Can the universe be infinite towards the past?
In his Conjectures and Refutations, Karl Popper mentions one of Kant's theses from his antinomies as follows:
[quote=Karl Popper]The first proof begins by analyzing the idea of ??an infinite succession of years (or days, or any other equal and finite time intervals). This infinite succession of years must be such that it continues forever, and never comes to an end. It can never be completed: an infinity of years elapsed is a contradiction in terms. Now, in his first proof, Kant simply argues that the world must have a beginning in time, since otherwise an infinite number of years would have elapsed at the present moment, which is impossible. This concludes the first proof.[/quote]
Maybe I don't quite understand Kant's argument as Popper presents it, but: isn't that as fallacious as arguing that the series of negative integers cannot be infinite because otherwise it could never reach -3?
The statement that the universe cannot be infinite towards the past because that would imply going through or traversing an infinite number of events to get to the present seems false to me, since it seems to assume that in traveling such a series of events one goes through or traverses from an initial moment to the present, while this infinite universe towards the past by definition has no initial moment.
If, on the contrary, the journey begins at some point in the past which is not an initial moment, it does not matter how much one goes back in the timeline, the events and time from that moment to the present will always be finite, and there is therefore no impossibility in a universe whose time is infinite to the past.
And it makes no sense to say "but the journey begins before the temporal events begin", because there is no point in time in which they begin according to this model (again, by definition).
I guess one could argue that time doesn't have to elapse or be traversed “from some moment in time to some other moment in time”, but then it's not clear to me what is meant by “elapsed” or “traversed”.
Maybe someone in the forum can enlighten me about this.
[quote=Karl Popper]The first proof begins by analyzing the idea of ??an infinite succession of years (or days, or any other equal and finite time intervals). This infinite succession of years must be such that it continues forever, and never comes to an end. It can never be completed: an infinity of years elapsed is a contradiction in terms. Now, in his first proof, Kant simply argues that the world must have a beginning in time, since otherwise an infinite number of years would have elapsed at the present moment, which is impossible. This concludes the first proof.[/quote]
Maybe I don't quite understand Kant's argument as Popper presents it, but: isn't that as fallacious as arguing that the series of negative integers cannot be infinite because otherwise it could never reach -3?
The statement that the universe cannot be infinite towards the past because that would imply going through or traversing an infinite number of events to get to the present seems false to me, since it seems to assume that in traveling such a series of events one goes through or traverses from an initial moment to the present, while this infinite universe towards the past by definition has no initial moment.
If, on the contrary, the journey begins at some point in the past which is not an initial moment, it does not matter how much one goes back in the timeline, the events and time from that moment to the present will always be finite, and there is therefore no impossibility in a universe whose time is infinite to the past.
And it makes no sense to say "but the journey begins before the temporal events begin", because there is no point in time in which they begin according to this model (again, by definition).
I guess one could argue that time doesn't have to elapse or be traversed “from some moment in time to some other moment in time”, but then it's not clear to me what is meant by “elapsed” or “traversed”.
Maybe someone in the forum can enlighten me about this.
Comments (148)
How do you imagine negative time for yourself? Kant spoke of time, which clearly has a beginning and is always positive. And the past for us is also a positive time. Relative to zero
In physics , the notion of actual temporal infinity is metaphysical in the literal sense of meta-physics, i.e it is a proposition that cannot be falsified, verified or even weakly evaluated through experiments.
However, there cannot be any empirical evidence on the basis of the observable universe to posit a past of any particular length. Therefore, the idea of a potentially infinite past is both perfectly consistent and the least assuming position to adopt. This position is adopted by presentists, who view the past and future as logical constructs that are reducible to sense-data. It's also compatible with quantum mechanics, due to the fact that QM has perpsectivalist retrocausal interpretations.
Quoting SimpleUser
I suspend judgement as to the question whether time had an absolute beginning or not.
Quoting SimpleUser
In this antinomy, Kant considered a universe which is infinite towards the past, which by definition has no beginning, and argued that it is logically inconsistent. Leaving aside the fact that later he argued that we cannot apply the notions of space and time to things that we do not experience (which I think is correct), i.e. the universe as a whole, my point is that the argument he used to prove that the universe cannot be infinite to the past doesn't appear valid regardless.
Quoting sime
Could you elaborate a bit on how it's incompatible with asymmetric causality? I'm not very well acquainted to the idea.
Quoting sime
If by “reversing the direction of causality” you mean that we must go back into the chain of causes and arrive at a first cause, why must we? Doesn't that already assume that the universe must be finite towards the past, and thus beg the question?
