x_x where this value is always 1. That summation has an identifiable magnitude, aleph_null. That is a past where for every specific k” there are unlimited onward earlier stages, the whole is a transfinite span.
Such cannot be traversed in steps, so there is some b, a finitely remote first stage.
Sigh. Mathematically the real number line extends infinitely far in the positive and negative directions. There is no ‘first’ step or stage or number. You can take limits to positive or negative infinity, it’s done all the time. This has nothing to do with the lifespan of our universe.
As far as we can tell, our universe can into being at one particular point a finite amount of time ago, in the past. Was there even ‘time’ before that? It seems there should be but I’ve heard some physicists say that doesn’t make any sense. It’s beyond my ken for sure.
If you think the universe was created by God then presumably God existed before that creation event. When did God come into existence? If God has always existed and always will exist then there would be no first stage or moment from that God-level perspective.
So when you say there is some remote first stage are you saying that’s when God came into existence or . . . .
JVL,
the mathematical structures, quantities and sets involved are the core of Mathematics and as was linked were shown — as was already linked — to be necessary, world framework entities applicable to any possible world including this one therefore. We are here talking about the antecedent logic of structure and quantity applicable to any distinct world, not an axiomatised logic-model framework (that is accountable to such things) that indeed may or may not apply depending on good fit.
Further to this, kindly stop tilting at a strawman caricature of the issue on the table, enough has already been shown and worked out above to show that I have used the structure of number facts that establish the narrower and wider number line to address what is implicit in a claimed beginningless past of this world and its quasi-physical antecedents said to be the sub universe in which a fluctuation started our world. The sub universe is a speculative model, used in part [I am not claiming sole motivation] as gateway to claim a quasi-physical reality without beginning. Sometimes, in recent years, it has been termed — very inappropriately — nothing[ness].
Towards the end of your comment you inadvertently reflect key gaps in current education regarding logic of being; what we are grappling with underneath the exchanges on a causal-temporal world/ source world without a beginning. Yes, the singularity points to a beginning of our causal-temporal world and beyond that we are dealing with a quasi-physical world. Did you notice how I count by stages not years save in scare quotes indicating a crude approximation? This is part of why.
The quantum fluctuation, expansion story points to a quasi-physical extension, which is causal and so also temporal and energy dynamics driven, leading to the validity of such a counting by stages. The point above is that such a world . . . in effect a remote descendant of the preferred steady state cosmological model replaced by the big bang model through the force of observations such as cosmic microwave background blackbody radiation (a quantum process BTW) . . . is itself constrained not to be beginningless by the structure of temporal succession by finite stages.
So, the physical observed cosmos began, and a speculative bubbling quantum foam subuniverse or the like also would have a beginning. These cannot credibly be root of reality.
We thus come to logic of being.
Some proposed entities cannot be in any possible world [PW]. A square circle and the like have contradictory core characteristics and cannot be actualised — impossible of being. Other things can be in at least one PW, like a unicorn likely will be within 100 years as a genetically engineered curiosity people would pay for. Similarly, a fire contingently exists on fuel, oxidiser, heat source and combustion chain reaction. Such are possible beings and contingent ones.
There is another class of possible being, beings or entities that are framework to ANY possible world and so necessarily exist in all PWs. These are necessary beings. (We already saw some, in relevant core mathematical entities and structures.)
Further to such, we have the true nothing, non-being. Were there ever utter non-being, that has no causal capability and such non-being would forever obtain. By contrast, a world manifestly is; so there never was utter non being. Something always was, the reality root, source and well-spring of possible and actual worlds. The issue is, of what nature.
First, causal and powerful. Required to be well spring of worlds.
Second, independent of all antecedent beings and not assembled from independent parts. That is, necessary not contingent.
Third, eternal (as opposed to temporal and contingent on prior entities and causal conditions). We can see this from, say, how twoness cannot not be and did not spring from utter non being. Nor, can it go out of existence, as long as distinct identity is there, anything is there, twoness obtains, fabric and framework to reality.
In that context you can see the error of conception above in speaking of a serious candidate necessary being thusly: “When did God come into existence.” The proper issue for God or for any other serious candidate NB — flying spaghetti monsters, great pumpkins and pink elephants etc need not apply — is possible or impossible of being. If possible, in at least one PW, and as framework to PWs, in all.
Yes, from an eternal God-perspective, a beginning makes sense, and from within, we can see evidence of a beginning and even get a ballpark on how long ago.
Krauss’ “nothing” quantum foam sub universe bubbling up sub-cosmi is still causal-temporal and is not a viable candidate.
WJM’s mind in which worlds exist is a candidate, I happen to believe he errs in how he has tried to dismiss the physicality of our world.
As for identifying a root-level mind with God, a key issue would be that we are inescapably morally governed through first duties of responsible reason (just look at the implicit duty appeals above) so the root reality needs to be able to bridge the IS-OUGHT gap. That can only be done in the reality root and the only serious candidate for that would be the inherently good, utterly wise creator God, a necessary and maximally great being.
That’s not an arbitrary conglomeration of characteristics, each is in fact microcosm and holographic with the others, i.e. each facet points to the others and in turn is contributory to the others. We have to deal with the whole package.
Is such an entity impossible of being? It has not been plausible to argue such since Plantinga shattered the logical problem of evil half a century past pretty nearly. Those who would dismiss face a stiff challenge.
KF
In that context,
F/N Craig here may help https://www.reasonablefaith.org/writings/question-answer/is-a-beginningless-past-actually-infinite KF
KF,
At first we were talking about X and you were talking about Y. Now you’re on to Z, α, β, γ, &c., apparently waving shiny objects to lure us away from the original topic.
PS: Here is a key clip from the just linked:
Where, earlier in the clip:
There is more but this should help to frame clarification.
I do agree with WLC that in an infinite past, there must have been an actually infinite series of events. Interestingly, he states that number of such past events must be aleph-null (and not aleph-1 or some larger cardinal).
I really don’t think I have anything else to meaningfully contribute to this thread. I’m only mentioning that so no one thinks I left for some other reason. I’ll keep reading it though!
F/N: In that context, and i/l/o the wider number line captured by R* and constructable through the surreals method, what are Z and R?
An almost simplistic fist step answer is, at root, counting numbers from zero with their property that the immediate von Neumann successor to any counting number is also a counting number, with their additive inverses are Z. This means, both that any specific counting number k is finite, bounded and exceeded, and that the number of such is automatically beyond any finite bound. Their additive inverses simply give us negative integers, with mirror image properties.
We have our mileposts. And our ellipses of unlimited continuation.
Next, ratios of integers, Q, are the rationals, then the irrationals are numbers made up from power series of rationals without recurring cycles, i.e. they are not rational. The most relevant power series are bases ten, two, sixteen and sixty, with decimal or r-al representations being compressed power series. That is, we fill in the standard continuum, with property that between ANY two distinct reals another can be interpolated, so with a Dedekind schnitt, there is no nearest neighbour, another ellipsis appears.
Beyond, we can have infinitesimally altered numbers r –> r + dr, central to calculus. Where the reciprocals of infinitesimals are transfinite as was discussed. And yes, we can with profit speak of hyper- integers and hyperreals etc. Using 1/x as catapult we interconnect the whole span.
KF
I will point out that in all those responses, KF didn’t answer a couple of simple questions about whether he thinks the past is finite and has a beginning.
JVL
Can you imagine the absolute absence of space ? Nonexistence of space is not a space full with something(cement). 🙂
Humans are equipped with a limited set of tools to understand only few things essentially for fulfilling their purpose in this universe.
When someone ask you “who made God”? you can only laugh because is like ask you “Who made God who is not made? “
KF,
You said above something to the effect that any model of an infinite past must implicitly assume “stage” coordinates k such that for every m in Z, k < m. That is, stages at infinite remove from the present.
I haven't seen anything approaching a rigorous argument for this, just vague claims that this or that is not being "reckoned with".
Do you have an argument that you believe would be fit for publication?
PS to my #260:
If you did have such an argument, it would likely be the most significant development in the philosophy of time of the last 50 years (and perhaps ever). That’s one reason I’m skeptical.
F/N: What about, what does it mean to be eternal and what is eternity?
This one is hard, but may most profitably be addressed through logic of being informed by possible worlds, thus the issue of a root of reality. That is, as a first idea, eternity is the domain of the necessary being world root and it is the root world, the one from which others can or do come from. It is in that light that we can see the issue of framework for all possible worlds.
Beyond this, there are many ideas, in philosophy and in theology or even in popular thought. Those come later.
KF
DS, we have already seen why for the claim of a beginningless past in a causal-temporal finite stage* successive world, first the beginninglessness implies a past of scale aleph_null, then as stepwise traversal of the transfinite is not feasible, that is an infeasible supertask. The past of this causal temporal world and the suggested quasi-physical sub-universe behind it, was finite. KF
PS: Duration, as stages, e.g. “years.” This sets aside the zeno paradox type situation where we have infinite series that converge in finite time, as calculus demonstrates.
VL, I did not answer as to personal belief precisely because I SHOWED why the past of a stepwise successive, finite stage causal-temporal world that is actually without beginning would be of transfinite duration. From that, as we know that a transfinitye stepwise traverse cannot complete, this is not a valid model of the actual past. The past, as was thus SHOWN, is finite for our world and for a suggested quasi-physical subuniverse behind it will have been finite, i.e. there is a finite bound that marks a beginning point. KF
DS & VL, kindly see 236 above inter alia https://uncommondescent.com/intelligent-design/the-problem-with-most-theological-doctrines-and-the-theological-argument-for-mental-reality/#comment-715253 KF
KF,
Agreed.
I disagree. There are no “supertasks” involved here. There are sequences of infinitely many tasks/events occurring over an infinite interval, and the possibility of that is exactly the issue in question. The claim I’m interested in is that one can show that such a scenario is logically and/or mathematically impossible, à la Mr Bencze.
JVL:
Question-begging.
An infinite past is incoherent. And it appears that only word salad can try to save it as a concept.
🙂 What a joke. Proponents of infinite past just mix together real time and maths concepts make an illogical stew and are very prouds.
It is KF mixing together real time and math, I think, not those arguing about the possibility of an infinite past. I certainly am not doing that, and have made that clear, and I don’t believe Dave is doing it either. Also, I think JVL has been clear about that being two separate issues.
