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Atheists Believe “Truth” Has Magical Properties

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At comment 60 in this thread about self-described atheistic materialists who want portray themselves as being moral yet having no basis by which to be moral in any objective sense, Seversky says in response:

“However, it is a choice between able to be good in a way that actually means something and actually matters,…” to whom? That’s always the unspoken part of such a claim. Meaning only exists in the mind of the beholder and something or some one only matters to some one. Believers fell better if they believe that their lives have meaning and matter, which means they need a Creator to whom they matter.

Notice that, according to Seversky, meaning is an entirely subective pheonomena. IOW, in Seversky’s worldview, being good an entirely subjective narrative.  It only exists in a person’s mind.  There is no means by which anyone can be “good” in a way that is objectively valid and objectively meaningful (meaning, it is good to the mind that is the ground of existence, or god).

In the very next paragraph of his response, Seversky attempts to portray an atheist’s happiness as somehow more real than a theist’s happiness, as if the quality or value of ones experience of happiness would be increased if it referred to something objectively real. He uses a quote from Karl Marx to attempt to get his point across:

The abolition of religion as the illusory happiness of the people is the demand for their real happiness. To call on them to give up their illusions about their condition is to call on them to give up a condition that requires illusions. The criticism of religion is, therefore, in embryo, the criticism of that vale of tears of which religion is the halo.

So, after I make the point that being good would have more validity and meaning if it referred to an objectively real commodity, Seversky shoots that down by insisting that being “good” can only be a subjective narrative. Yet, he seems to think that happiness – which which would obviously also be a subjective state of mind in his worldview – can be of a higher quality if it was generated by a correspondence to objective reality (giving up illusions, as Marx said).

In that thread’s OP I said:

This is the tragic nature of the good, moral atheist; they want their good acts to be somehow more real or better than an act a religious fanatic considers and feels is good, but alas, under the logical ramifications of atheistic materialism, their good acts would be the factual, physico-chemical equivalents of Jihadis who felt they were doing good by driving planes into buildings. There is no source distinction between any act anyone does.

Seversky seems to agree with this about morality, but is apparently holding on to the idea that happiness is somehow different; that the happiness generated by physico-chemical processes under an atheist/materialist narrative is somehow of better quality than the happiness experienced by theists, as if the happenstance correspondence of one set of chemically-produced beliefs to physical reality would necessarily mean a concomitant better quality of happiness.  Seversky is apparently asserting that the quality of ones mental state of happiness is proportional to how closely ones beliefs happen to comport with physical reality.  Seversky is free to try and support this assertion, but we all know he cannot.  All this can possibly be is part of Seversky’s anti-theistic narrative; there’s no reason (that I know of) to believe that a theist’s happiness is somehow of less quality than an atheist’s.  Nor is there any reason to believe that theism confers any evolutionary disadvantage.

Under atheistic materialism, there are no bonus points after you die for  believing things that happen to be true, or that happen to correspond to factual reality.  Seversky’s only recourse then, in countering what he refers to as my “Pascal’s Wager” style argument, is that atheistic materialism somehow bestows a happiness quality advantage during life. Perhaps he might extend that argument to include some other ways that atheistic materialism produces some real-world experiential advantage. I’d like to see him or any other atheistic materialist try to make that argument either through logic or some kind of scientific evidence.  It is nothing more than a materialist myth.

The theme here is that for atheistic/materialists it appears to be important to their mythic narrative that atheistic/materialism conveys upon them some sort of meaningful experiential advantage over theists; that somehow, in some real sense, atheism is superior to theism and that it somehow demonstrates some sort of individual superiority (at least in the sense of setting aside “illusions” – which is a recurring theme.). The problem is that the nature of their worldview logically precludes that from even possibly being the case; they cannot deliberately understand and accept true things because their consciousness, sense of free will and responsibility are illusions generated by uncaring matter.

Note how the illusion of self, self-determination and free will that refers to itself as “Seversky” claims that illusions such as he can “set aside” false,  illusory beliefs and reap some kind of factual benefit.  This is an enormous metaphysical myth – that somehow something that is itself an illusion can set aside illusions and see and understand “the truth”, and that such a recognition will be somehow substantively rewarded in some way that escapes other illusions of self that refer to themselves as theists, as if some illusions of self are better than other illusions of self, and as if such a difference substantively matters.