Whether or not it contradicts our intuition, that is no ground for rejecting physical models with an actual infinite past, since many physical discoveries also contradict our intuitions and are nonetheless true.
Quoting sime
I mean, it's currently finite towards the future (up to the present moment).
Whether time has an absolute end at some point in the future I do not know, though physicists assure us that the universe very likely will come to freeze completely (such is one of the most plausible theories at present anyway).
I guess one could argue that even in such a completely static universe, time still passes, in which case the future time would be infinite.
But at any rate, why would an infinite future, in the sense I have described, be incompatible with an infinite past?
Quoting sime
Here I probably agree with you: I don't see how such a proposition could be falsified.
Quoting sime
Hmm, I'm kind of puzzled with regards to this idea of a universe with a “potentially infinite” past.
I mean, the past is either finite or it's infinite, right? What is meant by “potentially infinite” then?
Negative integers have a necessary originating condition, so arriving at -3 is not impossible. The totality of the series of integers is infinite, but a particular member of the series is given by the mere assembly of count from whatever arbitrary origin. Now, the infinite divisibility of an aggregate quantity, represented by numbers, on the other hand, would make arriving at -3 impossible.
With respect to Kant reflected in Popper, the world exists, which makes explicit a necessary origin in time, therefore the time of the world cannot be an infinite series, even if time itself, is, irrespective of phenomena. And while space is infinitely divisible, the world is already a whole conceptual aggregate in itself which immediately defines the limits of its own finitely divisible space. The tacit understanding here is, if divided too far, in order to conform to the infinite divisibility of space in general, but regarding only that space the world inhabits, the world is no longer conceptually identical to its original, hence the incurrence of a “transcendental illusion”.....the very thing the antinomies make apparent.
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Quoting Amalac
Interesting. Where do he prove that, exactly? I don’t know of it, and couldn’t find a reference in the texts for it. As far as I understand the antinomy, he describes the confines of it, to certain determinations, of which there is the world, and there is nature...not Nature, nor reality in general, just the constituency of whatever is being considered at the moment....but only makes reference to the universe as a object in the refutation of its viability in any argument with respect to the world.
In fact, I don’t think he attempted to prove the universe cannot be infinite to the past, for to do so is to exchange a phenomenal object of sensibility, which is solely determined by the pure intuitions of space and time thus a possible experience, for an intellectual object of understanding, which cannot be so determined at all thus can never be an experience. If anything, he proved the universe cannot be argued to be infinite to the past, or infinite in any relation to time or space, under the same conditions from which the world is so argued.
But...maybe I missed something, so I’d welcome a little help.
By asymmetric causality, I am referring to either the belief or definition of causality such that causes come before their effects. This is a physically problematic assumption due to the fact that the microphysical laws are temporally symmetric.
Quoting Amalac
The realist interpretation of potential infinity is that it is epistemic ignorance of the value of a bounded variable. For the realist an unobserved variable has a definite value irrespective of it's measurement or observation . Hence for the realist, the value of a variable is either actually infinite or it is finite, with no third alternative.
Likewise, the constructive interpretation of potential infinity also refers to a bounded variable whose value if measured, is necessarily finite. The difference is, it doesn't assert the existence of any value until as and when the value is constructed. In computer programming terms, a potentially infinite natural number in this sense refers to a natural number variable that is lazily evaluated . Only upon evaluation, does the variable possess a definite (and finite) value.
The logic of a potentially infinite past in this constructive sense is superficially demonstrated in the video games genre known as "roguelikes", where a player assumes the role of an adventurer who explores a randomly generated dungeon that is generated on the fly in response to the player's actions.
The existence of the games are effectively a demonstration of the coherence of retro-causation that is conditioned upon the players present choices. Of course, a realist will be quick to point out that the implementation of such games demonstrates nothing of the sort, being as it is an ordered sequence of instructions with a beginning and end. The deficiency of the realist interpretation of the game must therefore be argued by other means, such as by the Quantum Mechanical refutation of local causation + counterfactual definiteness + no conspiracy.
In the current context regarding the truth of past-contingent propositions , a constructive interpretation of history is that a past cause of an event does not exist over and above the construction of presently existing historical information. For example, if the present state of the universe is compatible with Jack the Ripper having any number of historical identities, then according to historical constructivism Jack the Ripper did not exist and does not exist until as and when his/her identity is constructable from historical information. And because historical evidence is rarely conclusive, the constructivist is forced to reject the assignment of a definite truth value to most, if not all, past-contingent propositions.