Sandy,
For my part, I’m just responding to folks in the anti-infinite-past camp. They make semi-mathematical arguments against it, some of which are clearly flawed. Someone has to stand up for the truth. 🤷
VL, have you seen my response to Wigner, here? How, specifically, is that not applicable to addressing traversing a finite stage, stepwise, causal-temporal collection of stages? KF
DS, it is uncontroversial that we cannot traverse a transfinite span stepwise in finite stages. KF
ET @268,
Or to put that comment another way, if God created time, then what happened before God created time? If God created space, then where was God before there was space? And if God created white beards, was he beardless before that? : P
-Q
Re 273: Absolutely true. It would be nice if you could distinguish our acceptance of that (and not keep repeating it) with the claim, which we are making, that a beginningless past does not involve “traversing a transfinite span”.
KF,
It is in fact controversial. Otherwise no one would be debating the possibility of an infinite past.
Do you have a source for this claim, btw? Where the traversal is beginningless of course.
Hi Dave. You and I just said contradictory thing, perhaps, about KF statement that “it is uncontroversial that we cannot traverse a transfinite span stepwise in finite stages”, but I think we’re on the same page. Here is a summary of what I’ve been saying. Perhaps you can let me know if we are seeing things differently, or not. Thanks.
1. KF’s statement says that if two numbers on the real number were an infinite distance apart (a “transfinite span”), then you couldn’t “traverse” the span: that is, you couldn’t go step-by-step through a sequence of integers to get from one to the other. I think this is true.
2. However, there are no such points! All points on the real number line are a finite distance apart, so there are no “transfinite spans.”
3. In particular, a beginningless past doesn’t produce a “transfinite span”. A beginningless past means that there is no limit to the points in the past, but nevertheless every point in the past is still a finite distance from now.
4. Therefore, KF’s claim in 1. above doesn’t apply to the situation of a beginningless past.
5. I have tried to clarify the conclusion by contrasting a potential vs an actual, completed infinity
5a. A potential infinity is an unbounded sequence that can go on forever, such as the integers in either direction. These are what we’re talking about.
5b A completed infinity is a set-theoretical concept of the entire set. It is not, and can not be, created by successive additions to a potential infinity.
6. This is where KF is confused by conflating these two ideas, as if somehow a succession of integers could span out to the “end” of the entire set, which is a meaningless concept. KF is saying that we can’t complete an actual infinity through a series of steps, which is true, but infinite past proponents are not making that mistake. Saying that the past is beginningless is not the same thing as saying the past is a completed actual infinity.
Viola Lee,
I might have misunderstood KF, but I thought he was talking about a situation like counting upward through all nonpositive integers. And where the “span” of this set is infinite in the sense of being unbounded.
If you tried to count “downwards” from zero through the negative integers, you would have a potential infinity- an unbounded set. You could never complete the counting, and you would always be a finite distance from where you started.
However, you can’t turn that around and count “upwards” because there is no specific starting point – no beginning – to count upwards from.
Does that make sense?
Don’t forget that, unlike a number line, time can either expand or contract. Some guy named Einstein said something about this regarding gravitational fields and velocity. So, you could go back a finite amount of time, but you might have to traverse an infinite amount of time to get back to where you started if time (actually space-time) starts expanding. Hmmm.
-Q
Viola Lee,
Certainly I can’t count through all the nonpositive integers in increasing order. But the infinite past hypothesis posits that there are infinite sequences of events/stages which can be indexed by the nonpositive integers, where temporal order corresponds to the usual order on Z. I don’t think we can refute this hypothesis using only math or logic. I also don’t think it can be refuted using the same premises that show it’s impossible to traverse an infinite sequence of events which does have a first event.
Q, we are not dealing with the micro-view of time, where relativity is relevant and time is relative to observers moving in different frames of reference. We are dealing with a cosmological, energy dynamics driven view that addresses the origin, development and roots of the cosmos, said to be about 14 BY old. KF
DS & VL,
Kindly, look at 236 again. At each point where one ponders n now and looks back to a k’ in the far past (actually, beyond the big bang) one is by selecting that k’ immediately partitioning the past into two zones. First, the finite span d = n – k’ = n + k. Second, the onward, UNLIMITED span beyond any such finitely remote k’ i.e. k’-1, k’-2 etc without limit, let us call this o.
The magnitude of o, as shown above, is that of a divergent series equivalent in successive partial sums to the von Neumann construction of the naturals. The relevant scale of o is therefore aleph_null. As a consequence, the duration of the past on a beginningless model is d + o which is aleph_null, transfinite.
Yes, there is a property that once we select any two specific integers, the interval between them is finite. However, there is the further property of unlimited succession of integers “outward” from 0. In the case of n, those would be future times constituting a potential infinite in the sense of unlimited continuation. However, there is an asymmetry with the past, as each past stage had to once have been “now” and then was succeeded by an immediate, causal-temporal successor in the chain to the current stage.
It is that requisite that forces in the d + o sum in pondering the magnitude of a beginningless past. It is transfinite and not feasible of traversal in stage, next stage, following one etc steps.
To see that, let me exploit the construction of Z from N, by augmenting with additive inverses, so the sets Z+ and Z- are mirror images of the same scale, aleph_null.
Begin from 0 and count forward in steps to k, the span obviously being k. However, again, there is an onward traverse, k–> k+1, k+2, etc without limit. This onward span beyond any finite k is of scale aleph_null, again. So, at any finite k we attain to, we have not even begun the transfinite traversal, its full magnitude lies before us. And that remains so whether we contemplate it outwards from 0 or inwards from w, order type of the naturals considered as ordered succession per von Neumann construction.
Now, just to be clear on the additive inverse mirror image point:
0 –> 1, 2, 3 . . . .
0 –> -1, -2, -3 . . . .
One to one correspondence, with same cardinality or scale.
The inward traversal from -w to 0 along the negative integers will by symmetry have the same challenge as just shown. Traversal of all negative integers as standing in as labels on past finite stages beyond the big bang as zero point, traversed stepwise, is implicit traversal of a transfinite span and cannot be completed.
In fact, traversal of a transfinite as opposed to a finite span, in finite stage steps, cannot even properly begin. One is in the position of chasing an ever receding mirage.
This is part of why we can symbolise, point to and indicate construction approach of such a set but cannot completely list it.
Given the necessary being, framework character of the relevant sets, applying in principle to the stages in succession is legitimate.
The crucial point is that we must differentiate between reference to pairs of integers labelling stages, n and k’ (which allows us to readily calculate span in stages) and the existence of the onwardness property, together with the significance of the arrow of time factor.
KF
@Kairosfocus
🙂 Of course past infinite is a logical flimflam. Would be more obvious and entertaining if you change “time” with “causal chain” to tame the savage matemathical colt.
Sandy, we have a time-cause link in a step by step chain, which is further constrained by energy flow dynamics (thermodynamics). I have emphasised finite stages to avert side-tracks into Zeno paradox debates. We shall see where this brush fire goes to. KF
🙂 Don’t worry ,Zeno was a troll.
VL,
Today is Parliament, but I will pause to comment on points, i/l/o above:
>>1. KF’s statement says that if two numbers on the real number were an infinite distance apart (a “transfinite span”), then you couldn’t “traverse” the span: that is, you couldn’t go step-by-step through a sequence of integers to get from one to the other. I think this is true.>>
Nope, I am noting that something that extends without finite limit will not be spanned in steps; this averts pathologies of logic to be discussed below.
I similarly note that if we specify any far negative k’, the very definition of integers brings in k’-1, k’-2 etc without onward limit. This is the whole forest that must not be lost sight of for the trees.
It is part of why I have emphasised that the ellipses of transfinite, unlimited extension are structural.
>>2. However, there are no such points! All points on the real number line are a finite distance apart, >>
Whenever we specify two integers k’ and n, there are unlimited onward extensions by the very definition that embeds unlimited succession.
When we contemplate causally successive stages that have been labelled in succession with the integers, there is an asymmetry. The actual past has to have actually occurred, the future is only a potential infinity.
>>so there are no “transfinite spans.”>>
Failing to notice the forest for the trees. We are interested in the whole span of the past including k’ to n which is d, finite, AND o, which turns out to have magnitude aleph_null.
Recall, to select or symbolise particular integers is to imply the onward unlimited extensions beyond.
>>3. In particular, a beginningless past doesn’t produce a “transfinite span”. A beginningless past means that there is no limit to the points in the past, but nevertheless every point in the past is still a finite distance from now.>>
The onward part is in fact transfinite by the definition of integers.
>>4. Therefore, KF’s claim in 1. above doesn’t apply to the situation of a beginningless past.>>
False, error carried forward. The problem is the onward extension beyond ANY particular past time stage labelled k’ we may choose.
>>5. I have tried to clarify the conclusion by contrasting a potential vs an actual, completed infinity>>
I note, however every stage of the past, the actual past has to have actually occurred. That is, it was once the present then was succeeded stage by stage to now, in steps. Just as, Sunday, Mrs Barrett was a nominee, Monday she was voted on and sworn in, today, she is an Associate Justice of the US Supreme Court.
>>5a. A potential infinity is an unbounded sequence that can go on forever, such as the integers in either direction. >>
counting outward from zero and defining their transfinite nature by pointing.
The issue is, the past has to have been actualised, every step of the way to now. That is where the specification of some k’ brings in the onward, prior stages that had to have been traversed to get TO k’ on a beginningless past assertion.
As noted regarding n, going forward we do have a potential infinity that will never be completed in steps
>>These are what we’re talking about.>>
Not quite, there is a missing of the forest as a whole for too narrow a focus on the trees.
>>5b A completed infinity is a set-theoretical concept of the entire set. It is not, and can not be, created by successive additions to a potential infinity.>>
Yes.
>>6. This is where KF is confused by conflating these two ideas, as if somehow a succession of integers could span out to the “end” of the entire set,>>
No, I am pointing out the implications of an actual past and that any time we specify a k’ there is an unlimited onward prior chain that would have had to have been traversed to get to k’
At no stage am I talking of ENDs but I do talk of zones or the like.
>>which is a meaningless concept.>>
Strawman, inadvertent.