If atheistic materialism is true, then we all have the beliefs we have and act the way we act because such things are caused by physico-chemical forces that have no regard for the truth-value of such thoughts and beliefs.  Additionally, there is no “I” that has supernatural power over what these materials and forces happen to generate.  It’s not like we would have the power to stop a physical process from producing a false belief because that belief is false; our idea that it is false would also be a sensation produced by the same blind physico-chemical forces that produced the false belief in the first place.  Those forces equally produce true and false beliefs and thoughts (wrt factual reality) and also generate our ideas that such thoughts are true and false.  If factually true beliefs happen to coexist with a higher-quality experience of happiness, how on Earth would one evidence such a claim, or be confident that the view of the evidence and logic wasn’t actually false?

It’s far more likely (under Seversky’s worldview) that false beliefs confer some sort of experiential advantage because, if atheistic materialism is true, that is what nature has actually selected for – the supposedly false belief that god and/or a supernatural world exists.  Also, Seversky seems to think that it is important to have true beliefs rather than false ones; but why? Surely he realizes there is no factual basis for the claim that holding a true beliefs confers a better quality of experiential happiness.  Why bother defending the idea that if a programmed biological automaton happens to think things in correspondence with reality that this also happens to correspond with a better quality of (ultimately) illusory happiness? So what if it does?  If Seversky’s worldview is true, our levels of happiness are entirely caused by forces beyond our illusory sense of control and self-determination. In fact, individual happiness itself is an illusory experience of an illusory self; yet Seversky claims the sense of happiness of one illusion of selfhood is less illusory than that experienced by another illusion of selfhood.

What the take-home point here is that Seversky and others, even though they assert themselves atheistic materialists, still argue and act as if they and others have some supernatural power to deliberately discern true beliefs from false and deliberately overpower the physico-chemical processes of the brain to force them to correspond to true beliefs; that true beliefs somehow magically confer a better quality of experiential happiness; that true beliefs are somehow magically necessary or important when it comes to life and the human species.  It is just as likely that false beliefs are necessary both to long-term survival and for higher quality experience of happiness, and that atheistic materialism is an evolutionary dead-end that cannot compete with religious faith when it comes to factually thriving in the real world because it corresponds to physical reality.

The idea that “truth” can be deliberately obtained, forced onto physico-chemical processes, and that it confers upon illusory “selves” a higher quality happiness or evolutionary advantage is an enormous materialist fantasy.  For them, truth is the equivalent of a magical commodity capable of overriding, transforming and guiding physico-chemical processes, and they have utter faith in its ability confer both immediate and long-term benefits to them and humanity.  One wonders if materialists ever thought that, in an actual materialist world, perhaps an illusion of self working under the illusion of self-will with chemically-caused thoughts might actually require false beliefs in order to function successfully and thrive in the factual world, and that is why such beliefs are so widespread and so pervasive historically?

Well, no.  Because whether they admit it or not, whether they realize it or not, they still think truth is in itself some sort of transcendental, supernatural commodity that fundamentally matters and necessarily affects our lives in a positive way if we can deliberately ascertain it and live by it.

 

 

 

 

