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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
Querius, That's an infinite series. If that's what you mean in #496, then I would interpret the entire calculation to be about infinite series. You have calculated:
9n = (9 + 0.9 + 0.09 + ...) − (0.9 + 0.09 + 0.009 + ...)      = 9 + 0 + 0 + ...
which results in n = 1 + 0 + 0 + ... (which you truncated to n = 1). You could have also done it this way:
9n = (9 + 0.9 + 0.09 + ...) − (0.9 + 0.09 + 0.009 + ...)      = 8.1 + 0.81 + 0.081 + ...
and we are back to n = 0.9 + 0.09 + 0.009 + ... or even:
9n = (9 + 0.9 + 0.09 + ...) − (0.9 + 0.09 + 0.009 + ...)      = 9 + 0.9 − 0.81 − 0.081 -... ...
So n = 1 + 0.1 − 0.09 − 0.009 −... as well. I honestly don't see much connection between this example and our discussion of an infinite past.daveS
October 30, 2016
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DaveS evaded the question @497 with
Well, is it a sequence or a series? Those are two different things. Please tell me precisely what you mean by 0.999… .
What would you call 0.9 + 0.09 + 0.009 + 0.0009 . . .? -QQuerius
October 30, 2016
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DS, my assertion is not the issue, the logic of an infinitely long chain of finite stage links is. KFkairosfocus
October 30, 2016
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KF,
DS, if there was an actual infinite past, there were actual once present stages that have been succeeded by stages to now that comprise the infinite span. One that is endlessly beyond any finite counting number.
You've asserted this time and again.
To say there were infinitely many finite stages that are all finitely remote is incoherent.
You've also stated many times that the notion is "incoherent", but have never backed that up with a proof. If you think you have one, why not write it up formally and post it here?daveS
October 30, 2016
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DS, if there was an actual infinite past, there were actual once present stages that have been succeeded by stages to now that comprise the infinite span. One that is endlessly beyond any finite counting number. And, given the finite, cumulative stages in the chain an infinite number of such stages will yield an infinite temporal distance for some past stage, say w. To say there were infinitely many finite stages that are all finitely remote is incoherent. This is not a convergent series or sequence. Yes the sequence of partial sums so far as we can calculate will be finite but the very point is it goes on endlessly which is not finite. Where also, time accumulates causally forward step by step, posing the challenge of traversing an endless, infinite span in steps; which is a non-starter. Again, we have no warrant for claiming an infinite actual past for the physical-temporal world. KFkairosfocus
October 30, 2016
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Querius,
The sequence 0.999… is an infinite series and is asymptotic to 1. The LIMIT of 0.999… is 1, but 0.999… is not the same as 1.
Well, is it a sequence or a series? Those are two different things. Please tell me precisely what you mean by 0.999... .daveS
October 30, 2016
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DaveS, The sequence 0.999... is an infinite series and is asymptotic to 1. The LIMIT of 0.999... is 1, but 0.999... is not the same as 1. The logic here is actually analogous to yours. We're simply mapping a mathematical representation of an infinite series onto a presumably infinite space-time universe, performing some mathematical operations and coming up with the answer that since the infinite series is proved finite, thus the infinite space-time universe must also be finite. So, do you agree that mapping this mathematical representation onto reality is ludicrous? -QQuerius
October 30, 2016
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Querius,
Ok, let’s have some fun with a sequence that asymptotically approaches 1, namely 0.999… – If n = 0.999…, does anyone object to 10n = 9.999… ? – Does anyone object to 10n – n = 9 ? – Does anyone object to 9n = 9 ? – Does anyone object to n = 1 ? – But we originally defined n = 0.999… – Thus, we can triumphantly conclude that an infinite sequence asymptotically approaching 1 is actually a finite number, and that by projection, an infinite universe must therefore be finite. Does anyone else think this is a stupid application of mathematics?