Quoting Mww
Doesn't seem that explicit to me, how does that follow? (1. The world exists, 2.???, 3. Therefore, the world has an origin in time)
Quoting Mww
I meant as in “apparently prove”, since by Kant's reasoning one can also “prove” that the universe cannot be finite towards the past.
So the conclusion of the antinomy is that there is no scientific sense in the very question: “is the universe finite or infinite towards the past?”, right?
But my point was that even his “apparent proof” seems invalid.
:up:
The universe probably does have an origin, as it appears to have starting conditions, but that doesn't veto counterfactual worlds with infinite histories. The key, as you say, is getting past our everyday intuitions based on a universe that did have starting conditions, and in taking relativity seriously.
Quoting sime
Ok, I'm fine with this.
Quoting sime
Hmm, ok.
So it's sort of like the universe, in the sense that it is constantly expanding. But supposing one could “catch up” to the expansion (in some possible world), would there be anything beyond the expansion, or would space somehow “end” there? (maybe I'm just very confused about this matter).
Quoting sime
I'll plead ignorance about this point, I don't know enough physics to comment on that.
But I guess my point is that the notion of “cause” may not be applicable to the total, as Russell pointed out in his famous debate with Copleston.
If we see the universe as a “set” or “collection/bundle of events”, then there may be no sense in asking what its cause is, just as there is no sense in asking what the cause of “the set of all ideas” is, in the same sense as we would ask what the cause of a rock, or of lightning, is.
But then again, Russell did also say that matter could be seen as a way of grouping events into bundles, so maybe there is a sense in asking for the cause of sets after all.
That’s fine; it doesn’t have to be explicit to you. I said with respect to Kant reflected in Popper, in which there is no 2.???. That the world exists and therefore has a necessary origin in time, is an analytic...tautological....truth of logic, insofar as its negation is impossible.
As a matter of dialectical interest, though, how does the statement not follow, from your point of view?
Quoting Mww
Seems to me like that would only be true if the universe were finite towards the past, which doesn’t seem tautologically true, since if it were, no philosophers or physicists would argue about it: they would all agree that the universe is finite towards the past.
Or perhaps I’m misunderstanding and you are talking about the other thesis, which holds that the universe did have a beginning, in which case yes: by definition it does, but only because Kant assumes for sake of argument that it does have an origin in time, to show how that assumption leads to a contradiction, as well as the antithesis which holds that it doesn’t have an origin in time.
Evidence that the universe is finitely existent in the past is provided by the mathematically logical necessity of singularities. If singularities are real phenomena, then the existence of the universe follows the same logical criteria as is followed by the world. Thing is, experience informs us of the phenomenal reality of the world, but cannot inform us of the phenomenal reality of the universe or of singularities. Can’t use the criteria for what it is possible to know, in determinations for what is not.
Right. As you point out, a notion of causality cannot play a role with respect to any data-set that is regarded as complete and self-contained. This creates a conflict within realism, for realists tend to simultaneously assert i) the transcendental reality of causality, ii) the transcendental existence of a completed universe whether finite or actually infinite, and iii) that counterfactual propositions have a definite truth value independent of actual measurements and observations.
By contrast, if the reality of an inter-subjectively complete universe is denied, then causality can not only retain it's useful meaning as referring to the potential outcomes of an intervention relative to an agent's perspective, but also it's ontological status to a limited extent, albeit not necessarily as a linear ordering of events from "past" to "future". Bayesian networks come to mind here.
Quoting Mww
If you have to look for evidence in support of that proposition, then it's no longer a tautology. It may be logically necessary given the laws of physics that govern the actual universe, but these laws themselves are not logically necessary (as in: they could have been different, and could even change in the future).
As for singularities, if you are talking about gravitational singularities, then I guess you are refering to the Big Bang being one.
Well, I seem to remember that some scientist (was it Sean Carroll? Lawrence Krauss?) said that the Big Bang is a sort of placeholder for our ignorance, the limit to how far back we can know the cosmos.
There are some things that are not too clear to me: Is the Big Bang the cause of the observable universe? Or is it the cause of the universe in an absolute, all-encompassing sense (both the observable and the unobservable universe)?
Because I'm refering to the universe in the second, all-encompassing sense.
Now, I know some people say that time “appeared”, so to speak, with the Big Bang, but that seems problematic to me for many reasons, one of them being that it is not clear that time actually exists outside our minds, and if it doesn't exist outside our minds then there is no sense in saying that time appeared with the Big Bang, since in that case time “appeared” when the first subject who imposed time onto what he perceived appeared. Such was Kant's point of view, for instance.