Comments
DS, ex hypothesi of an infinite, completed actual past there must be once present times or stages that have now receded into the transfintitely remote past, if infinite is to have any meaning. Otherwise subtly infinite has become a synonym for finite, as the claim "all past times are only finitely remote" implies. KF PS: You will see that my point is that the proposal of a w leads to impossibility hence I reject the hyp of the infinite past.kairosfocus
November 2, 2016
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KF,
The point is, to claim an infinite actual past implies a succession from some point in the endlessly remote past — w for convenience — that must stepwise traverse that endlessness to reach the big bang (a convenient 0 point) then onwards to now across what 13.8 BY or so?
Where is the proof that this w exists?daveS
November 2, 2016
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DS, I note in re:
In a finite past, there must exist some natural number M such that all past moments occurred less than M years ago. For example, physical evidence indicates that all past moments occurred less than 15 billion years ago. An infinite past is one that is not finite. Under an infinite past, for each natural number M, there must exist at least one moment that occurred more than M years ago. That follows by simple logic, by negating the condition for “finite past”.
What I have pointed out ever so many times is that "each natural number" is per its quantitative structure a set that endlessly extends in succession from 0, e.g. von Neumann:
{} --> 0 {0} --> 1 {0,1} --> 2 . . . {0,1,2 . . . k-1} --> k {0,1,2 . . . k-1, k} --> k+1 [for any particular successor we reach or represent] . . . . --> [That is, without end, i.e. endlessly.]
Thus, your case M generalised to any member of the succession glides over that pattern of endless succession. Which pattern is crucial for the matter on the table. For as we have repeatedly seen, once endlessness is present we can see that we may match 1:1 as follows -- I here clip 513:
P: 0, 1, 2, 3 . . . . B*: k, k+1, k+2 . . . . This implies that {0,1,2, . . . . } is infinite as a proper subset can be matched 1:1 with it endlessly, and it also implies that the collective cardinality of the set of 0.1 inch pitch marks on P and B* — effectively the natural numbers from 0 — are the same, that is aleph null. This results from exactly the impact of onward endlessness of succession so any finite truncation of B at some finite k (giving us B*) has no material effect on that onward endlessness. Aleph null thus stands in for, the numerical magnitude of countable endlessness. (Which, explains its seemingly bizarre properties such as A-0 – 1 = A-0, finite non-zero positive integer r x A-0 = A-0, etc. I trust this is able to help you see what I am getting at.) Indeed, starting from 0 is just a convenient point, any arbitrary but finite k would do to exhibit the property. As a further direct consequence, we cannot exhaust such endlessness in steps from a 0 or a k etc. Logic of structure and quantity speaks decisively.
The point is, to claim an infinite actual past implies a succession from some point in the endlessly remote past -- w for convenience -- that must stepwise traverse that endlessness to reach the big bang (a convenient 0 point) then onwards to now across what 13.8 BY or so? That endless traverse: . . . . w, w-1, w-2 . . . . 0, 1, 2 . . . s_n --> can be matched 1:1 from w on to: T: w, w-1, w-2 . . . . P: 0, 1, 2, 3 . . . . B*: k, k+1, k+2 . . . . Thus the traverse to 0 cannot be physically completed in succession. We have no warrant to put up an actually completed temporally successive past of origins. KFkairosfocus
November 2, 2016
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Folks, notice, applications of the potential infinite, critically dependent on pointing to an onward endless continuation and a limit informed by relative rates of going to 0 or "infinity" . . . what L'Hosp's rule is all about. Where, the point is, in the limit of expansion of the radius without limit -- as radius of curvature increases to the potential infinite -- the arc of a circle approaches the tangent at the point, that is, tends to a straight line. But we cannot actually physically instantiate that limit. We never physically achieve the infinite, we exploit its conceptual properties. KF PS: The classic geometry result about circ/diameter = pi is indeed dependent on the idealised mathematical world of "the plane" or a 3-d flat space. Load space up with energetic, massive entities and we start going into a very bendy situation . . gravity. Here, there be sleeping dragons who do not like to have their tails tickled.kairosfocus
November 2, 2016
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Querius,
When the denominator approaches 0, the quotient increases toward infinity, except when the numerator also approaches 0, in which case a numeric ratio might be established using L’Hôpital’s rule.
It could also be that the quotient neither approaches infinity nor a finite value, depending on the behavior of the numerator. But with this caveat, that's exactly what I said in #522. What are you disagreeing with?
In contrast, the referenced link shows what happens when the numerator and denominator both approach infinity. This is clear as day to anyone except a disingenuous Darwinist.
Yes, the cited example is clear. The fraction approaches -3/5 as x approaches infinity. This is all shown working with finite real numbers only, and none of the steps show infinity being divided by infinity.
Since you’re apparently clueless about space-time deformations and PI—that the computed ratio of PI changes with the size of a circle in a non-flat universe, your feeble attempts at convincing anyone of the applicability of mathematical concepts of infinity to the real universe are obviously unreliable.