It's certainly another non sequitur. You started with the equation x = 0.999..., and to understand its meaning, we must interpret the right-hand-side. The usual interpretation is that it's the limit of a particular sequence, and equals 1. So there's really no need for the next few lines. In any case, 0.999... does equal 1. It is not true that the infinite sequence itself is a finite number; rather its limit is. How this could be construed to show that an infinite universe is finite escapes me.daveS
October 30, 2016
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Once again, I feel like I'm shouting at the ocean waves. Mathematics cannot be mapped against the real world. Mathematics provides a useful model of reality, but it is not congruent with reality. What is it about Kurt Gödel’s incompleteness theorems that is not understood here? Ok, let’s have some fun with a sequence that asymptotically approaches 1, namely 0.999... - If n = 0.999..., does anyone object to 10n = 9.999... ? - Does anyone object to 10n – n = 9 ? - Does anyone object to 9n = 9 ? - Does anyone object to n = 1 ? - But we originally defined n = 0.999... - Thus, we can triumphantly conclude that an infinite sequence asymptotically approaching 1 is actually a finite number, and that by projection, an infinite universe must therefore be finite. Does anyone else think this is a stupid application of mathematics? -QQuerius
October 30, 2016
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KF,
Ds, the logic is simple.
Ok, let's see.
Time emerges stage by stage as present circumstances give rise to their immediate successors (including actions by agents who are self-moved).
Sounds fine.
Successors go on to the next stage and of course earlier stages fade into the past.
Yes.
The claim of an infinite actual and beginningless past therefore implies that at any given stage s, there were already past stages that recede in a sequence beyond any finite count, i.e. endlessly.
I would phrase it differently, but we might be in agreement here. At any stage s, the set of moments in the past of s is infinite. For any natural number M, there exists a point t in the past of s such that the time interval between t and s has length exceeding M years.
Factoring in time, on this view there have to have been actual once present stages that are now infinitely remote, endlessly remote but which stage by stage succeeded to the present.
*Record scratch* This is where we hit the non sequitur. The existence of these "endlessly remote" stages does not follow from the preceding statements.
Alternatively, as duration is a count metric of some sort per a unit yardstick between stages in the chain, if EVERY past stage is only finitely remote, the past is not infinitely deep.
No. This is contrary to the dictionary definition which you posted (voluntarily!). Do you now disagree with that definition? For reference, the Merriam-Webster definition that you posted:
extending beyond, lying beyond, or being greater than any preassigned finite value however large <infinite number of positive numbers>
daveS
October 30, 2016
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Ds, the logic is simple. Time emerges stage by stage as present circumstances give rise to their immediate successors (including actions by agents who are self-moved). Successors go on to the next stage and of course earlier stages fade into the past. The claim of an infinite actual and beginningless past therefore implies that at any given stage s, there were already past stages that recede in a sequence beyond any finite count, i.e. endlessly. Factoring in time, on this view there have to have been actual once present stages that are now infinitely remote, endlessly remote but which stage by stage succeeded to the present. I simply labelled one such w. Alternatively, as duration is a count metric of some sort per a unit yardstick between stages in the chain, if EVERY past stage is only finitely remote, the past is not infinitely deep. For on this claim, there are no non-finite durations from stages of the actual past to the present. The problem with a stage w is of course that the endless intervening span cannot be traversed in finite stage cumulative successive steps. As is easily seen. We have no warrant to claim an actually infinite past. KFkairosfocus
October 30, 2016
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KF,
You will see that I have taken careful effort to stress that w is not a start-point, the implication is that for any value of a past stage there is onward endlessness before that. So, much of your comment above misses the point.
Well, yes, I never assumed, nor did I imply, that w is a start point.
The issue at core is, given the causally linked stepwise sequential nature of time, a claimed infinite actual past must have in it endlessly remote points that then pose the onward need to traverse endlessness to get to now.