I don't know how we could know if time exists outside of our minds or not.
Quoting Mww
Maybe here is where I misunderstood you, I thought you were using the words “world” and “universe” as synonyms.
But I agree with Kant's conclusion: there is no sense in asking such questions about the universe as a whole.
It's quite clear why Aristotle thought that way; after all, the definition of infinity is such that the very notion of completion/an end is incompatible with it.
The only supposedly actual infinity I'm aware of is the set of natural numbers {1, 2, 3,...} but then it's an axiom [something arbitrarily assumed as true].
Suppose we do accept that there are actual infinites like in set theory vide infra. If so, an infinite past maybe one of the possibly many actual infinities out there.
Argument A
1. For any given point in time, one can always ask what preceded it temporally? [premise]
2. If for any given point in time, one can always ask what preceded it temporally? then, the past is infinite [premise]
3. The past is infinite [1, 2 MP]
Argument B
4. There is no actual infinity [premise??]
5. If there is no actual infinity then, false that the past is infinite [premise]
6. False that the past is infinite [4, 5 MP]
As you can see, line 6. False that the past is infinite, requires premise 4. There is no actual infinity [in bold]. The problem is the subargument 1 through 3 with the conclusion 3. The past is infinite, seems perfectly sound. If so, one option we have is to abandon the belief, albeit itself reasonable as per the definition of infinity, that 4. There is no actual infinity.
Put simply, an infinite past is an actual infinity [completed].
Quoting TheMadFool
What about the series of negative integers? It has no first term of course, but it ends in -1, so that it is “completed” in that sense. Why can't the timeline of the universe be like that (with -1 being the present, so to speak)?
If being “completed” means that one must be able to write down all of the elements of the series, then why should we accept that criterion as the one which determines whether a series of elements can “exist” or not?
I'm afraid you misunderstood me or did I not get what you're saying?
The past is infinite and an actual infinity at that; after all, we're at some point in time (this now) that can be only if infinite time did pass [another way of saying completed/actual infinity].
I like what you said :point: "...if being "completed" means that one must be able to write down all the elements of the series..." I think you're on the right track.
I’m not supporting the proposition, but merely stating it. The solutions to the field equations support it, which are not subject/copula/predicate propositions, but mathematical formulations, and while not analytical, are nonetheless true. If otherwise, the entire human system for knowledge certainty is in serious jeopardy, regardless of its adaptability to changes in observational data.
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Quoting Amalac
Laws don’t govern the universe; they are human constructs representing how the universe appears to govern itself. In that regard, I agree you are correct, in that they are only as certain as the observation data from which they are derived. Mathematical certainty is not predicated on the apparent operation of the universe, in that they must be certain under any conditions whatsoever, no matter what we discover about the universe. Mathematics is our creation; the world is not.
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Quoting Amalac
Nope. Using the concepts....the words.... as you are.
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Quoting Amalac
Nor do I. Theoretically it cannot, but you know what they say about theories.
Quoting TheMadFool
But when someone says an infinite amount of time “passes”, if they don't mean that it passes from some moment in time to some other moment in time (which clearly cannot be the case), then I do not understand what is meant by “passing”. In the case of a universe with an infinite past, the idea that time must “pass” from a beginning moment all the way to the present seems false, since by definition such a universe has no beginning moment:
Quoting Amalac
Quoting TheMadFool
If that's what you mean, that what's your response to this?:
Quoting Amalac
Meaning: Why is whether it is “enumerable” or not the way to determine if it's possible or not?
Quoting Mww
Ok, but you said before that it was a tautology, which seems untrue: the universe is not by definition finite towards the past, which would be the case if you could deduce that from the definition of “universe” alone, there would be no need for empirical observation.
I said that the world exists and therefore has a necessary origin in time, is a tautology, a analytic truth.
Review my arguments below.
Argument A
1. It makes sense to ask about a time before any given moment in time
2. If it makes sense to ask about a time before any given moment in time then, the past is infinite
Ergo,
3. The past is infinite [1, 2 MP]
Argument B
4. We are in the present, the now
5. If we're in the present, the now and the past is infinite then, the infinite past (has passed) is an actual/completed infinity
6. We're in the present, the now and the past is infinite [3, 4 Conj]
Ergo,
7. The infinite past (has passed) is an actual/completed infinity
You're bothered by how if the past is infinite, time has no beginning and ergo, you contend that time couldn't possibly pass. This, if you really think about it, is just another way of expressing the idea that the past is finite. In other words, there has to be a beginning for time = the past is finite. Simply put, a petitio principii - you can't claim the past is finite because the past is finite.