I'm aware that in some geometries the ratio of circumference to diameter for circles depends on the diameter, in fact that's why I raised the possibility that the geometry of space is hyperbolic in the first place. The ratio circumference/diameter approaches infinity as the diameter approaches infinity in the hyperbolic case (and hence does not approach a finite value).
And you’re still evading the problem of Godel’s incompleteness theorems when attempting to map a simple system of mathematics, which you don’t understand, onto the real world.
I suggest we try to get straight on matters of freshman calculus before considering Gödel's work. Finally, I'll echo wd400's comment. We're now talking about limits of real-valued functions, rather than dividing the circumference of an "infinite circle" by its diameter, which I initially objected to.daveS
November 2, 2016
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When the denominator approaches 0, the quotient increases toward infinity, except when the numerator also approaches 0, in which case a numeric ratio might be established using L’Hôpital’s rule. In contrast, the referenced link shows what happens when the numerator and denominator both approach infinity. This is clear as day to anyone except a disingenuous Darwinist.
Are you forgetting about the word "approach" in this? The limit as x approaches zero (from the right) of 1/x is infinity. But 1/0 is still undefined. The reference you are talking about deals with exactly what Dave said, finding a limit -- "You must mean some limiting process, considering only circles of finite diameter, right?".wd400
November 2, 2016
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SA, yes a claimed actually completed stepwise infinite past of a [quasi-]physical space-time domain is not strictly mathematical. It is however quantitative and structural, where mathematics is perhaps best understood as the logic of structure and quantity. Thus, mathematical considerations are significant and here the issue is, there are serious challenges in implying stepwise, finite-stage traversal of a transfinite span from the remote past (in context one cannot say "of origins"1) to the present. My point has been, that the relevant logic imposes constraints on what is feasible, in particular that stepwise, finite stage actually completed traversal of a transfinite, causally cumulative chain of events is not feasible once endlessness is a material issue. That is, we are inherently not warranted to speak of an actually completed temporal past precisely because of its stepwise, finite stage progressive nature. Yes, we can speak of the progressive potential infinity of the future, but we cannot simply map the equivalent to the negative integers to past stages to the proposed chain of the past and then announce it as an assumption that holds default absent demonstration otherwise. KFkairosfocus
November 2, 2016
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I'm apparently in the Dead Parrot skit again. Your argument is falsified, dead, negated, kaput, busted. It's an ex-argument! It's not pinin' for the fjords or resting or stunned. When the denominator approaches 0, the quotient increases toward infinity, except when the numerator also approaches 0, in which case a numeric ratio might be established using L’Hôpital’s rule. In contrast, the referenced link shows what happens when the numerator and denominator both approach infinity. This is clear as day to anyone except a disingenuous Darwinist. Since you're apparently clueless about space-time deformations and PI---that the computed ratio of PI changes with the size of a circle in a non-flat universe, your feeble attempts at convincing anyone of the applicability of mathematical concepts of infinity to the real universe are obviously unreliable. And you're still evading the problem of Godel's incompleteness theorems when attempting to map a simple system of mathematics, which you don't understand, onto the real world. Knowing that you resist even the most trivial truths, I have no illusions about you're willingness to agree to anything that I've demonstrated, much less admitting you were wrong. So I'm just amused to see you digging yourself deeper and deeper into an increasingly embarrassing position for the sole benefit of the other readers here. So go ahead. Keep digging. -QQuerius
November 1, 2016
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nmdaveS
November 1, 2016
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When a value approaches 0 in the denominator of an expression, what do you get?
Could be any number, or perhaps no number at all...wd400
November 1, 2016
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Querius,
When a value approaches 0 in the denominator of an expression, what do you get?
That depends on the behavior of the numerator. The limit of the fraction could be 0, some nonzero number, infinity or minus infinity (meaning it increases or decreases without bound), or not exist (meaning it neither increases/decreases without bound nor converges to some finite value).
If the concept of a circle with an infinite circumference eludes you, how much less credibility do you have in trying to convince anyone of the possibility of space-time being infinite?
I'm starting to suspect you're not being serious.
Did you ever bother to look up the link I gave you in #519? It falsifies your position about ratios of infinities. But i guess you can’t bring yourself to admit that you were wrong.