>> KF is saying that we can’t complete an actual infinity through a series of steps, which is true,>>
Decisive.
Put that with the implication that every past stage (duly labelled with a unique integer) has to have been completed in succession to now.
Mix in, any time we select some deep past k’ with that label, there is an onward unlimited prior chain that had to be traversed to get TO k’.
That is easiest to see if one accepts that all hyperreals are valid numbers and labels, so an explicit descent from a transfinite hyperreal H’ to now makes the transfinite traverses — plural — obvious. See, as at 236 above (note use of integers to give unique labels to stages of discussion):
. . . . H’-1 — H’ — H’+1 — . . . . H’/2 . . . . [–//–] . . . . k’-1 –k’ — k’+1 — . . . -1 — *0* — +1 — +2 . . . k-1 — k — k+1 . . . . [–//–] . . . . H/2 . . . . H-1 — H — H+1 . . . .
However, our education inadvertently makes the reals seem more real than the hyperreals, both infinitesimals and their reciprocals (the transfinites), or even the complex numbers. So, we have to practically speaking narrow focus to the reals mileposted by the integers, noting the ellipses of unlimited extension.
. . . . H’-1 — H’ — H’+1 — . . . . H’/2 . . . . [–//–] {{{ . . . . k’-1 –k’ — k’+1 — . . . -1 — *0* — +1 — +2 . . . k-1 — k — k+1 . . . . }}} [–//–] . . . . H/2 . . . . H-1 — H — H+1 . . . .
The same result obtains, once we see the unlimited extension beyond any particular k’ we may choose.
That is built in, you cannot eliminate it by narrowing focus to an imagined succession of pairs and airily saying between every pair of integers there is a finite span. The very act of choosing highlights that you are chasing a mirage, you cannot exhaust pairwise choice, that too is a supertask.
That is, it is logically impossible to exhaust Z by selecting pairs in order to evaluate the span between the pairs. That is structural, built in.
Every time you pick a pair, boom, the onward extensions kick in, without limit.
>>but infinite past proponents are not making that mistake.>>
The mistake I am seeing is the error of missing the onward unlimited past extension to be traversed to get to k’, this leads to the chasing the mirage of exhaustion of Z by successive choice of pairs. That too is a stepwise, successive process that can be labelled in steps. It will be a potential infinite but cannot actually exhaust Z. Or even Z- plus 0 to n.
>>Saying that the past is beginningless is not the same thing as saying the past is a completed actual infinity.>>
Error, for causes as identified.
KF
KF,
Ok.
The collection of stages prior to k’ is in 1-1 correspondence with N, so it has cardinality aleph-null. Yes.
Yes.
Ok. Looking forward to a groundbreaking argument.
Inwards from w? I’m guessing the “w” stands for ω? And inward meaning ω “downward” toward 0? If so, that’s not at all like the traversal of the nonnegative integers Z in increasing order. This looks like a repeat of the “you can’t count down from infinity” argument.
Furthermore, the infinite past hypothesis does not include ω as a time coordinate (for stages/events). All time coordinates of stages are integers. ω is never “the present”, and more to the point, -ω was never “the present”.
Second to last sentence in #288: “All
timecoordinates of stages are integers.”DS, I trust my most recent above clarifies. I am using w for convenience for omega, and the directions of inward traverse to 0 are being given, as opposed to outward from 0; we cannot easily speak of descent or ascent without confusion for some; as algebraic values increase in the R-ward direction so for instance k’ is less than 0 and k’-1 is of greater magnitude L-wards but is algebraically less than k’. I trust the challenge of exhausting Z or the subset to n pairwise will help to clarify the structural challenge. KF
KF,
This is true (in the context of stepwise processes occuring in time), but irrelevant.
Dave writes, ” All coordinates of stages are integers. ? is never “the present”, and more to the point, -? was never “the present”.
That is the key point.
DS, on the contrary, it undermines the claim that VL was using. At every pairing, the onward lurks, destroying the attempt by turning it into chasing a mirage. KF
KF,
I don’t see that.
In any case, process described here:
is similar to a traversal in the wrong direction, so it’s not clear it has any implications regarding the possibility of a traversal in the right direction.
And we all understand the basic properties of the integers, e.g., for any integer k, there are infinitely many other integers less than k, and infinitely many integers greater than k. Nothing is being overlooked. We’re discussing properties of Z that a primary school student would easily understand.
Edit: The traversal in the right direction does have an endpoint: S_0 or “the present”, so there are never any mirages visible.
“All time coordinates of stages are integers”. 🙂
“All … coordinates of stages are integers.”
Actually any number has to obey certain rules to be considered a time representative.
You don’t play with numbers like they can represent anything you want.
All coordinates of stages are integers (I shouldn’t have included the word “time”).
Sandy,
Are there integers that could not be valid time (or stage) coordinates?
We can verify very easy “past infinite” theory.We build a chronometer to obey their rule … 😉
DS, the problem is real and relevant. In fact, it reveals just how intractable the problem of bridging an unlimited expanse [here the reals mileposted by the integers] is. To consider, let us fix the end point of pairing at n, now. Let us go to our general remote past number k’, marking a stage remote by d = n+k from n. Immediately we do so, there are onward stages k’-1, k’-2 etc without limit, comprising o, the onward span of stages not captured by the finite duration d. This onward span of stages o can readily be shown to have onward span aleph-null, as was shown in 236 above. Obviously k’ is representative, it can freely be extended to any value we please. Immediately, we see that the problem is general. At each time when we establish a finite span n+d to any k’ then there is an onward span o of magnitude aleph_null, in the past and prior to k’ where it is the nature of a causal temporal succession, that all stages prior to k’ (aleph_null worth) would have had to be traversed to reach to k’. This is where the transfinite traverse appears at every stage of the attempted span of durations between integers, here acting as unique labels on the claimed beginningless succession of stages. It cannot be evaded. KF
Hi Dave. I want to offer my thanks (and perhaps my apologies) for your digging into this topic again. You warned me early on about how it might go, and then you wound up getting involved again. It’s been instructive from both a mathematical and a psychological point of view. I’ll let 292 be my parting comment (with ? being ?, because my copy-paste of your comment didn’t work.) Good luck with however longer this plays out, and maybe some other interesting mathematical topic will come up here sometime.
KF,
Re: #299, those very elementary mathematical facts are true, but so what?
Viola Lee,
Thanks. I’m sure I’ll get ‘im this time! 🙂
DaveS – you’ll need an infinitely long thread to do it, though.
DS, the so what was given. The supertask is manifest. But then, any matter attached to philosophical and worldview concerns will be contentious and will bristle with difficulties, objections. the issue is balance on comparative difficulties, and enough has been put to show this. It is clear that a claimed beginningless past implies a transfinite traverse of order aleph_null, which instantly emerges every time a far past point k’ is put on the table. KF
Bob O’H,
That’s ok, I packed a lunch 🙂
KF,
I agree with some of your post. This is clearly not a supertask because of the infinite time interval. However, it is a beginningless sequence of tasks, which has its own difficulties. IIRC, WLC leaves it at that, without trying to show such a sequence is impossible.
DS, the first problem with transfinite traverse is that one reason why it does not complete is it does not properly begin. As we immediately see from addressing the representative remote past stage, k’. KF
When someone is advertise about “past infinite” through the lens of maths then those numbers have “to represent” the time dimension, for example in maths 1 is not the cause of 2,but when we talk about time -{best representative for time is the cause-effect framing}- all the numbers have to be in a causal chain: 1 is the cause of 2, 2 is the cause of 3,3 cause 4 ,etc…
Between 1 and 2 in maths are an infinity of rational numbers , in time dimension there is no number between 1 and 2 😉 because 1(mom) is the cause of 2 (child) and all infinite numbers between 1 and 2 are just nonsense in our discussion about past infinite.
In this frame there aren’t minus (-) values . Frame start from 0 when first cause manifested and we (present time )are a positive number on the line between 0 and infinite.
Kairosfocus @282,
Exactly. For probabilities to exist, one presupposes the passage of time.
– Without preexisting material objects, how could the difference between a millimeter and a light-year be determined?
– Without a preexisting periodicity, how could the difference between a day and a thousand years be determined?
According to Einstein, there’s no central clock for the universe.
– Relative time differences are profoundly relevant near the edge of the event horizon of a black hole as compared to a location on earth.
– Differences in the passage of time have been measured between atomic clocks on the earth compared to ones in high-altitude airplanes.
– According to Gerald Schroeder, the relative passage of time during the initial faster-than-light cosmic inflations (there might have been more than one) are profoundly different than what we observe on earth now.
But I understand your focus on the mathematics. Ok logically . . .
1. Can the real numbers between -1 and 0 be traversed in time?
Yes. Otherwise, we couldn’t get from yesterday to today.
2. Are the positive and negative real numbers a larger infinity than the infinity between -1 and 0?
No, they’re equal in size. If you disagree, please write the authors of this paper to let them know that they’re wrong:
https://www.quantamagazine.org/mathematicians-measure-infinities-find-theyre-equal-20170912/
3. Therefore, the infinities of the real numbers on a number line can also be traversed in time.
-Q (ED)
Bob O’H @303,
Har har!
-Q
Querius,
Didn’t we know that already? We already have elementary examples of 1-1 correspondences between (-1, 0) and R. And I’m sure KF agrees.
I think that paper is about something else.
Infinity does not exist in our universe. Nothing is infinitely large. Nothing is infinitely small. These concepts only exist in our minds. We can imagine them but can not give any examples of them.
Extremely useful but no real world examples.
The only numbers that exist are positive integers and in reality are also in our heads as we enumerate external realities. No negative numbers. No rational numbers such as fractions. No irrational numbers such as pi or e or the square root of two. No lines, no circles, no squares, no right angles.
All are extremely useful but no actual examples in reality. All make life better but are just constructs in our minds. They help us to communicate and make things. They make life better.
Introducing the possibility of an infinite past has some interesting implications. Nothing can fail to exist if it is physically possible. Just go back far enough and the odds it will happen gets to be certainty. Including this same exact discussion down to all the words, commas, periods and spaces. And an infinite number of times. How ironic!
The same thing with the multiverse. Everything is possible an infinite number of times.