That remains to be demonstrated. You've simply asserted such a point "must" exist. In a finite past, there must exist some natural number M such that all past moments occurred less than M years ago. For example, physical evidence indicates that all past moments occurred less than 15 billion years ago. An infinite past is one that is not finite. Under an infinite past, for each natural number M, there must exist at least one moment that occurred more than M years ago. That follows by simple logic, by negating the condition for "finite past". No "endlessly remote" points required.daveS
October 29, 2016
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DS, again, I do know the difference between an endless potentially infinite climb from a start point and a claimed completion to date of an endless ACTUAL descent. You will see that I have taken careful effort to stress that w is not a start-point, the implication is that for any value of a past stage there is onward endlessness before that. So, much of your comment above misses the point. The issue at core is, given the causally linked stepwise sequential nature of time, a claimed infinite actual past must have in it endlessly remote points that then pose the onward need to traverse endlessness to get to now. Such cannot be traversed in finite stage steps. You have no basis for getting the U operator unit to now. As for an infinite succession of finitely remote past stages with finite steps, that is plain out ruin by incoherence in this case. What can be said is that what we can reach to will be finite but there is onward endlessness beyond. But this is not an abstract set, this is a claim about causally cumulative stages of time and there is no basis for accepting that endless past cumulative finite stages can reach now, stepwise. KF PS: Perhaps I should not have said "isomorphic," as that was likely to be misread. The positive and negative integers are mirrored around 0, effectively by multiplying through by -1, so they have the same basic "shape" and scale in the sense of cardinality. My use of a tape and fold over addresses this. Climbing down to 0 from an infinitely far zone is as far a span -- endless -- as trying to climb up to the same sort of remote zone.kairosfocus
October 29, 2016
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KF,
I simply first showed why the two order types are isomorphic; can be placed in full 1:1 correspondence, where the span in steps will be the same, and where the 0.1 inch pitch is relevant to showing that we are dealing with finite stage intervals.
The two sets {0, 1, 2, ...} and {..., -2, -1, 0} are not isomorphic as ordered sets, assuming we use the same ordering "less than" on both, if that's what you're saying. When you state:
Can you completely climb a ladder with an infinite number of rungs?
and
But now, we see that just as we cannot climb to the transfinite by successive (ShR,1) finite stage steps of U, a (ShR,1) unit on the tape to far LHS cannot traverse the same span rightwards from the endless, transfinitely remote left zone to reach to k, as beyond any given value say w in that far left zone, there would be the same endless span to traverse.
it suggests to me that you're not appreciating the distinction between traversing {0, 1, 2, ...} and {..., -2, -1, 0}, both from left to right. Simply put, the fact that I cannot complete an ascent of an infinite ladder does not tell me I cannot complete a descent of the same ladder. That's why I'm asking you to remove completely any mention of traversing {0, 1, 2, ...} from left to right. (Edit: If your statement about climbing the ladder in your response to AhmedKiaan was just concerning infinite sets in general, and not meant to be connected to the issue of traversing an infinite past, then that's fine of course. However in your (ShR, 1) illustration, it appears you are saying that because we cannot complete a "shift-right" traversal of {0, 1, 2, ...}, therefore we cannot complete a shift-right traversal of {..., -2, -1, 0}, and this does not follow.)
The issue then is, was there a w?
No. What we do have is an actual infinite collection of past moments, all finitely remote from the present, and for each natural number M, at least one of these moments (in fact infinitely many) occurred more than M years ago.daveS
October 29, 2016
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AK, we are deliberately not dealing with the Reals, but with integers and more broadly ordinals in the wider context of the surreals, to bring out the nature of finite stage successions in ordered sequences. Where the key point is that to claim an actually completed infinite past that arrives at the present, one implies -- as opposed to, acknowledges -- that there were stages that were once the present [think, U operator sitting there], but have now been surpassed as one stage gives rise to the next causally connected one in sequence, and to the point that now a typical such case w is infinitely remote in time or equivalently is in a transfinitely far LHS zone. You are forced to give up the claim of an infinite actual past, on the consequences of such a claim. A mathematical, conceptual transfinite is fine, a potential transfinite where succession can continue endlessly (but never attains transfinite scale) is fine, but an actually physically completed transfinite succession of stages is not fine at all; it is incoherent and impossible of being as core characteristics stand in mutual ruin: one cannot both span and not be able to span a transfinite real world succession in finite step successive and cumulative stages. KFkairosfocus
October 29, 2016