Yes, it shows how to evaluate the limit of a fraction when the numerator and denominator increase and decrease without bound, respectively. It doesn't demonstrate L'Hôpital's rule, but rather how to transform the fraction (without changing the limit) so that the numerator and denominator both have finite limits, allowing the basic limit theorems to be applied. Nowhere in the calculation do we divide infinity by infinity.daveS
November 1, 2016
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DaveS, When a value approaches 0 in the denominator of an expression, what do you get? If the concept of a circle with an infinite circumference eludes you, how much less credibility do you have in trying to convince anyone of the possibility of space-time being infinite? If space-time is a sphere, and ellipsoid, a cone, a cylinder, a hyperbolic paraboloid, an ellipsoid, or even an irregular shape such as the T-shirt you're wearing, the value for Pi will vary with the size of the circle you create on it. If Pi never varies regardless of the size of the circle, then the space-time you're working with is flat. That's how you could know. As I said, if you can't imagine these relationships, you shouldn't be arguing about infinities. Did you ever bother to look up the link I gave you in #519? It falsifies your position about ratios of infinities. But i guess you can't bring yourself to admit that you were wrong. But everyone else can see it . . . -QQuerius
November 1, 2016
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Querius, I know L'Hôpital's rule, and have used it many times, and you don't actually divide infinity by infinity in carrying it out.
Yes, the ratio of a circle to its diameter is always Pi in a flat universe, regardless of the size of the circle. increasing the size of a circle to infinity is exactly what you’re proposing with space-time.
But I don't recall you saying you were assuming flat spacetime. You said you were describing a method to measure the curvature of spacetime. You could of course consider larger and larger circles of finite diameter, but infinite circles? The concept makes no sense. That doesn't mean that the infinitude of spacetime itself makes no sense.
If space-time is curved, then Pi will vary with the size of the circle—it doesn’t matter what type of curvature being considered.
That's what I was getting at when I asked what would happen if space is hyperbolic.daveS
November 1, 2016
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DaveS,
You don’t really mean dividing two infinities, do you? And getting a ratio of pi? That makes no sense. You must mean some limiting process, considering only circles of finite diameter, right?
Sorry, I didn't mean to make your head explode. Why don't you go ahead and read this: http://spot.pcc.edu/math/clm/section-ratios-of-infinities.html That infinities can be involved in indeterminate ratios can also be demonstrated in L'Hôpital's rule where you divide by an expression that approaches zero. Yes, the ratio of a circle to its diameter is always Pi in a flat universe, regardless of the size of the circle. increasing the size of a circle to infinity is exactly what you're proposing with space-time. If space-time is curved, then Pi will vary with the size of the circle---it doesn't matter what type of curvature being considered. -QQuerius
November 1, 2016
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daveS
An infinite universe (unbounded metric space) means that there are points arbitrarily far apart: for any distance d, there are points that are of a distance at least d apart.
Ok, this was helpful, thanks. The way I read this: d = distance between any two points. Therefore, any two points are separated by some distance d. Distance d must necessarily be finite and there can be no points which are at an infinite distance apart.Silver Asiatic
November 1, 2016
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Silver Asiatic,
It’s not “endless” necessarily (since the present is claimed as the termination) but “beginningless”.
Agreed. This has been a significant issue throughout the discussion.
If there were no points that were at an infinite distance from others, then it couldn’t be an infinite past.
No! Don't go to the dark side! :-) I can say that this is a very unorthodox position. If you read the dictionary definition somewhere above, and this passage from the wikipedia entry on the shape of the universe, you will see how "infinite" is normally used:
An infinite universe (unbounded metric space) means that there are points arbitrarily far apart: for any distance d, there are points that are of a distance at least d apart. A finite universe is a bounded metric space, where there is some distance d such that all points are within distance d of each other.
I will stress that the d's above are always taken to be finite.
In order for a maximally powerful being to create an infinite space, that being must transcend beyond or outside of the space that is to be created. That is what is meant as a transcendent entity or being. It would include maximum power as well as maximum extension beyond any created reality. Anything that would exist as created-being, would find the source of its existence from the maximally powerful entity that is the fullness of being (doesn’t receive existence from anything else, but possesses all of it and distributes through creating other beings).
Ok, that's fine. I had in mind something like the Christian God.daveS
November 1, 2016
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daveS
Even if a maximally powerful being attempted to create an infinite space ...