So it interesting to watch discussions that seriously posits a reality for these things that don’t exist. I don’t expect my comment will make any difference since I made it before during a previous discussion on infinity. But there will be an infinite number of past and future cases where it will make a difference.
DaveS,
The paper suggests otherwise:
-Q
Jerry @311,
Yes, I agree. Platonic Idealism.
The fact that a mathematical relationship fits the data does not imply that the math is true, only that it’s useful.
And in physics, it’s sometimes necessary to simply things down to “massless elephants sliding around on frictionless ice.” You don’t want the crazy elephants breaking through the ice. Or something like that.
-Q
Jerry & Q, yes, physical near-circles etc are imperfect. However that does not render abstracta untrue or only models. Including the famous ratio of circumference to diameter. The key quantitative structures are part of the framework of any possible world, and associated constraints on the logic of structure and quantity are pervasive, indeed the root of the success of math in the physical sciences. KF
Querius,
Well, the map y = (1/pi)*arctan(x) – 0.5 gives a one-to-one correspondence between (-1, 0) and R, showing that the two sets have the same cardinality.
You’ll find a description of the “p” and “t” here. The elements of p and t are families of sets of natural numbers with certain properties.
DaveS @315,
My drift was simply that arctan is asymptotic at both ends, unlike a line. It might turn out that arctan might match some observed time function better under a new theory. Consider the non-linearity of time dilation near a black hole as another, different example.
-Q
DS,
Following up on your infinte time traversal claim, I point back to 236:
Notice, the underlying problem is again moving from any given now forward through the stage by stage next-step succession. What happens here is that whenever one attains to some k forward from a relevant zero point, the same issue of aleph-null onwardness confronts:
0, 1, 2, 3 . . . . –>
k[+0], k+1, k+2, k+3 . . . . –>
[These two sets are 1:1, connected by a bijective transformation, so they are both transfinite and of scale aleph_null. That is, we here see the well known result that subtraction of a finite number of elements from a transfinite set leaves it at being transfinite.]
That is we see continued finite stage addition but never an actual completion of a transfinite span through finite increment. Chasing the mirage yet again. The extended grand number line of the hyperreals readily shows how finite ascent from an explicitly transfinitely remote point L-ward will not reach a finite span from 0.
. . . . H’-1 — H’ — H’+1 — . . . . H’/2 . . . . [–//–] . . . . k’-1 — k’ — k’+1 — . . . -1 — *0* — +1 — +2 . . . k-1 — k — k+1 . . . . [–//–] . . . . H/2 . . . . H-1 — H — H+1 . . . .
However, as noted, our education tends to make the reals seem more real than the hyperreals, and there is a fixation on the finiteness of span between any two specified naturals or integers (and of course, reals bracketed between successive naturals). The key to seeing the wider picture, again, is to recognise the “outwards” unlimited extension beyond any k or k’, so that we see that the outward zone beyond such is of scale aleph_null. Relative to k’:
. . . . H’-1 — H’ — H’+1 — . . . . H’/2 . . . . [–//–] {{{ . . . . k’-3 — k’-2 — k’-1 — k’ — k’+1 — . . . -1 — *0* — +1 — +2 . . . k-1 — k — k+1 . . . . }}} [–//–] . . . . H/2 . . . . H-1 — H — H+1 . . . .
So, within the span of R, we find an implicit transfinite traverse to reach to k’ by ascent from the zone L-ward of k’. The same we contemplated in seeing that the span to k’ from n implied also the onward unlimited L-ward span beyond k’ of scale aleph_null. Trying to traverse it in steps L-ward beyond k’ would be a futile supertask, and by symmetry descending the same span would be similarly an infeasible supertask.
We are still left with the conclusion that for a temporally-causally successive stage world there was a finitely remote beginning.
Stepwise, finite stage traversal of an explicitly or implicitly transfinite span is an infeasible supertask.
KF
Q, yes, there is no absolutised observer in Einstein’s world and yet he and his colleagues contemplated on GTR a cosmological world with a grand time scale. This is the context of his inadvertent discovery of the cosmological constant which he put up to stabilise the fine-tuned steady state model. As you will be familiar, we routinely contemplate this in discussions of the bang and timeline of approximately 14 BY (with current physical span inferred at about 92 bn LY), we even observe H-R plots for and infer ages of star clusters based on breakaway from the main sequence to head to the Giants bands. Such clusters are of course [originally] gravitationally bound zones with a common origin and history so the bigger stars burn out first creating the breakaway point and branch to the giants branch. These turn on the Hubble expansion factor for expansion as a whole and dynamics of giant H-rich clouds collapsing into hot balls prone to turn fusion furnace emitting large quantities of light for clusters. In this sense, there is indeed an inferred cosmological scale common clock driven by energy flow dynamics in a cosmos prone to form stars and galaxies etc. KF
KF,
Yes, this traversal, which has a beginning, will never exhaust the positive integers.
Hm, well my education didn’t have that effect. Obviously the real numbers are much more familiar, but in my view, the hyperreals and surreals are exactly as real as R. The infinite-past cosmologists seem to prefer to stick with R, perhaps in part because they find it unnecessary to posit time points separated by infinite intervals. If you do introduce such things, then you are talking about a sort of “serial multiverse” which is extravagant.
Yes, if you tack inaccessible points onto the original model, you end up with an impossible traverse.
Again, we don’t need to see any “wider picture”. Everyone involved in this discussion is well-versed in the properties of R and Z. Just demonstrate that a beginningless, stepwise traversal of the negative integers, in increasing order, in time, is impossible. Then get it published and enjoy the fame and fortune. 🙂
Dave writes, “Yes, if you tack inaccessible points onto the original model, you end up with an impossible traverse.”
Great. That is a point that was constantly in the back of my mind. Posit an extension of the real number system that is by definition separated from the reals by an infinite gap, and then claim you can’t traverse it. Well, duh.
Viola Lee,
And how about the infinite real-number gap between -1 and 0?
-Q
DS, Did you notice that I highlighted the reals and that the aleph_null magnitude is of reals [i.e. integers] labelling stages beyond a finitely remote past point? I was explicitly shifting focus to the reals and to the implicit presence of a transfinite in the onward, without speaking of any representative transfiniter hyperreal. Notice, the triple double brackets. KF
What is in your head is indeed only a model. Just as is the weightless elephant or frictionless ice. The circle is only perfect in our minds so is a circle or pi any more real or true than the weightless elephant?
I came to this understanding from a paper I wrote in a college philosophy course on the nature of a number, teaching math, being in a PhD program in math and learning about the physics of the universe. Nothing I said undermines the usefulness of math or other possible models and certainly not the basic laws of physics.
All these gyrations with infinite sets or infinity are interesting and maybe useful for something but really don’t represent anything real. Just as the circle in our head does not have an actual exemplar in the world.
I pointed out the absurdity of an infinite past above as a consequence of postulating it. I have not seen any usefulness for holding it other than to give the middle finger to those who believe we live in a created universe. But I’m sure it will be ignored as people want to argue over ideas that only exist in our heads.
Does this mean that something infinite cannot exist somewhere/somehow? No, it just means within our sensory world it doesn’t exist and we can only use our imperfect/finite understanding to create what such an infinite existence may be like.
An interesting question is “are we part of an infinite existence and are unable to comprehend it?” For example if something is infinite then would it have any bound and not include our universe? Otherwise how could it be infinite if it was bounded? Of course, we may not be able to truly comprehend just what infinite means only that we have no examples of it.
Q writes, “Viola Lee, And how about the infinite real-number gap between -1 and 0?”
??? There are no gaps between the real numbers. Not sure what point you are making.
Viola Lee: There are no gaps between the real numbers. Not sure what point you are making.
Well . . . let’s just say between any two real numbers you can find another one. Which is also true for the rational numbers. In both case the average of the two numbers works nicely.
I think what Querius was saying was that there are infinitely many real numbers in the gap between -1 and 0.
Irony!!!
These so called “real” numbers do not exist in reality. They exist only in our minds.
KF,
Yes, so I guess you weren’t making such a simplistic claim as I implied.
The figure:
The issue is whether a traversal of the bolded sequence from left to right is possible.
Yes.
I can’t remember what n was, and I can’t really parse what you’re saying here. [Edit: Perhaps the descending traversal? More on that below].
Two issues:
1. It’s not a supertask. Why do you continue to use this misleading terminology? From SEP:
Anyway, when I see this term, I’ll translate to “an infinite, beginningless sequence of tasks, with an endpoint”.
2. I thought we settled this “symmetry” issue when HeKS was involved in these threads years ago. Ascending the span is not symmetrical with descending the span, and I think you agreed. We are talking about the ascent, not the descent, so let’s cease to speak of the descent.
Thanks, JVL, @325. That’s probably what Q meant. Although I still don’t know what “how about” he might be referring to.
“Aristotle said the past is infinite because for any past time we can imagine an earlier one. It is difficult to make sense of his belief about the past since he means it is potentially infinite. After all, the past has an end, namely the present, 🙂 so its infinity has been completed and therefore is not a potential infinity.”
https://iep.utm.edu/infinite/#SH4d
End of story. Absurdity remain absurdity even when talked by Aristotle.( adaptation from John C. Lennox “Nonsense remains nonsense, even when talked by world-famous scientists.”)
Jerry: These so called “real” numbers do not exist in reality. They exist only in our minds.
Perhaps not (and ‘real’ is just what mathematicians agreed to call them), BUT I did use the ratio of the diagonal of a square to a side to help lay-out the grid on an archaeological site, within a margin of error obviously! :-). And e turns out to be pretty useful as well especially in Euler’s Identity (one of Kairosfocus‘s favourite equations), some differential equations, and modelling population growth (other bases are available of course). And that pesky pi does seem to turn up an inordinate amount of times across lots of applied disciplines.
So, yes, all models are wrong but some are useful. The weirdest one for me is using imaginary numbers in physics applications. Complex analysis turns out to be very pretty mathematics.
The more we study the quantum realm the idea of discrete, countable objects gets slipperier and slipperier so perhaps the real world is less discrete than we think. If everything is just clouds of probability then how do you model that without real numbers?
I never said they were not useful. In fact I said just the opposite.
I have a background in math and physics and had a fellowship to Duke University PhD program in math which I pursued. But left to go into US Navy for a more interesting life. I decided I loved math but not the people in it and didn’t want to spend the rest of my life with them.