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DS, I simply first showed why the two order types are isomorphic; can be placed in full 1:1 correspondence, where the span in steps will be the same, and where the 0.1 inch pitch is relevant to showing that we are dealing with finite stage intervals. Had you looked more closely at what I actually did, I was first highlighting that we have in effect a computational exercise, amenable to register transfer type operations. Per those operations against a backdrop that one is claiming that there was an actually infinite past that through stepwise, right-shift finite stage causally connected +1 increment succession, eventually gave rise to the present. This means that to claim an actually infinite past, then there was some stage that was actual as present but now has been succeeded by a span that makes the stepwise distance from then to now beyond any finite value, i.e. it is endless given the structure of the naturals. We are not claiming a potential infinity, we are claiming an actual, rightward increment, completed one. So, symbolise w as a typical time in that transfinitely remote past zone . . . notice, I am not saying it had a leftmost terminus, just the opposite, I am simply saying that ex hypothesi, it was there as actual and suceeded up to now . . . and put a ShR, +1 step incremental operator, U, on it. Let it proceed, w, w+1, w+2, etc to the right, the forward temporal direction. Will U ever reach some k', a finitely remote point on the tape [mirror image to the k we used above], left of 0? Answer, this is the same scale of span that a U cannot traverse in steps on the RHS from k on, as k on is 1:1 matched to 0,1,2 etc. Folding the U on the right over starting at k mirrored in k', the ShR operator will never lead on to the positive mirror of w, w*. Nothing being changed of material significance, we see no reason why a U would be able to stepwise span from w to k' on the LHS beyond 0. (While we are at it, let us label for future reference the double sided endless tapes P' and B'.) An endless or transfinite span cannot be traversed in sets. The issue then is, was there a w? If there was an infinite past span there had to be on the LHS of B'. But this gives rise to the absurdity of sitting in the present and speaking of how we could not get here. The obvious answer is, there was no w. The temporal domain is well-ordered and incrementally advancing from a true zero-point, which we here label k' for convenience. Rather like the case with temperatures when it was discovered there is a natural, absolute zero. Counting in years of the Christian Era and going to a down count before it, or doing much the same with the big bang, ends in the same result: these arbitrary zero-points point to an absolute zero point, a beginning to the [quasi-] physico-temporal world we inhabit. Which points onward to the need for a necessary being atemporal root of reality as required for a world to exist. For, were there utter non-being (a true utter nothing) then as non-being has no causal capacity, such would forever obtain. If a world now is, something, a world-root, always was as a key framework for any possible world to exist. That is the discussion is about necessary beings in the end. An infinite LHS to the [quasi-] physico-temporal domain is not a credible candidate to be such a necessary being world root. Job opening: wanted, a necessary being, capable of being causal root of a physico-temporal world, must be a-temporal in character and capable of accounting for the evident signs of design in the physical world and the world of life. Should also be able to explain responsible rational, morally governed freedom required to be able to have such discussions as this. There is only one serious candidate who will show up for the interview: the inherently good creator God of ethical theism, a necessary and maximally great being, worthy of loyalty and of the responsible and reasonable service of doing the good in accord with our nature. After centuries of debates and discussions of alternatives, that is where we are back to; before consulting any particular scriptural or traditional system of theology. And yes, such issues lurk here. In these waters there be big sharks. KF PS: I take it that it is readily seen that an infinite succession of successive finite, finitely separated values from 0 to RHS or LHS, not amounting to an infinite span of thought exercise tape will be seen as absurd. To explore, ponder U as a ShR,+1 increment machine and U' as the mirror machine tat will traverse ShL, -1 increments, and let us consider that the machines are a flipped switch distinct. In short one and the same incremental step machine can be ShR or ShL by +1 or -1 increments as necessary, just flip a mode control bit. (And yes, I am exploiting the fact that computational machines and systems are physical instantiations of clusters of operators and registers that store variables etc. An operator transforms one or more preimage functions or variables into image functions or variables.)kairosfocus
October 29, 2016
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AK, Google's biases are notorious now, though not anywhere as bad as the hatchet jobs at Wiki. KFkairosfocus
October 29, 2016
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This site doesn't even come up in Google searches for "Intelligent Design" anymore.AhmedKiaan
October 28, 2016
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"Given any natural number M, there is a w such that the interval between w and the present exceeds M years. That’s what “infinite past” means. There need not be any particular w such that the interval between w and the present exceeds M years, for every natural number M." Anyone who doesn't understand that simply does not understand basic Real Analysis, with regard to series and function theory. This is not really arcane stuff, but laypeople generally don't know it. But what I don't understand is why the people who inhabit this site are trying to have conversations about topics that none of them know anything about. It's like you guys want Bob Oh and DaveS and one or two others to slowly teach you whatever topic you ask questions about, but then you reject the answers. This site is baffling to me.AhmedKiaan
October 28, 2016
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KF,
PS: To address omega vs omega-star (or star omega) simply fold the blue tape over at 0 and change the sign. The negatives are the mirror image of the positives — as the virtual half universe (of in principle unlimited extension) behind a mirror points to.