As for the passage of time, we're here, in the now, right? Considering the past is infinite (see proof above) and we're here, in the now, time has passed.
If you are not using the words “world” and “universe” as synonyms, then what's the difference between the two?
Quoting Mww
Right, but that would mean that we could deduce the proposition “The world has a necessary origin in time” without experience, merely by analysis of the concept “world”, right? I don't think that's the case, but maybe you could show me how that proposition is analytic.
It appears this "world" or "universe" isn't a simulation after all. Infinite computing power is required for an infinite past. I don't know if I should laugh or cry.
Quoting TheMadFool
If there is no beginning in time, then yes.
Quoting TheMadFool
If 1 is true, then yes.
Quoting TheMadFool
That does follow if 1 and 2 are true.
Quoting TheMadFool
If the past is infinite, then the infinite past is an actual/completed infinity, if by that one means merely that it is the case in reality. But that does not imply that an infinite amount of time has “passed” up to the present moment.
For I ask: From/since when to when did it pass? You can't say “From the beginning of the universe to the present day”, Because there is no “beginning of the universe” in this model.
And if you say, it passes from some moment in the past that wasn't the beginning up to the present moment, then a finite amount of time has passed, not an infinite amount, and that poses no problems.
Quoting TheMadFool
No, did you read my OP? I'm trying to show that there is nothing logically inconsistent about a universe with an infinite past, against what Kant tried to “prove” with one of his theses.
I'm saying an infinite amount of time has not “elapsed”, but also that that doesn't contradict a universe with an infinite past.
Quoting TheMadFool
No, what I'm rejecting is Kant's argument which states that the universe couldn't have been infinite towards the past because that would imply that an infinite amount of time would have elapsed up to to the present moment.
That one would be the one that begs the question, by assuming tacitly that the universe must have had a beginning in time: It assumes that such an infinite universe both has and doesn't have a beginning in time, which is just a way of creating a strawman of the person who holds that the universe is infinite towards the past.
Quoting TheMadFool
If you look at my previous posts again, you'll see that I don't have a problem with the idea of time passing, but with the idea that “if the universe has an infinite past then an infinite amount of time must have passed”.
So, if you are saying that, that's what I'm rejecting.
But if you insist: From/since when to when did it pass? It must have passed from some moment in time to some other moment in time, right?
The world is a phenomenon, an object of experience, now that we’ve witnessed it in its entirety from outside its limits; the universe is not. If the universe is the condition for space and time, it cannot be a phenomenon determined by them. Trying to equalize them, is, as the Good Professor says, “...a mere subterfuge...”, nevermind the lengthy exposition on why this is so.
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Quoting Amalac
I don’t know how that would be possible, if the world is a particular thing but the universe is all particular things in general. Claiming the last because of the first would be induction, which everybody from Hume onward, epistemologically worthy of his letters, says is unreliable. Besides, claiming anything empirical without the regulation of experience is not sufficient for knowledge.
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Quoting Amalac
How the universe has a necessary origin in time? Hmmmm.....I don’t think that can be shown, unless it can be shown the origin of the universe is simultaneous with the origin of time.
Anyway.....does that work for you? Don’t forget we’re doing metaphysics here, not hard science.
Quoting Mww
Ok, so according to this distinction the universe is never experienced as a phenomenon, unlike the world, right?
You say that we've witnessed the world in its entirety, but then what do you make of philosophers and physicists who speak of unknown parts of the world, and parts we have not observed yet or of whose existence we are not even aware at present? If those are part of the world, surely it can't be said that we've witnessed the world in its entirety.
On the other hand, if we define the world as all the phenomena we've experienced and whose existence we're currently aware of, then I agree that it must have had an origin in time (though I'm not sure about that being an analytic truth).
Quoting Mww
That would mean that the universe “begun to exist” (so to speak) “at the same time” as time. But I thought that the universe, according to you, was the condition for space and time, in which case wouldn't that imply that the universe is determined by time, contrary to what you said? I thought only phenomena could have origins in time, meaning the universe, as you defined it, would have no origin in time.
Also, that would seem to imply that there was time before the origin of time (for how else would the universe originate at the same time as time?), which is surely absurd.
Or else what do you mean by “origin in time” when speaking about the universe?
We could start with an anecdote attributed to Wittgenstein:
Seems to violate our intuition and the principle of sufficient reason. Fair intuitive argument.