Joined the Navy to see the world. Got to go to 5 continents. Then got a non science related graduate degree from Stanford. Ended up seeing all 7 continents at least twice. Much more fun than math and people were more interesting.
Definitely understand the usefulness of math from basic arithmetic to partial differential equations.
Viola Lee @328,
Can one traverse the infinite number of reals between -1 and 0?
JVL @330,
Nicely stated!
Jerry @331,
Haha! Love it!
-Q
DS, there is also an infeasible supertask, which is not completed. KF
And then there was quaternions.
Q, I believe the word “traverse”, as we have been using it in this discussion, means to progress by discrete intervals, such as we might do by moving through the integers from 1 to 10. The reals are infinitely dense, so I don’t think the word “traverse” applies in the same sense. Your question brings up continuity, as opposed to discrete quantities, which is substantially different.
Sure, we move through an infinite number of reals every microsecond, if you wish, or through any infinite number of points in any spatial interval.
KF,
No, you’re engaging in dishonest debating tactics here. To an almost Trumpian degree. 😛
If you disagree, describe the sequence of infinitely many tasks accomplished in a finite time interval.
Any debate on infinity.
Will Godwin’s law be extended to Trump?
Unfortunately, we have accomplished essentially nothing in a finite amount of time.
Jerry: And then there was quaternions.
Shudder. Thank you for bringing up painful memories!
From Wikipedia: (some of the formatting predictably fails)
Nothing is infinitely small!
I have a question. Is the objective here to accomplish anything?
Yes, at least in part (contrary to what I said facetiously above). Engaging in these debates sometimes helps me clarify my own position. The inevitable tangents are also interesting for their own sake.
DS, please. When I first met the term it was precisely in the context of the INFEASIBILITY of such a task, which is why I have consistently used it in that sense. KF
VL, the issue is the reals mileposted by the integers and it is the integers labelling identifiable distinct successive stages that we have been interested in. KF
Yes, KF, I know that, and was explaining that to Querius.
Viola Lee,
Great! So since all infinities have been proved to be equal, then traversing a hypothetically infinite number line given an infinite amount of time is possible right?
https://www.quantamagazine.org/mathematicians-measure-infinities-find-theyre-equal-20170912/
I would also remind you that so far there’s been no objection to traversing an infinite amount of time in the future (currently in progress) over an infinite amount of time, of course.
-Q
Q, all infinities are not equal. There are more reals than integers: that is, the integers have cardinality aleph_null and the reals aleph_one. As Dave pointed out before, I don’t think the article you linked to mean what you think it means.
Se fgsrs fvsdv jluigu cdxf bkdfh.
Are you Latvian, Sandy? 🤔
Viola Lee,
Why were mathematicians surprised that two specified infinities were equal? My argument is that if one infinity is traversable (as you agreed), then any other infinity is also traversable.
If not, then why can we traverse an infinite future but not an infinite past? Aren’t these two infinities equal in size?
-Q
Q, you write, “Why were mathematicians surprised that two specified infinities were equal?”
Have you read at least the first part of the article you linked to? It clearly explains why the natural numbers is a “smaller” infinity than the real numbers. It also explains that the sets they were studying, p and t, were sets of subsets of other sets, a complicated topic in set theory, not just sets of numbers. It was not obvious that the cardinalities of t and p were equal, and it took some very difficult mathematics to prove they were.
On the other hand, the article shows why the cardinality of the natural numbers and the rational numbers is the same, and it’s an elementary proof taught in countless books about number theory.
You write, “why can we traverse an infinite future but not an infinite past? Aren’t these two infinities equal in size?”
I don’t think anyone has claimed we can traverse an infinite future if by traverse you mean move in discrete steps to the very end of it. We can keep walking without end into the future and we can keep walking without end into the past (thinking of this simply as meaning moving along the integers on a number line). You can traverse a potential infinity without end, but doing will never complete the actual infinite set.
You write, “My argument is that if one infinity is traversable (as you agreed), then any other infinity is also traversable.”
I don’t think I agreed to this if by traverse we mean taking steps of equal size. Yes we can move from 0 to 1 and move through an infinite number of real numbers, but that is not “traversing” in the same way as we are using the word here.
Q, there is an objection that we can span the gap between a potential infinite of unlimited succession in finite stage causal-temporally linked steps and an actualised infinity traversed in any achievable span of time. Every time we reach some k, k+1, k+2 etc extend unlimited before us. KF
“We don’t know what we want, but we do know we want something we don’t know.”
DS, the just above is also relevant to your remark above suggesting transfinite stepwise span in transfinite already traversed time. Due to the asymmetry between the actually traversed past and the to be traversed potentially unlimited future (BTW, not our heat death prone cosmos where in finite time, energy resources to fund causal-temporal processes would be exhausted . . . absent external “injection”), we must reckon with how the future is built beyond any given actual “now” point. We cannot span that gap between the potential and actual infinite. At every k* beyond some n* in the deep past, we would be succeeded by k*+1, k*+2, etc, so at every stepwise succession to and beyond such a k* we remain in the zone of finite but potentially unlimited advance. The infeasible supertask to try to span the transfinite in finite stage steps remains. Further to this, relative to our now, n, as we saw from 236 etc, any k’ in the deep past is such that the actual past (as modelled to be transfinite) would partition into the finite duration n+k = d to reach from k’ to n and the onward claimed traversed past involving k’-1,k’-2 etc without limit, o. Where o clearly has magnitude aleph_null. On essentially the same grounds it cannot have been traversed and so the model of a beginningless past implies a completed transfinite span — every attempt to pair n and a representative k’ has o beyond — and turns out to be structurally infeasible. The entity, a causal-temporal world is structurally constrained to be finite in the past and only potentially transfinite in the future. This may then be physically further constrained by potential heat death, absent external energy injections. And indeed, the steady state model at least as presented to me way back before the consensus shifted decisively had a built in low scale, unobservable energy conservation violation at cosmological level. KF
Sandy, that sounds a lot like C S Lewis and his yearned for joy beyond our temporal world, sehnsucht. KF
VL, we here tread in what is terra incognita for many. This is part of why I plead for some basic exposure to the domain shown in the wider span of numbers, featuring the hyperreals, the surreals framework and at least some recognition of the transfinite zone. The p and t equality of course is a surprising result that opens up further deep technical work, but the problem of a hole in our exposure to the domain of quantity is manifest and starts at a more basic level. KF
DS, is that what Latvian or the like look like when butchered by WP? KF
KF,
I’m pretty sure the exposure they’re getting here is having an effect opposite to what you intend. Or perhaps no effect at all, given the walls o’ text, quadruple ellipses, triple double brackets, &c. that are skipped over by most.
That snippet that Sandy posted actually looks like ‘regular’ Latvian to my eyes. 🤷
@Kairosfocus
Hmmm… Peter Kreeft , is that you? 🙂
I guess the domino(effect) is perfect image to represent time in a causal chain.
Few unescapable constraints for aplicability of maths:
1-has to be a first piece to be moved ( even we don’t know which particular piece from a “presupposed” past infinite is)
2-that very first piece starting the domino effect has to take energy from outside the system because if were something inside the system capable to start domino effect would already be started from infinity.
3- we know for sure that this domino effect will cease in the future (entropy -Big Chill 🙂 ) unless…outside the system energy is injected by the whatever caused first piece of domino to start.
Now apply the maths on this system.
Sandy,
The challenge is to refute the hypothesis without using arguments involving physics. The posts that kicked all this off claimed to show an infinite past is impossible using elementary mathematical/logical arguments that would fit on a postcard.
I thought it was from the Necronomicon.
DS, this exchange is not going to be an education in the wider number line. KF
DS, the issue will pivot on logic of being, and in particular on logic of structure and quantity. the point is, is a beginningless past inherently transfinite, though it be implicit. Yes. Is a transfinite span of finite stages spannable stepwise? No, as a potential infinite does not become an actual infinite by stepwise increment. KF
KF,
Yes, some metaphysical premises have to be invoked, particularly regarding how time works. But of course no premises that beg the question [edited]. I would add that the infinite past hypotheses does not involve a potential infinite becoming an actual infinite).
PS to my 363:
Under the infinite past hypothesis, at _any_ stage, the past is a “completed” infinite and the future is a “potential” infinite. This fact never changes.
@DaveS
🙂 Why should someone debunk what nobody can demonstrate in the first place( using 100% maths )that past infinity exist ,because time dimension belong exclusively to physics and to be translated in maths have to bring its attributes into maths world, all attributes not only one you like it(I played with google translate in latvian =ne tikai viens, kas jums pat?k. Funny!) .
You can’t use 100% maths and obtain a conclusion related to time without using time in the first place. 🙂
Sandy,
You should ask this of Laszlo Bencze, William Lane Craig, GJ Whitrow, and others who have attempted to do so!
Can you link to their alleged attempts?
DS, it was not only attempted but shown. And others have long since. Beginninglessness of a linear succession entails traverse of a transfinite, and the actual past has to be actual, it cannot merely be potential. The numbers are just labels that distinguish units, the units in succession are where the spanning would have to be. At this stage, and for some time now, I have been for cause pretty comfortable with the conclusion. What becomes relevant is how extreme and odd those trying to avoid a beginning to the temporal-causal past have to be to even be able to persuade themselves. A sign. KF
Sandy, the numbers figuratively attached to the stages simply allow us to distinguish them, the reality is in the succession of stages that would have to span a transfinite of scale aleph_null to reach here, but that is exactly the problem, aleph_null is the term for the scale of the unlimitedly growing counting numbers that cannot be exhausted by counting. Once we can fairly show the past on assumption of no beginning, would be of that scale, we can comfortably conclude it cannot be spanned in step by step succession. Those who wish to assert otherwise and try claims like the span between any two integers is finite — actually, between any two identified integers, where there will be unlimited onward succession — fail. As was shown. KF
KF,
Yes, just as I stated in #364.
KF,
Well, just about everyone believes the past is in fact finite, based on physical evidence. What I find extreme and odd are these arguments of yours—it can be an interesting challenge to parse and pick them apart, however.
@Kairosfocus
Sleight of hand . It’s same trick for children as Zeno paradox .