Yes, but if you reflect the traversal of {0, 1, 2, ...} as well, you end up counting down through the negative integers. That's the wrong direction. The relevant traversal is counting up through the negative integers.
DS, I suggest, first that endless succession is pivotal, especially when time is factored in. Second, that the pivotal question is what does an infinite past mean in a context of causally connected causal succession from past to build up to present; we do have to face and adjust our analysis to the known properties of temporal, causal succession.
As I said, I'm not interested in discussing "endlessness"; there has to be a translation into standard mathematical terms.
It is appropriate to call a day or year or stage of the cosmos or whatever quasi-physical order or domain of reality that preceded it and was beyond that span from now w for reference; w is just a label for an arbitrary stage that ex hypothesi was once the present but now has been succeeded by so many stages that the countable span to it is greater than any finite value we can reach.
I'm sorry, KF, but that's not what your dictionary definition states. Given any natural number M, there is a w such that the interval between w and the present exceeds M years. That's what "infinite past" means. There need not be any particular w such that the interval between w and the present exceeds M years, for every natural number M.daveS
October 28, 2016
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PS: To address omega vs omega-star (or star omega) simply fold the blue tape over at 0 and change the sign. The negatives are the mirror image of the positives -- as the virtual half universe (of in principle unlimited extension) behind a mirror points to. And this does not eliminate the issue of an infinite actual past requiring stages like w to have been real. The traversal in steps challenge does not go away.kairosfocus
October 28, 2016
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DS, I suggest, first that endless succession is pivotal, especially when time is factored in. Second, that the pivotal question is what does an infinite past mean in a context of causally connected causal succession from past to build up to present; we do have to face and adjust our analysis to the known properties of temporal, causal succession. Third, that such a succession is amenable to counting, thus to the sort of thought exercise analysis of relevant sequences as above. Finally, a duration is between two stages, e.g. WW2 ran from Sept 1939 to Sept 1945. In this case, to claim an infinite past is to imply that there were moments that were once the present but are now remote beyond any finite and bounded value. It is appropriate to call a day or year or stage of the cosmos or whatever quasi-physical order or domain of reality that preceded it and was beyond that span from now w for reference; w is just a label for an arbitrary stage that ex hypothesi was once the present but now has been succeeded by so many stages that the countable span to it is greater than any finite value we can reach. Where, time then moves inexorably forward in stages from w, allowing us to count, w, w+1, w+2 etc, which then brings up the by reason of hyp infinite and countable span from w to now that would be beyond any finite span. If you don't like such an actual stage, then stop suggesting an actual physical, infinite past. We may then ask about temporal, finite stage causal succession since w to today, on the claimed infinitely remote past. Where time definitely proceeds in the sort of causally successive stages as mentioned. The challenge of bridging an endless, transfinite span that is of cardinality aleph null emerges. KFkairosfocus
October 28, 2016
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KF, A few comments: 1) I think you could easily omit the word "endless" from your argument at this point. It seems you are talking about countably infinite totally ordered sets, so can we make that change? 2) I request that we make no reference at all to traversals of sets of order type ω such as {0, 1, 2, …}. The set of past moments I am considering has order type ω*, and propositions that hold for sets of type ω do not necessarily hold for those of type ω*. 3) It appears to me you are getting this infinitely remote past point w by working with the set {0, 1, 2, …}. In view of #2 above, I would ask that you prove the existence of this w in some other way, without bringing up the traversal of the nonnegative integers.daveS
October 28, 2016
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DS, Pardon, but I don't believe your claims such as the just above at this point; they are far too rhetorically convenient in a context where too much water has gone under the bridge. For nearly a year, we have discussed exactly this point and I freely acknowledge that you have been helpful to me, e.g. in pointing to the surreals. We both know that ellipses are routinely used in representing sequences and series, often in a finite and bounded context, sometimes in a context of onward continuation without bound. In this situation the distinction has become important and I have simply used the four dot version for that. Long since, in the spirit of Turing, I used the pink vs blue 0.1 inch pitch punched tape thought exercise to show how end-less-ness (=endlessness) arises and has crisp meaning and significance. P: 0,1,2 . . . --> B: 0,1, 2 . . . --> Take B and shift-left (ShL) the tape to some finite k (i.e. register transfer type operations), but retain the un-end-ing continuity to the RHS: P: 0,1,2 . . . --> B: k,k+1, k+2 . . . --> That is, the onward continuation continues in 1:1 correspondence, the end-less-ness to the RHS continues to hold even after an equivalent ShR by an arbitrarily large but finite k stages by a unit (say, U) sitting on the tape that moves in +1 increments; bounded by the onward continuation k+1, k+2 etc [notice that representation of the unbounded ellipsis]. This has several implications, but the first is that the cardinality of P and B even after the ShR, k times, is still the same, to wit aleph null. Both are transfinite, countably so. Secondly, after arbitrarily large but finite steps of advance of U to k, the onward set is in effect a transformed form of the first, much as we see in fairly familiar cases: 0, 1, 2 . . . --> x 2 in each position: 0, 2, 4 . . . --> +1 from 0 on: 1, 3, 5 . . . --> Where all three have the same countable transfinite character. And where the transfiniteness is shown by being able to put a 1:1 match between the full set and what is a proper subset. With, a critical feature being the continuation of the tapes to RHS without upper bound. (NB: It is reasonable to simplify to four dots.) There is a third significant implication. Namely, that the end-less unbounded continuation to the RHS implies that one cannot traverse the whole set in finite steps. Using (ShR, k) to summarise the multi-step operation of U of a +1 increment rightward k times, we see that at any finite k regardless of how arbitrarily large it is, there will always be onward k+1, k+2 etc, which can be matched 1:1 end-less-ly with the unshifted tape marked with the counting numbers on a 0.1 inch pitch. That is, no stepwise advance U to the RHS of any arbitrarily large but finite scale, k, can exhaust the endlessness. Which, by now, is again shown as to what it means exactly. Thus, one cannot traverse endlessness of the type exhibited by the counting numbers in finite stage steps. Now, time is of like character, where one stage gives rise to another immediately following through a causally tied succession, analogous to the (ShR, 1) by U. Time's arrow can be seen in the accompanying accumulation of entropy, i.e. degradation of concentrations of energy towards heat death. Going to time forward from now, we see the distinction between a potential and an actually completed infinity. The former is feasible, one may (ShR, 1) unit U any arbitrarily large number of onward steps, which need not be of equal finite temporal duration (think of this as speeding up or slowing down the clock rate driving the +1 process for U). Now, extend the tapes to the LHS in a similar pattern, in a mirror image: P/B: . . . . --> -(k+2), -(k+1), -k, -(k-1) . . . -2, -1 // 0, 1, 2, . . . k, k+1, k+2 . . . --> That is, the tapes are now endless to LHS also. Fold B at 0 so that the (ShR,k) by U that pointed R now will match the tape to L in 1:1 correspondence. The shifting unit can now do the (ShR,k) on B from 0, and will match -k as we have folded by 180 degrees. The same property of endlessness and frustration of traversal to completion obviously applies to LHS as to RHS. But now, we see that just as we cannot climb to the transfinite by successive (ShR,1) finite stage steps of U, a (ShR,1) unit on the tape to far LHS cannot traverse the same span rightwards from the endless, transfinitely remote left zone to reach to k, as beyond any given value say w in that far left zone, there would be the same endless span to traverse. This I have represented by choosing some w in that zone, for argument: . . . . w, w-1, w-2, . . . . -(k+2), -(k+1), -(k, -(k-1) . . . -2, -1, 0, 1, 2, . . . s_n [= "now"] . . . --> The (ShR,1) unit, moving rightwards beyond w will not be able to traverse the endless span in successive, cumulative +1 steps, as we see: P: 0, 1, 2 . . . . B: w, w-1, w-2 . . . . showing the same 1:1 match property to countable endlessness. Where, reverting to time, a claim of an endless past must imply that there were actual past stages w that were once the present -- = the (ShR,1) unit once sat there -- but stepwise succession (advance to the next stage of time, repeated and cumulative) has continued to now. Therein lies the problem, that stepwise succession would have to do what it cannot, successively span an endless span of cardinality aleph null. Again, we have no warrant to speak of an actually completed infinite past that has by cumulative stages given rise to the present. Instead, it makes better sense to speak of a finitely remote beginning at a -k point, where of course I have used 0 to mark the big bang event. That is we reckon with claimed quasi-physical antecedents to the present observable cosmos and could readily address branches, budding, fluctuations giving rise to bubble sub-cosmi, oscillating worlds, parallel domains and whatnot. Finally, I suggest that what has made communication difficult is the path of endless objections and looping back as though previous discussions and clarifications have not happened. I trust the extended P/B tape discussion above will allow us to now proceed. Especially given its concrete nature and its ability to use the concepts of register transfer algebra and thus of computation. KFkairosfocus
October 28, 2016
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AhmedKiaan, Yes, this particular line of discussion has generated little or no returns. KF,
As for endlessneess I am astonished that you find it so difficult a concept as it is directly tied to the unlimited succession of naturals in +1 steps, and to the point that for any given finite k, we can succeed equally without end, k+1, k+2 etc and put in 1:1 correspondence with {0,1,2, etc}.