OK then, a definite earliest moment it is, a t=0 if you will.
The Big Bang stuff gives an age of about 14 billion years of the known/observable universe.
If we were to humor the cosmological argument (of religious apologetics), we're led to believe there was an "outside", "atemporal" cause of it all.
Yet, then the question is why 14 billion years, and not some other age, any other age actually?
Seems to violate sufficient reason again.
Everywhere, counterintuitive implications everywhere? Should we just make stuff up? Drop sufficient reason (in this case at least)? Are we back to square one? A non-infinite "edge-free" universe?
I'd say we should follow Kant's view on this matter:
[quote=Karl Popper]What lesson did Kant draw from these puzzling antinomies? He concluded that our ideas of space and time are inapplicable to the universe as a whole. We can, of course, apply the ideas of space and time to ordinary physical objects and physical events. But space and time themselves are not objects or events: they cannot even be observed, they are more elusive. They are a kind of framework for things and events, something like a box system, or a recording system, for observations. Space and time are not part of the empirical, real world of things and events, but are part of our mental equipment, of our apparatus to capture the world. The appropriate use that can be given to them is that of observation instruments: when observing any event we usually place it, immediately and intuitively, in an order of space and time. Thus, space and time can be considered as a frame of reference that is not based on experience, but is used intuitively in experience and is appropriately applicable to it. This is why we are inconvenienced when we misapply the ideas of space and time, and use them in a realm that transcends all possible experience, as we did in our two proofs on the universe as a whole.[/quote]
It's my general observation that when physicists talk about infinity they usually mean something entirely different than the way mathematicians use the term. They usually do mean unbounded, or even "really, really big." In the case of eternal inflation, though, my understanding is that they really do mean that time is literally infinite, actually infinite, in the future. That's the only way they can get the math to work out. As far as Penrose's endless cycles, I don't know if he believes they go forever in the past and the future, but I don't see why they wouldn't. In the theory, at least.
I side with the physicists on this.
Your account looks pretty accurate to me. This argument does nto show that hte universe could not have an infinite past.
SO the question arrises as to how accurately it represents Kant's argument.
And a different question would be how modern cosmology treats such things.
Quoting Banno
Well, here's Kant's argument from my copy of the Critique of Pure Reason:
[quote=Kant]Suppose the world does not have a beginning in time. In this case, an eternity has elapsed until each given instant and, consequently, an infinite series of successive states of things in the world. Now, the infinity of a series consists in that it can never be finished by means of successive syntheses. Therefore, an infinite past cosmic series is impossible and, consequently, it is an indispensable condition of the existence of the world that it has had a beginning, which is the first point that we wanted to demonstrate.[/quote]
It's perhaps not quite the same as Popper's interpretation, if taken literally, but it is very similar, and seems open to the objection I gave in the OP.
Infinite Regress.
Quoting Amalac
:up:
Quoting Amalac
Bravo! :up:
Quoting Amalac
The proof that an infinite amount of time has passed rests, in my humble opinion, on the proposition that the past is infinite. You claim to have no problems with an infinite past but then you say you can't accept that "if the universe has an infinite past then an infinite amount of time must have passed". It doesn't add up. :chin:
Quoting TheMadFool
Oh dear, just answer the question: Assuming the universe was infinite towards the past, and that an infinite amount of time passed all the way to the present, since which moment down to the present did it pass? Since when to when did it pass?
Oh, here it is:
https://books.google.co.uk/books?id=Vt02DwAAQBAJ&pg=PA121&lpg=PA121&dq=wittgenstein+1+4+1+point+3+pi+recite+backwards&source=bl&ots=drDGa7JnGK&sig=ACfU3U0vbOTOEOidWOnN8bql44DahvKw6A&hl=en&sa=X&ved=2ahUKEwixvO60pvjwAhULlRQKHUwkB98Q6AEwBnoECAUQAw#v=onepage&q=wittgenstein%201%204%201%20point%203%20pi%20recite%20backwards&f=false
This question has an underlying inconsistency. When you assume "...the universe was infinite towards the past...", you shouldn't be asking "...since which moment down to the present did it pass? Since when to when did it pass?" because that question, whatever else it is, presupposes a beginning, a starting point, to time - the "which moment", the"when" in "when to when".
It's difficult to wrap your head around such matters. Before you know it, you're going around in circles.
Quoting TheMadFool
So you are saying that an infinite amount of time “passed” in that infinite past universe, but not since any particular moment in time. What do you mean by “passed” then?
Great question and I don't have a good answer but for what it's worth, I offer my own point of view below.