In order for a maximally powerful being to create an infinite space, that being must transcend beyond or outside of the space that is to be created. That is what is meant as a transcendent entity or being. It would include maximum power as well as maximum extension beyond any created reality. Anything that would exist as created-being, would find the source of its existence from the maximally powerful entity that is the fullness of being (doesn't receive existence from anything else, but possesses all of it and distributes through creating other beings).Silver Asiatic
November 1, 2016
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An infinite past is not a mathematical construct. It's not "endless" necessarily (since the present is claimed as the termination) but "beginningless". With an infinite collection of points from past, there would be a point that is an infinite, not finite, distance from some other point in the collection (sequence, series). If there were no points that were at an infinite distance from others, then it couldn't be an infinite past. Assuming an infinite past requires that the concept of infinite be realized. Again, an infinite past requires that there be points which are at an infinite distance from some other point. Assuming an infinite past assumes we can isolate (define) that infinite distance and assign it to a point. N is a point at an infinite distance from some other point. If X is an infinite set of points, then X must contain at least one N. If X does not contain N, then all points in X are at a finite distance from all other points. If X does not contain N, therefore, X is not an infinite set. So, if X is an infinite set, N is a point at an infinite distance from some other point. A point at an infinite distance, cannot be shifted-left. N - 1 = N. This is mathematically incoherent. More importantly, N cannot be isolated as a finite point because to do so would mean it could be mapped to a finite distance from all other points. But N is at an infinite distance from some point. So, to assume an infinite past would require that there be at least one point that is at an infinite distance from some other point, and this cannot be demonstrated mathematically, logically or physically.Silver Asiatic
November 1, 2016
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KF,
Pardon, but latching on to a descriptive word, “endless,” and rhetorically pretending it is meaningless or hopelessly vague does not answer to the core issue.
It's not that it's meaningless, but rather that I've never been able to get clear on what you mean by it. Is there any difference between "endless" and "infinite" (or perhaps "countably infinite")? I haven't been able to find one as yet. Presumably the term doesn't absolutely defy translation into standard mathematical language. If there is no difference, why not use "infinite" instead? If there is a difference, cite an example of two sets/sequences/whatever, exactly one of which is endless but not infinite (or vice-versa).
That actually already shows the incoherence in your claim. If a chain exists and ALL its links are finitely remote from here and now in steps, then the whole chain perforce must be only finitely remote from here and now in steps.
Do you agree with the definition of "finite" I gave in #491? If so, then if the whole chain is finitely remote from the "present", there must be some fixed natural number M such that every link in the chain is fewer than M steps from the present. For example, perhaps M = 100. Then the chain could have at most 100 links, counting the present as a "link". That's what you are saying, correct? Unless there is a particular link infinitely many steps from the present, the chain actually has some (finite) natural number of links, has finite length, and in fact has two ends. Even if a maximally powerful being attempted to create an infinite space and inside it, a chain with countably infinitely many links, each a finite number of steps from one end, it would fail. Likewise, if this deity attempted to arrange an actual countably infinite collection of meter sticks end-to-end (say to the right of some initial meter stick), then the deity would end up with either 1) only a finite number of meter sticks placed, for example maybe 10^120, or 2) an assemblage of meter sticks where at least one of them is an infinite number of meters from the initial meter stick.daveS
November 1, 2016
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DS, Pardon, but latching on to a descriptive word, "endless," and rhetorically pretending it is meaningless or hopelessly vague does not answer to the core issue. It seems to me you want to have your cake and eat it, claiming an infinite past then trying to suggest per some mathematical fast footwork that his is consistent with ALL past actual times/stages being finitely remote. That actually already shows the incoherence in your claim. If a chain exists and ALL its links are finitely remote from here and now in steps, then the whole chain perforce must be only finitely remote from here and now in steps. The mathematics you have cited ends up in a fatal ambiguity between finite and infinite. I have long since argued that there is a flaw in the relevant chain of reasoning. Namely, yes, any particular value of counting number we can reach to in steps from 0 or express in some notation (e.g. palace value or scientific) will be finite in value, and any finite k can be exceeded by k+1, k+2 etc onwards without end. Thus, we see that what we can reach is finite but a material part of the structure of the set of counting numbers from 0 is their continuation in succession without end. That is, endlessly. The infinity lies in that endlessness, not in the fact that we can bound and exceed any given finite value endlessly. Indeed, I have repeatedly shown:
P: 0, 1, 2, 3 . . . . B: 0, 1, 2 3 . . . . Then, use the U operator and Sh-L the B tape by k (equivalent to Sh-R the U unit by k successive cumulative steps from 0): B*: k, k+1, k+2 . . . . So we may 1:1 match: P: 0, 1, 2, 3 . . . . B*: k, k+1, k+2 . . . . This implies that {0,1,2, . . . . } is infinite as a proper subset can be matched 1:1 with it endlessly, and it also implies that the collective cardinality of the set of 0.1 inch pitch marks on P and B* -- effectively the natural numbers from 0 -- are the same, that is aleph null. This results from exactly the impact of onward endlessness of succession so any finite truncation of B at some finite k (giving us B*) has no material effect on that onward endlessness. Aleph null thus stands in for, the numerical magnitude of countable endlessness. (Which, explains its seemingly bizarre properties such as A-0 - 1 = A-0, finite non-zero positive integer r x A-0 = A-0, etc. I trust this is able to help you see what I am getting at.) Indeed, starting from 0 is just a convenient point, any arbitrary but finite k would do to exhibit the property. As a further direct consequence, we cannot exhaust such endlessness in steps from a 0 or a k etc. Logic of structure and quantity speaks decisively.
The term endless as extended to the space-time world, precisely describes that if there were an actually infinite chain in time and/or space, then there would be links in it:
. . . . o-o-o-o-o- . . . -o-o-o| (here and now) | –> . . .
that would be endlessly removed in steps from here and now. But, that is a logical abstraction. When we deal with the temporal world of stages or states and their cumulative causal consequences, advancing step by step in a chain, we see the problem surfacing. To claim that there is an endless or infinite past implies that there were moments say w that were once the present but have been succeeded, step by finite stage step, until now has been reached. But that is not all, it is that the span of those successive intermediate steps has been of endless character, that is of cumulative magnitude Aleph-null (A-0 for convenience). But as was seen yet again, a stepwise chain cannot span endlessness. (By way of contrast a continuum is everywhere infinitely dense with points that are valid members. It can have ends but so soon as it has extension in space or in an abstract domain, it has cardinality c, continuum, which is of course in excess of A-0. This is why I have insisted all along on speaking in terms of the stepwise chain with finite stages. Of course, we have had another debate on the use of 1/m = M as a catapult between the very small and the very large. During which, I suggested on the sur-reals, that the hyper-reals were readily seen as representing a range of the transfinite beyond the first span of endlessness to lead to omega, so that we have two spans of endlessness between. Then using the catapult the other way, 1/M --> m, an infinitesimal. Just as a model, one that would in some way fit the way such are used. We then can get the continuum [0,1] and more significantly the span of continuum between (0,1), which then can be shifted by addition to fill in the naturals to get the positive reals, and mirrored to get the negative reals. Of course the sur-reals can be inserted as giving us a vast span of numbers great and small.) Coming back, it should be clear what I am pointing to, again. Going on, we have the problem of not only endless succession in finite stages, but of the problem of source. Something cometh not of non-being as it has no causal powers. Were there utter nothing, then such would forever obtain. Thus, if there is a world, something always was. That root of reality cannot be temporal and successive, so we see that the concept of eternity and eternal, necessary being capable of causing a world such as we see makes perfect sense. That this sounds a lot like the God of ethical theism (especially when we factor in evident fine tuning that sets up a world in which C-Chem aqueous medium cell based life is possible then actual based on information systems, and as we ponder the sort of moral governance behind rational responsible freedom needed to be able to credibly have a reason-based discussion) is a point to be respected and pondered, not sneered at. KFkairosfocus
November 1, 2016
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Querius,
Let’s imagine an extremely large circle . . . in fact, so large that its circumference is infinite. Its diameter would also be infinite, but the ratio of the two infinities would be Pi. In other words, space-time is flat.
You don't really mean dividing two infinities, do you? And getting a ratio of pi? That makes no sense. You must mean some limiting process, considering only circles of finite diameter, right? If so, why would the limit of this ratio be exactly pi? What if space is hyperbolic? Why would the limit have to exist in the first place?
From there, we can extrapolate that any linear direction is an infinite circle and the ratio of its infinite orthogonal would always be Pi, which clearly produces a contradiction since the circumferential direction and the diametric direction are arbitrary and interchangeable. Thus, a flat space-time cannot be infinite.
?? I can't parse this. "any linear direction is an infinite circle"? [Edit: I think I understand what you were saying---Any line is an "infinite circle"; one problem is, as I mentioned above, you can't divide the circumference of an "infinite circle" by its diameter.] Anyway, as I stated before, I do accept that mathematical models have limitations, if that's what you're getting at.daveS
October 31, 2016