DS, the context as you know is Krauss et al and their sub-universe model (sometimes called “nothing”). KF
Viola Lee,
Yes, and I re-read it and stand corrected on the article.
But, going back to when you said this:
You’d already indicated that it’s possible traverse an infinity of real numbers between -1 and 0. That’s actually all I need for my infinity logic.
Imagine that I’m driving along a long, straight freeway. You drive along side me and roll down your window and yell, “Hey, have you been driving on this freeway for very long?”
“Yup,” I call back. “You’ve been watching me for the last hour.” (-1 to 0)
You answer, “Yes, I did see you traverse the freeway for the last 70 miles, but how long have you been in your car driving on this freeway?”
I answer, “I’ve been driving on this road forever.”
“Wait a sec,” you reply, “You can’t traverse infinity because infinity is not a place.”
“Yes, it’s not a place,” I reply, “but I told you I’ve been driving forever and so I’ve traversed every bit of freeway until now. And I’ve been driving the speed limit the whole way.”
How does this translate into math?
The point on the timeline that we assign to 0 is not stationary, and there’s a 1:1 correspondence between any arbitrary segment on that timeline freeway and the amount of time it took to traverse it.
If I’ve always been functionally (pun intended) traversing the timeline freeway, then of necessity, I traversed every bit of it over an infinite amount of time as well. But, since I cannot traverse infinity, therefore I cannot have been driving on the freeway forever.
Does this work for you?
My original argument about traversal actually doesn’t require an any higher cardinality of sets of infinities. As I said before, substitute any “arbitrarily large number such as googolplex” (which can be traversed) for “infinite.” The physics and cosmology of the universe as currently understood is incompatible with this amount of space-time.
I also mentioned the Plank length, which pixelates space-time to increments of about 1.6×10^-35 m, extremely small but not infinitely so. However, I should have noted that Dr. Sabine Hossenfelder objects to this interpretation of Planck length, ascribing it instead to the deficiency of the energy density needed for increasingly finer granularity in measurement, which would stop when the energy density required would generate a black hole. Here’s how she describes it:
Does nature have a minimal length?
https://www.youtube.com/watch?v=nyPdIBnWOCM
One of the many problems with applying mathematics to physics is encountering singular limits. You might enjoy Dr. Hossenfelder’s description here:
Singular Limits – problems with mathematical extrapolations
https://www.youtube.com/watch?v=f8fqAOLJdtE
Have you ordered Swann’s book yet? 😉
-Q
KF,
Thanks, I’ve never read about Krauss’ model. I’ve been thinking more in terms of some models I dug up on arxiv.org some time ago (which I also have not read much about).
DS, Krauss is only one advocate. IIRC, Hawking and others have argued more or less similarly. Until the 60’s – 70’s (and there are always bitter enders) a steady state eternal model was first dominant then a strong school, then was in many cases reluctantly given up on the microwave background evidence etc. That, I think is part of the backdrop to Russell’s claims in his 1948 IIRC debate with Copleston. And more. KF
Q, you will notice, I have consistently spoken to finite scale discrete stages. That would be like counting distance by mileposts on your highway. KF
Kairosfocus,
Yep, you sure did. Just took me a while. 😉
My perspective is that the origin point on the number line is in motion, not stationary, and that I could take any arbitrary segment as a traversal function/automobile. Finally, I realized that I needed to maintain a separation between time and the number line/freeway.
Still, I could be wrong . . .
I’m reminded of the old problem that has two locomotives heading toward each other on the same track. No, this won’t end well. Also, a point-sized, super-fast wasp travels from one headlamp to the other, repeatedly turning around and flying to the headlamp of the other train, back and forth.
The velocities of each locomotive and the mad wasp is given as well as their initial separation. One is asked how long before the trains collide and how far the point-sized wasp flies before it’s crushed. The answers can easily be calculated and they’re finite. But notice that the *number* of trips that the point-sized, super-fast wasp makes is infinite. An infinite number of trips is traversed in a finite amount of time.
-Q
@Querius
Do you still believe the stork brought you? A point-sized stork. 😉
Q,
The question seems to be much different when all the “trips” are identical in length and duration. It’s trivial to move your finger 1 mm, but it’s not even clear it’s possible for something to move an infinite number of millimeters. That’s something that will never be observed ‘directly’, in any case.
Q, you are restating Zeno’s paradox of convergent series where trips take shorter and shorter until they converge. KF
Kairosfocus,
Yes, but there’s more to it. The total length of the super-wasp’s travel can be computed from its given speed and the time it takes for the trains to collide, but the number of trips it takes cannot be computed.
-Q
DaveS @380,
In my math problem, you can observe the two locomotives heading toward each other and their eventual collision, You can observe the wonky wasp zipping between the locomotives. You can calculate the location and moment of impact. However, you cannot count the number of trips the wasp took, which is infinite.
-Q
An infinite amount of mathematicians walked into a bar. The first ordered a pint, the second ordered a half pint, the third ordered a fourth-pint, etc. The Bartender eventually walked up and gave them two pints and said: “you mathematicians don’t know your limits.”
Q, you can know the magnitude, aleph_null, as that is the number of terms in an infinite, convergent power series. The known total distance comes from known speed and time to impact. KF
Kairosfocus,
Ok, let’s try it out.
The locomotives start 200 miles apart.
Locomotive 1 (L1) travels at 40 mph
Locomotive 2 (L2) travels at 50 mph
The wasp (W) travels at 100 mph
a. How far did the wasp travel?
b. How many trips between the locomotives did the wasp make?
My point in this silliness is that the wasp actually traversed an infinity of trips.
-Q
222.22 (repeating of course) miles?
And yes, countably infinitely many trips.
DS, I think part of the point is that transfinite quantities have strange properties that are largely unfamiliar to us and are counter-intuitive. Here, countably infinite means aleph_null in scale. KF
Q, start with inferred time to collision, where 40t + 50t = 200, so t = 200/90 = 2.222 . . . hrs. D = v*t so distance cumulatively flown at 100 mph is 222.222 . . . miles, which is the sum of the trips flown, the vast majority of terms being in the short interval just before impact. KF
Now imagine running the experiment backward, so the trains back up from the point of impact until they are 200 miles apart. How far does the wasp travel? How many trips does it make?
Nope. A necessary condition to resolve this problem is that you must not be a maths literate. 🙂 In the last second before the 2 trains will meet(40m apart) will be the last trip of wasp because in that last second wasp max speed is
psysically restricted to only 40m/s .
🤦
https://upload.wikimedia.org/wikipedia/commons/e/e9/Emojione_1F421.svg
Sandy writes, ” A necessary condition to resolve this problem is that you must not be a maths literate.”
I have been beset by this problem too many times: People not well versed in math think they have solved a problem when they in fact don’t understand basic ideas.
This is a funny reaction
Viola Lee: I have been beset by this problem too many times: People not well versed in math think they have solved a problem when they in fact don’t understand basic ideas.
Welcome to the club.
JVL,
Be nice. I don’t think Viola Lee intended to join your club. 😉
Besides, our little wasp has a sister who also likes to make infinite numbers of trips on a timeline.
-Q
@ViolaLee
Funny you didn’t have a complaint to:
1. In reality motion is fluid while in maths is displayed as many static images that’s why so many “paradoxes” involving motion 😉
2. Interchangeable use(in a deceitful way) of 2 different referential frameworks :the macroscopic framework (eye level ) and the microscopic one even if an undetectable margin of error in macro repressent more than whole micro framework .Maths doesn’t have “problems” with infinite “zoom in /out” or “margins of error” .
3. Wasp would need an infinite amount of energy to do an infinite number of trips.
4.Point wasps don’t exist.
5.Wasp would be pulverized when land on first headlamp (100+50=150miles/h )
therefore we know how many trips has finished 🙂
Maths when is not correlated objectively with psysics is full of……paradoxes.
Sandy writes, “1. In reality motion is fluid while in maths is displayed as many static images that’s why so many “paradoxes” involving motion.”
Hmmm. Do you know calculus, Sandy?
Sandy,
The little point wasp and her sister are mathematical manifestations of physics fantasies right along with massless elephants sliding around on frictionless ice.
As Sabine Hossenfelder and many others have pointed out, mathematics is a set of logical systems that can be applied to the cause-effect relationships in physics, but they provide no guarantee that they’re anything more than useful tools. Every equation is at risk of being replaced with a new equation or a new mathematics when additional data emerges. And there are many different types mathematical systems that are incompatible with each other.
So, when trying to apply infinities, topologies, calculus, or linear algebra, pragmatism rather than extrapolation is the only measure of success. But if the math doesn’t hold up or is inordinately complex, it’s quickly discarded for a different mathematical approach.
In this case, the question is whether the infinities of a number line can be applied to space-time. I think it works only within relatively narrow boundary conditions.
-Q
daves:
How many points are there between two points 6″ apart? How long does it take to draw a line connecting the two points?
ET, a good question, to which on continuum framework the answer is c, continuum magnitude. One can draw a Line” in a second or less, and of course the continuum brings in the Zeno effects and convergent transfinite series completed in finite time as successive partial sums converge, KF
ET: How many points are there between two points 6 inches apart?
As many as you want.
Q, in addition to physical models and axiomatised logic models, there are embedded structures and quantities bound up in the logic of being of any possible world. Basic quantities are involved, starting with N and its close related structures. Such is a key reason why mathematics is so powerful. KF
Any so called line connecting any disjoint positions is nothing but a series of discontinuous specks of some material (including pixels on a computer screen). Our mind tricks us into thinking they are connected but everyone reading this knows they are not connected and the specks are finite.
Of course all of these specks when viewed through some magnification process will then appear very jagged to the mind. Any continuous entity is an illusion and only exists in our minds not in reality.
But for practical purposes we can assume there is such a thing as a line and it is continuous and our lives are much better because we do. But arguing over the number of numbers there are between any two entities is nothing more than a mental gyration and similar to arguing over how many angels can dance on the head of a pin.
The number of numbers will always be finite.
Jerry,
But there are right and wrong answers to some of these questions. The subset (0, 1) of the real numbers has the same number of elements as the power set of N. The set (0, 1) does not have the same number of elements as N itself. And one can make arguments and provide evidence to support these statements. It’s not just idle speculation.