It can be said that both time and space are more or less the same concept [Minkowski space-time in which time is the 4th dimension].
That out of the way, does it make sense to ask about the passage of space. Nothing weird happens to our brains when we talk of space being infinite. I'm here in Dublin, Ireland and the space in front of me could be infinite and so too the space behind me and the same goes for up, down, the left, and the right of me and no one has any trouble accepting that. In fact, it seems so believable to imagine space like that (infinite in all directions) that it's become second nature to one and all.
Time, on the other hand, is viewed as something that passes and thus the difficulty some face in accepting an infinite past - time has to begin for the passage of time to make sense. After all, time passage is, all said and done, an interval which, by definition, requires at least two points (in time), a beginning and an end.
You might've already guessed what the nub of the issue is by now. It seems to be the difference in perception of space in time - space is static [we don't say space flows/passes and time is dynamic [we say time flows/passes]
Do we have valid reasons to justify such differential treatment of space and time? Why is time (thought to be) in "motion" and space (thought to be) is "motionless"?
If, just for the heck of it and nothing else, we stop treating time as something that flows and consider it as just another kind of space, the problem that we're discussing will be resolved - the concept of pass, passing, passage can't be applied to time, it would be a category error of sorts. If so, your question about between which two points did the infinite past pass becomes meaningless.
There are two ways of thinking about infinity: something that has no limit; and the other way, no matter how much you add to it, that is, no matter how far you push its limit, it will not end.
Kant is using the second way of thinking about infinity, and he says no matter how much you add to it, it won't end, but it won't be infinite, either. As long as you are in the process of adding, you have a finite number, and the finite number will never become infinite, as long as you are in the adding stage, even if the adding theoretically never ends.
This is an interesting concept to refute on an intuitive level.
The only way I can challenge it is by saying that the two ways to approach infinity both indicate a quantity that is infinite. As long as you stipulate that the adding will never reach a limit no matter how much of the thing you add to it, you can't divorce the one type of infinity from the other.
Once this equivalence has been established, then there is a way to assert that there are inifinite years ahead of us. We can't count them all by pushing the upper limit of the number of years we keep adding, no matter how many years we add to extend the reached limit of years in the future. But we know, because of the equivalence of infinity defined by the two ways, that there are an infinite number of years ahead of us.
And then it's clear that there are an infinite number of years that have passed already to the present day.
Quoting Amalac
Limits indicates a spatial boundary. Witnessing indicates observation. To witness an object from outside its limits merely indicates observing the object’s spatial boundaries. Observing a boundary has nothing to do with the experience of the total constituency of the object observed. In fact, the total constituency, the composition, of an object is immediately given because it is bounded, whether or not there is any experience of it.
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Quoting Amalac
I don’t think it logically correct to grant empirical causality from simultaneity. That every effect has a cause presupposes a time by which the cause is antecedent to the effect. If the universe causes time, and time is already presupposed, the principle of cause and effect self-destructs. Assuming the absolute validity of the principle, the only reconciliation is simultaneity, in which time is no longer presupposed, yet for which account is given.
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Quoting Amalac
There is no present. Questions predicated on impossibilities are irrational.
I will disagree. There is one way to think of infinity, and another different way to think of the infinite.
Infinity is its own thing; all that is infinite is each its own thing.
Which is Kant’s argument, among others. Fascinating or not, not wrong.
“...Now, just as the unit which is taken is greater or smaller, the infinite will be greater or smaller; but the infinity, which consists merely in the relation to this given unit, must remain always the same, although the absolute quantity of the whole is not thereby cognized....”
I can live with that, if you can.
Quoting Mww
This is actually not right. There is no such thing as "infinite" other than to describe a feature of infinity. If infinity is the same whether you take a smaller or a larger unit, then the infinite, which is an adjective, not a noun... hence the confusion. You are familiar with Kant. Has he actually defined the "infinite" somewhere, or he is just using this word? If he defined it, then his definition is different from "infinity", maybe; and therefore he can't equate the two.
I would really like to see Kant's explanation of what he envisions as the infinite. It is an adjective in modern English, but this has been translated, and the translations bastardized the original. Maybe we could ask you to give us the German words he used for infinite and infinity? or maybe we (that is, I, let's be frank) could ask you, like I said, a definition or an explanation what Kant means by infinite? he can't mean infinity when he says infinite, since he makes a distinct difference between the two (without explaining it, here; but elsewhere there may be an explanation.) I repeated myself enough times in this paragraph.