It's not the difficulty so much as the imprecision. And all the "custom" definitions, the ellipses of endlessness™ (now with four dots!) and so forth. It makes communication very difficult.daveS
October 27, 2016
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AK, can you write out -- yes, literally -- the complete set of natural counting numbers? Why or why not? Why do we usually represent much of that set with an ellipsis? Can you completely climb a ladder with an infinite number of rungs? Why or why not? If every stage of an infinite past has to have physically happened then given rise to its immediate successor and so forth, how, specifically can you arrive step by step at the present? What does this tell us about claiming there was an actually completed infinite past that has arrived at the present? KFkairosfocus
October 27, 2016
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Dave, it makes sense to you, and to me, and to philosophers and physicists and mathematicians. That's going to have to be good enough. It's just not true that every person in the audience is going to understand everything, and at some point, continuing to explain has diminishing returns.AhmedKiaan
October 27, 2016
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DS, an infinite past must have been endlessly beyond any finitely remote past point. As for endlessneess I am astonished that you find it so difficult a concept as it is directly tied to the unlimited succession of naturals in +1 steps, and to the point that for any given finite k, we can succeed equally without end, k+1, k+2 etc and put in 1:1 correspondence with {0,1,2, etc}. Where the order type of the naturals as a whole is omega, first transfinite ordinal, and the set exhibits cardinality aleph-null. Which, demonstrates the infinity by match with a set known to be infinite. The unlimited succession to infinite degree similar to the counting numbers produced by a von Neumann construction or the like is reasonably described by the term, "endlessness." Omega of course is never seen as successor by +1 increment to some large finite K*, so that K*+1 = omega. Endlessness as is represented by an appropriate ellipsis [I have recently used four dots to mark a difference from a finite, bounded succession] is integral to all this. KFkairosfocus
October 27, 2016
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KF,
DS, please address the issue of exactly what an infinite actual past means
I have, many times. For any natural number M, there exists/existed a point in time more than M years (or seconds, whatever your favorite unit is) before the present.
what it means for time to move forward
I don't think I differ greatly from you on this point. Time just does move forward. In the discrete sequences of moments we are discussing, the relevant "jumps" can be assumed to all have equal length (1 day, year, etc).
how one proposing an actually completed infinite past can avoid the impossibility of traversing endlessness to reach the present.
I'm simply not going to get involved in another discussion of "endlessness". If that concept makes sense, then I think one should be able to translate it into standard language that people use when describing ordered sets or sequences.
Time has a structure amenable to a step by step sequence, where it is clear that an infinite past must include actually once the present stages that are now endlessly remote beyond any finite value of passage of time.
It is not clear. At least not to virtually everyone who has published on this subject.daveS
October 27, 2016
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DS, please address the issue of exactly what an infinite actual past means, what it means for time to move forward and how one proposing an actually completed infinite past can avoid the impossibility of traversing endlessness to reach the present. As for mathematical proofs and notation, math is the logic of structure and quantity. Time has a structure amenable to a step by step sequence, where it is clear that an infinite past must include actually once the present stages that are now endlessly remote beyond any finite value of passage of time. Endlessness -- which seems to be your main point of objection, is implied by the simple logic that at any finite past "distance" k, we can go to the onward previous stages endlessly: k, K+1, k+2 . . . if there is an infinite actual past. But the same endless"distance" would have to be traversed in finite stage steps going forward to reach to now. But to so span endlessness as an attempt is necessarily futile. That is what you need to solve and reaching backwards and pointing on further backwards does not solve it. KFkairosfocus
October 27, 2016
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