That assumes one accepts some “ordinary” mathematics, which I believe most of us do.
“Most” being the operative word.
Actually is very strange that maths accept such a big lie that a line can contain an infinite number of points.
This lie can be easily debunked by measuring his thinness ( for example 0.01 inches)and knowing that has 6 inches.Result 6÷0.01=600 points. 😉 Maths very strangely fail to measure thinness of a line but has infinite zoom in measuring the lenght of a line. What in the world… 🙂
Sandy, It is a fact that any line can contain infinite points. Points do not have a physical measurement.
Of course it is idle speculation. It all exists in your head. Not in reality.
And I know a fair amount about mathematics though I forgot most of it. When I took the GRE exam on math for graduate school. I got 72 of 75 correct. I left three blank. The three questions I left blank were all on statistics because as an arrogant a**hole I thought statistics was beneath me and never bothered to study it. I had no idea what a standard deviation was.
Later I learned how stupid I was and actually taught a class in statistics once. And I support the movement to teach statistics instead of calculus in high school. Of course teaching both would be good but statistics is more useful for the average person.
But points don’t exist in our universe. Specks maybe. Entities smaller than specks exist but not points.
Sandy, here is the very first thing taught in a high school geometry course
from Undefined Terms, MathBitsNotebook.com
In geometry, formal definitions are formed using other defined words or terms. There are, however, three words in geometry that are not formally defined. These words are point, line and plane, and are referred to as the “three undefined terms of geometry”.
The descriptions, stated below, refer to these words in relation to geometry.
POINT
• a point indicates a location (or position) in space.
• a point has no dimension (actual size).
• a point has no length, no width, and no height (thickness).
While we represent a point with a dot, the dot can be very tiny or very large. Remember, a point has no size.
LINE (straight line)
• a line has no thickness.
• a line’s length extends in one dimension.
• a line goes on forever in both directions.
• a line has infinite length, zero width, and zero height.
• a line is assumed to be straight.
PLANE
• a plane has two dimensions.
• a plane forms a flat surface extending indefinitely in all directions.
• a plane has infinite length, infinite width and zero height (thickness).
Clearly, there is a difference between math as a body of abstract concepts, such as a point or a line, and our applying those concepts in real-world applications. Most of the discussion in this thread, including the problem about the “wasp” or about the continuity of points representing real numbers on the number line, are about pure math, not real-world applications.
Jerry:
They exist in mathematics and mathematics exists in our universe
Jerry,
I believe our minds, thoughts, and mental constructions are part of reality. Even if mathematics is just our mind’s way of dealing with the larger world, it’s still real.
Can you place 8 queens on a chessboard so no queen is attacking another? Yes, and we can determine this using our minds only. How do we reliably arrive at the correct answer in problems such as this if what we are doing is not “real”?
Jerry,
PS to #415: I probably misstated your position in that you didn’t say that “doing mathematics” isn’t real, but rather that some of the entities involved such as points and irrational numbers aren’t real.
If it’s not about real-world , why do you use real-world objects? I tell you why ,because external world triggered those internal human intuitions to discover maths laws and bewildering truth that this universe and math are married together.
Of course our body of maths knowledge has boundaries and those boundaries are pushed by pure math but we must not confound math boundaries with dumb math. From my point of view Zeno paradoxes (&co.) are just dumb maths not boundaries of maths where mathematicians try to aquire new knowledge about maths.
There are maths idealizers and maths haters , both possitions are just wrong because maths it’s like ore not like gold bullion,maths has a lot of waste ,but in the same time has pure gold. We don’t have to praise ore(because contain gold) ,we praise only what is gold from ore.
So do elephants that are weightless, frictionless ice and Obi Wan Kenobi.
Mathematics is logic applied to certain concepts. Most of these concepts are only in our heads and just approximate a real world entity.
So is logic real? Yes in a sense but I cannot point to a real world entity and say there it is.
The only numbers that have meaning in the real world are positive integers and this is best understandable by using some mental constructs only in our heads. All the rest of the numbers while extremely useful, are just mental constructs. I wrote a paper in a college philosophy course on what is a number and used basic set theory to illustrate it.
Similarly none of the geometric figures used in basic geometry have any exact real world existence just approximations. Like a line which is just a series of small dots that are irregular when examined up close by magnification. By the way I was introduced to geometry in sophomore year in high school and was so taken back by the logic that I finished our textbook by mid October.
It seems to me that all numbers are mental constructs, even the positive integers.
Does the number 1/2 not have any meaning in the “real” world?
Positive integers are just “in our head” also. That is, all math is made of abstract concepts and symbolic notations that we can apply to the real world in various degrees. Break a stick in half and you have a fraction. Draw a right triangle with sides of one unit each, and you have an irrational number as the hypotenuse. Have two people walk away from each other from a starting point and you have negative numbers. And so on. Pure math can be very powerful in describing the real world, but abstract concepts are a different kind of thing than physical objects. Yes, I can’t “point to” an abstract concept because that is something my mind is aware of, but I can use and manipulate symbols that represent those concepts.
So I agree with ET that math concepts are real and exist in our universe, just in a different way than physical objects do.
Yes in a sense. But look at it as similar to a word. Do words have real existence? A number refers to a real thing, a grouping of entities. All the sets of these real things such as apples that have a one to one correspondence represent a specific number.
So does the number exist? Does a word exist? Each refers to something in the real world (though not all words). But each itself is a mental construct. It just that a positive integer can point to something in the real world just as a word usually does.
Not really. Half of some entity is a completely different thing. If I have 8 of something 1/2 is 4 just a different positive integer. If I have 7 of somethings 1/2 is not anything that exist in reality.
Remember these are extremely useful concepts but not based in anything real. I can have half an apple but know that it is different from an apple.
Jerry, I agree that numbers and word “each refers to something in the real world. But each itself is a mental construct.”
But you seem to be using “real world” to mean “physical, material world. But mental constructs are real, just not in the same way that a rock is physically real.
To think otherwise is to dismiss the entirety of my mental experience as “not real.”
Never said that. Is Obi Wan real? He certainly exists in our heads and we can have long discussions on him but does anyone believe he is a real person in our world. One has to differentiate between what exist only in our heads and what exists in the real world.
This all started with discussions of various types of infinity. And I said infinity does not exist in the real world but only in our heads. I was just pointing out the obvious but no one wants to accept this. They want their imaginary worlds to exist even if it is only a dream. This in no way says that imagined worlds are not useful for the real world just as novels which are not real help us to understand and explain the real world.
And we all have had some wild dreams. Few would argue they represent reality but they are mental experiences.
I predict that soon someone soon will focus on the filtering process that our senses do between real world phenomenon and our minds interpretation of these perceptions. And the discussion will go off on another tangent.
Unlike a real rock , a real mental constructs could be false.
Kairosfocus @404 ,
Do you have in mind probabilities or tensors? Or are you thinking of more fundamental interactions as in cause and effect?
-Q
Jerry @405,
With that in mind, take a look at the first couple of illustrated pages in this amazing little book:
https://www.amazon.com/Prof-McSquareds-Calculus-Primer-Intergalactic/dp/0486789705/
-Q
Sandy @408,
. . . not to mention the limit to infinite points imposed by the Planck length.
-Q
Jerry: The number of numbers will always be finite.
If you give me a finite list of numbers I can always find another one. And another one. And another one after that. I can keep finding more numbers. So there cannot be a finite number of numbers.
Sandy: Actually is very strange that maths accept such a big lie that a line can contain an infinite number of points.
If you think you can list all the points on a line I can always find one you missed.
Maths very strangely fail to measure thinness of a line but has infinite zoom in measuring the lenght of a line. What in the world…
That’s because a line in mathematics has no thickness.
Sandy: From my point of view Zeno paradoxes (&co.) are just dumb maths not boundaries of maths where mathematicians try to aquire new knowledge about maths.
Other opinions are available.
Jerry: If I have 7 of somethings 1/2 is not anything that exist in reality.
If I have 7 oranges and I want to split them evenly between two people they each get 3.5 oranges; a perfectly acceptable and physically achievable answer.
Viola Lee @412,
It seems to me that Sandy and you are talking past each other (as in the non-existent intersection of skew lines in 3D). As you well know, some non-Euclidean geometries define only lines—points are undefined.
You seem to acknowledge Sandy’s objections in 413 and 421, although I’d add that my point wasp is slightly annoyed at being hemmed in with quotes. 😉
-Q
Sandy @426,
JVL will always be able to find points on a number line that are less than a Planck length apart. This falsifies his position.
Reality and mathematics do seem to join at probabilities such as wavefunctions. And their manifestations in our physical world enable such effects as fusion in our sun by means of quantum tunneling.
-Q
Only in your head. Not in the real world. In the real world there will be a maximum. It will be a very big number but after that there will be no more entities that represent something in the real world. Consequently no larger number.
No what you will have are six oranges and two other things which are no longer oranges. In actuality in the real world you will have 8 entities or two groups of four entities, not all the same.
Somebody wrote a song once called “It’s so easy.” When something is based on evidence and logic, it’s so easy to refute the nonsense that comes up especially from those who do not seem to live in the real world but only in their heads. I can imagine naturalistic evolution happening in someone’s mind. It’s just no one can point to a real world example that isn’t trivial.
I have a question. Does naturalistic evolution only exist in people’s minds? Is that why it is so hard to provide evidence against it since the evidence is from the real world and not useful against people’s imagination.
I wonder if this a fundamental difference between believers in ID and anti-ID. The latter live mainly in their imaginations and not in the real world. Something to explore!
A line is like a necklace of pearls. Please tell me what pearl I’ve missed. 🙂
Now you have the opportunity to tell us if exist one thing from this universe that have no thickness.
🙂 Truth have available only one “opinion”.
This it’s a masquerade because motion of Achilles is the same / not influenced ( let’s say 10 m /s )no matter into how many halves is cut that distance on a paper. 🙂
There is no logical connection between a runner and bystander mathematician who have a paper and a pen and cut halves of halves of halves and for that reason (of cutting distances in halves) runner will never finish that race. 🙂
Zeno(still at halfway of his dying breath) today in hospital reading messages on uncommondescent thinking :”-Man, mathematicians who push my paradoxes today are always at a half distance to become real mathematicians but another half… prevent them.”