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daveS, The "good enough" part isn't. As in my simplistic analogy, there are many ways to go wrong. Here's another example. Let's say space-time has a spherical curve to it. How would we know? One way is to create a large circle and find the ratio of its circumference to its diameter. The diameter direction is always orthogonal to a tangent to the circle. Larger circles will have smaller values of Pi. Let's imagine an extremely large circle . . . in fact, so large that its circumference is infinite. Its diameter would also be infinite, but the ratio of the two infinities would be Pi. In other words, space-time is flat. From there, we can extrapolate that any linear direction is an infinite circle and the ratio of its infinite orthogonal would always be Pi, which clearly produces a contradiction since the circumferential direction and the diametric direction are arbitrary and interchangeable. Thus, a flat space-time cannot be infinite. Am I willing to rest my case on those logical extrapolations? No. And I've not even reminded you of the falsification of mapping a mathematical system on reality from Gödel's incompleteness theorums. -QQuerius
October 31, 2016
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KF,
DS, you have built a system on a clearly incoherent claim (shown many ways) and seem to be judging the straight by the crooked. An infinite chain of finite stage links will be infinite in extent; thus some links in the far zone will be infinitely removed from now.
Do you have a rigorous proof, where all the "endless"es have been translated?daveS
October 31, 2016
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DS, you have built a system on a clearly incoherent claim (shown many ways) and seem to be judging the straight by the crooked. An infinite chain of finite stage links will be infinite in extent; thus some links in the far zone will be infinitely removed from now. Which brings us to the problem of traversing an endless span step by step. Cannot be done. There is no warrant for blanket assuming an infinite already traversed past so being here needs no grounds. That begs the core question and tries to shift the burden of warrant. KFkairosfocus
October 31, 2016
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Silver Asiatic,
It seems you are assuming that which needs to be demonstrated as coherent.
Well, I'm laying out my assumption for KF or anyone who else claims to be able to prove it's incoherent I'm not claiming I can demonstrate it is coherent.daveS
October 31, 2016
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daveS
I’m assuming that we have an actual infinite collection of past points, each of which is finitely many “shift-right” steps from the present.
It seems you are assuming that which needs to be demonstrated as coherent. You're starting with a present that is the endpoint of a past, infinite succession. So, you already traversed an infinite to arrive at today, but you're just including that traverse as part of your assumption. Sure, that's one way to do it, but the arguments against an infinite past argue against the point which you're proposing as a first premise that must be accepted. It's like starting with the proposition that "the universe will necessarily exist for an infinite amount of time" and then trying to see if that could be incoherent in mathematical terms. Of course it wouldn't but that analysis would add nothing to our knowledge.Silver Asiatic
October 31, 2016
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KF,
PS: I think the relevant point is that while 0.999 . . . as an infinite series [expressed in place value notation] converges to 1, step by step the finite partial sums are never 1.
I think he's (or she) is talking about the question of applying mathematical models to the real world, which is generally a valid concern. But it appears you and I agree to accept certain mathematical models [edited] as "good enough" for the present discussion. Anyone who disagrees will of course find none of this convincing.daveS
October 31, 2016
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KF,
DS, kindly explain to us how you get an infinite, forward, causally cumulative past arriving at the present without actually infinitely remote past times.
You are the one making the claim that such a scenario is incoherent, so it's on you to come up with a proof. Specifically, I would expect you to derive a contradiction starting with the premises I assume.
Without, incoherence that for example amounts to there were unlimitedly many FINITELY remote past stages joined in a finite-stage chain
That's what I want you to prove. Demonstrate the incoherence of this scenario by proving rigorously that it leads to contradiction. I'm assuming that we have an actual infinite collection of past points, each of which is finitely many "shift-right" steps from the present. Have at it.daveS
October 31, 2016
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PS: I think the relevant point is that while 0.999 . . . as an infinite series [expressed in place value notation] converges to 1, step by step the finite partial sums are never 1.kairosfocus
October 31, 2016
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DS, kindly explain to us how you get an infinite, forward, causally cumulative past arriving at the present without actually infinitely remote past times. Without, incoherence that for example amounts to there were unlimitedly many FINITELY remote past stages joined in a finite-stage chain -- which comes down in crude terms to finite link length x infinite number of lengths --> infinite chain and thus infinite length: . . . . o-o-o-o-o-o-o- . . . -o-o-o --> . . . so also chain links at infinite temporal remove from now. If every past point is finitely remote the past as a while is finitely remote because duration is point to point not oh we have a vaguely ongoing sequence. KFkairosfocus
October 31, 2016
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