Querius: JVL will always be able to find points on a number line that are less than a Planck length apart. This falsifies his position.
And what position is that exactly? I don’t think my mathematical stance is controversial so . . . . .
Jerry: Only in your head. Not in the real world. In the real world there will be a maximum. It will be a very big number but after that there will be no more entities that represent something in the real world. Consequently no larger number.
And what would that maximum be then?
No what you will have are six oranges and two other things which are no longer oranges. In actuality in the real world you will have 8 entities or two groups of four entities, not all the same.
Okay. So, can you buy a quart of ice cream? A quart being a quarter of a gallon? How about a pint of milk? Again, a pint being a fraction of a gallon. Do the only fractions that count the ones that have names?
Sandy: A line is like a necklace of pearls. Please tell me what pearl I’ve missed. ?
Take the segment between 0 and 10. Tell me what pearls you have and I’ll tell you which ones you’ve missed.
Now you have the opportunity to tell us if exist one thing from this universe that have no thickness.
I’m talking about mathematics NOT applied mathematics.
This it’s a masquerade because motion of Achilles is the same / not influenced ( let’s say 10 m /s )no matter into how many halves is cut that distance on a paper. ?
There is no logical connection between a runner and bystander mathematician who have a paper and a pen and cut halves of halves of halves and for that reason (of cutting distances in halves) runner will never finish that race. ?
No one suggests it’s an actual representation of the real world. But since we tend to think that mathematics is strangely able to describe the real world so well then why do we get these anomalies? That is the real question: do you think that mathematics being able to model the real world is an indication of intelligent design? If your answer is yes then why do these paradoxes arise?
Jerry,
I guess if you don’t mind a great deal of inconvenience, you can get by using only math that is reducible to positive integers and perhaps zero.
I have heard the argument many times: the fact that mathematics is capable of describing reality so well is an indication of intelligent design. IF that is true then all the mathematical paradoxes must be worthy of consideration and worth spending time wondering if they too point to some aspect of reality.
Yes or No?
Is reality composed along lines which lead to strange paradoxes or not?
JVL,
Yeah, that’s a head-scratcher there.
I never said anything like this so why make this comment. It is so specious given all that I have written on this subject that it becomes a 100% endorsement of everything I said. Thank you!!!
Jerry,
Yes, reading my comment again, I see what you mean.
I was trying to say that denying that 1/2 has meaning in the real world seems like an extreme position. It nicely captures the notion of 1 out of 2 things, 2 out of 4 things, 3 out of 6 things, etc., all at once.
It is probably possible to estimate a rough number of the total number of particles in the universe or at least an estimate of it. That would be a finite number.
Call it omega. There would be no other entity to point to after that. So while you could imagine a bigger number in your head, such as omega + 1 or any integer you want to add, it would not enumerate anything in the real world. So there would be no exemplar of it in reality. It would just be in your head.
Interestingly you could not get to infinity in your head because no matter how many times you add a number to something, the result would still be finite even if you could live a trillion years and this is all you did. Of course you could imagine you could live for infinity and do nothing but add numbers. But that is just another absurdity of believing in infinity. But remember I said using it in mathematics is very useful. But so is weightless elephants useful in physics.
You are missing the point. I never said fractions were not useful. They are extremely useful for normal day life.
A quart of ice cream or milk is a collection of millions of small particles. Say for example it is 10 million small parts in each quart. So if you divide either into two equal parts you just get this number divided by two or 5 million. But each is still a positive integer of these small particles.
In reality there are no milk molecules and milk is according to wikipedia
Each sub section of milk would contain individual molecules of this. In our example it would be 5 million each.
Now no one would do this because communication wise it is easier to call it something else but in fact whatever you call it is an accumulation of individual parts or a positive integer.
You are confusing what is in reality with how best to communicate something or calculate something or deal with something.
JVL,
Sandy was talking about real objects and distances. Likewise, Jerry wrote:
In reply, you asked him the following question:
The maximum number is determined by the increments of Planck distances. You cannot fit in any numbers smaller than that.
-Q
All I am trying to say is that discussions of infinity have no correlation with reality especially when it comes to numbers. This is from someone who wrote thousands of integral signs with 0 at the bottom and ∞ at the top. They can make interesting discussions though.
(I tried to type the infinity sign and it appeared on my Mac but not when posted. But I then pasted the HTML equivalent and it worked at least on my computer screen.)
Zeno paradoxes are not maths. Are just tricks. Why do you think “the half rule” in Achilles and tortoise is not applied from the start ? 🙂
Unless God is itself subject to linear time, the idea that God “created” anything is absurd. The idea of “creating” something necessarily implies that there was a time before that thing was created. From the “perspective” (I’ll explain the scare quotes below) of being everywhere and everywhen in one’s “now,” nothing is ever created. It always exists, has always existence, and will always exist, from God’s perspective, because all those things would exist to God as “now.”
This is about as good has human Reason can do. But one must remember that The Root, transcends time, and therefore all ideas about cause/effect, before/after, prior to the first moment of universal time, is meaningless to Reason. “Timeless eternity” is meaningless to Reason. It’s not that the Root is “in time” or “outside of time”, it’s that the very question of time whatsoever, as a positive or negative attribute, doesn’t apply. Whatever The Root is, it is a Black Box, radically different than any concepts .You’re not going to figure it out with Reason. Reason is based on relation and dependence, neither which is a property of the Root. One of the hints about some of It’s nature is our own consciousness. For example, the experiential difference between red and blue is not rational. Like The Root, it cannot be describe with words. It’s quality is a-temporal.
I’m not a fan of Kabbalism writ large, but the medieval Kabbalists did a pretty decent job of demonstrating the uselessness of human Reason to answer any questions about The Root (“Ein Sof” they called It). Same for the Vedic Hindu philosophers.
Mike1962
If 1 is true then 2 is meaningless.
We must not confound the being of God with the work of God .
Mike1962,
I agree with you. My point wasn’t so much to make claims about the nature of God, but rather to just show some problems that exist between how god is characterized and what those characterizations would actually mean and how it would conflict with most theological doctrines that purported those characterizations.
From looking over what few responses were actually on the subject, it seems to me those characterizations are finely tuned to fit their doctrinal requirements. They are not what I would call the “pure form” of those characterizations. IOW, omnipresence is really semi-omnipresence, which IMO is self-contradictory.
Jerry, the old connect the dots Sunday Comics drawings come into play: what is there BETWEEN the dots? That’s the real continuum. KF
I find it ironic in a world where God is trivialized or mocked that the most common expression of amazement in America today is
Especially by young people.
M62, Sandy, WJM,
that brings to the fore the issue of logic of being, with the factor that a causal-temporal, successive finite stage world is inherently contingent, credibly finite in the past and requires a necessary being root world.
Where, already, necessary being of great power and causal capability shows attributes and distinction from non-being. Also, eternal nature (not merely endlessness or beginninglessness in time). Further, that this world has significantly free, so rational & responsible, conscience guided creatures implies further attributes in what is now a translucent grey box with a window.
That is, to ground reality including our world, we need the inherently good so also utterly wise thence maximally powerful as creator compossible with goodness and wisdom. We are already seeing the holographic-microcosm principle at work, where one slice of the cake has all the ingredients and where each facet interacts with all and contributes to all. So, we can draw up a reasonable albeit only partial bill of requisites for such a reality root, and already see the outlines of the God of ethical theism as first and frankly only serious candidate.
For, flying spaghetti monsters fail the giggle test, evolutionary materialist scientism fails the rational responsible thinker test so is self-falsifying and more.
Yes, we can debate onward on schools of thought and traditions but we have here necessary being, universally relevant framework elements that are so strongly mutually entangled that serious reflection on one facet points to the others. No, we may have a dim grey box with window — “through a glass, darkly” — view, but that is not the same as an unbridgeable ugly gulch.
And, there is plenty of room for the God who is not only there but who is not silent, and is not passive. The Judaeo-Christian, prophetic, ethical, theological and redemptive tradition beckons.
KF
What is omipresence ?
What is semi-omnipresence?
How would be self-contradictory?
I agree with Mike62. The nature of ultimate reality is beyond our comprehension.
Kairosfocus,
Well stated. Our presence as intellectual and moral personages considering good and bad is a strong argument for our creator. Dr. Egnor’s neurological experiments also indicate that this activity is not physically located in a brain structure.
Sandy,
I think the omni- words are even more easily misunderstood than infinities. For example, Jesus, speaking of Judas, told his disciples as recorded in Matthew 2624 (NASB):
Notice that Jesus did not say that Judas was predestined to betray him from an omniscient perspective. We do have an amount of free will (or “free won’t”).
Viola Lee,
Yes, I also agree. But we seem capable of creating successively better inductive models of that ultimate reality. But they’re still models and we cannot prove that any model is the ultimate reality.
-Q
Q, my guess is that there would be wide disagreement about what those “successively better inductive models” of ultimate reality might be. There may be widespread agreement about “better” models of some aspects of reality, such as they physical world, but even there our models are only better in a practical sense: I’m not sure any of them could possibly be shown to be better in an ontological sense.
But I agree that all our theories are models that we have made, using abstract concepts, to try to have a framework for understanding the actual world around us.
Viola Lee,
Disagreements of the kind you’re talking about are often due to the lack of observable data such as in the case with string theory, pilot wave theory, and unified field theory for a few examples.
By “better,” I meant that they more precisely predict future measurements or they expand the boundary condition of their application. But whether they are any closer ontologically is actually unlikely. They’re just better mathematical models . . . for now.
-Q
I agree with those comments about the nature of the physical world.
Unfortunately, KF, your argument for that kind of God stems from a premise that has been shown to be false by current evidence; we don’t actually live in the kind of “world” your perspective requires as its postulate. Your worldview depends on something that can never be evidenced, even in principle, but that’s not really a problem in your worldview; it’s really the bedrock of it: faith.
Nothing wrong with faith, but when you ignore a self-evident existential truth by employing faith, you have abandoned reason for fidelity to ideology.
That’s news for me. Provide one evidence against christian God that don’t contain an unprovable assumption.
🙂 This apply to every human being, all spectrum from atheism to teism have faith, only different type of faiths . Yep, you are inc