The upshot is that since he does not equate the infinite with infinity, his proof breaks down because he is comparing apples with oranges, so to speak. He is proving there are no infinite number of years, because infinity contains infinite number of years, but the INFINITE does not.
Hence, Kant is pulling the wool over the eyes of some. He says that although we believe A is B, and we know that C is D, therefore A cannot be B. This is completely fallacious.
Make of these what you will:
“...A quantity is infinite, if a greater than itself cannot possibly exist....”
“...The true (transcendental) conception of infinity is: that the successive synthesis of unity in the measurement of a given quantum can never be completed....”
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Quoting god must be atheist
If the infinite is an adjective as you say, why can’t it describe a feature of a quantity? It may have been clearer if he’d said the unit is taken to be more or less, then the infinite will be greater or smaller. Still, this must be understood as a quantity approaches infinity by means of the more or fewer units in it.
Dunno how infinity can have features anyway. All it can ever be is an uncompleted series. Then it is only a feature of the series, described by its incompleteness.
As I said, for whatever it’s worth....infinity is a conception of its own, there is no object associated with it. That which is infinite, has as many conceptions associated with it as there are infinite things.
Anyway.....this is the kinda thing that can be played with all day, no one the happier for it beyond the time used for it not wasted somewhere else.
adjective, noun? :chin:
[quote=Bill Hicks]As long as we're making shit up, go hog-wild, you know[/quote]
But you don't have to, right?
Why? Are you expecting a gift?
Quoting Mww
What is the boundary of the world then? I guess you mean something like the CMB? But just because we cannot see beyond the CMB, that doesn't mean that there's nothing “beyond” it, so to speak, only that we could never see it in the actual world (though we could in some possible world, unless there's something logically impossible about it).
Quoting Mww
So by simultaneously you don't mean “at the same time”, what do you mean by that then? Logically simultaneous?
Quoting Mww
If there's no present, and an infinite amount of time has elapsed as Kant maintains in the first thesis, since when to when did it elapse?
Quoting TheMadFool
Well to go back to Kant, when he's speaking about time passing he means that time has “elapsed”. Surely, it wouldn't make sense to say that space “elapses”.
Even the Oxford dictionary defines the term as only applicable to time:
Elapse: (of time) pass or go by.
At any rate, time is certainly not in motion in the same sense in which a physical object is in motion, right?
Quoting Cuthbert
There are rigurous proofs of the irrationality of ?, so yes, that's logically impossible.
Following that example: We can never begin recting all the negative integers (from smallest to biggest), but that doesn't mean that there is no such thing as the set of all negative integers, likewise we can't recite all the digits of ?, but that doesn't mean that there is no such thing as the ratio of a circle's circumference to its diameter.
Whether it's “enumerable” or not doesn't seem like a good criterion for determining whether it is possible for it to exist or not.
...since when?
you are using it as a noun.
You used it as a noun when you quoted Kant.
I wish to know how the two concepts in Kant's definition are described: infinite and infinity.
This is where the buck stops. Until you enlighten me, we are stuck in this discussion.
Time elapses “since” some moment in time (not necessarily an absolute beginning in time of the universe) “to” some other moment in time.
If not, then I don't understand what you mean by “passed”.
Quoting Amalac
By "an infinite number of years that have passed" I meant "an infinite number of years each of which came after another".
If you want to pinpoint the phrasing to points in time, then "an infinite number of years have passed in a series of infinite number of points in time, each point being between two consecutive years." This is just one way of an infinite way of saying the same thing.
That doesn't answer my question.
“5 years have elapsed since 2016 to today” has a clear meaning for me, but “infinitely many years have passed since «never» to today” doesn't.
Something that happened/passed since “never” is something that in fact didn't happen/pass.
I did not say "It happened since never."
I answered your question. Which part of "infinite number of points each of which are between two consecutive years" do you not understand? I'm willing to work with you on that.
I would venture to assume that if you can conceptualize five years that have passed since a point in time, then you can also conceptualize one year passing since a point in time.
Quoting god must be atheist
Then since when?
Quoting god must be atheist
I thought earlier you said the question wasn't even legitimate. But anyway, just tell me how you define the term “passed” (what I asked you before).
“X amount of time passed” by definition implies that it passed since some point in the timeline to some other point in the timeline.
So if you say an infinite amount of time has passed up to the present day, then you must also say that it passed since some point in the timeline, otherwise I've no idea what you mean when you say an infinite amount of time “passed”
If you need to know how I defined "passed", which is a commonly used English term or word, then how can I be sure ahead of time that the terms I use in the definition will be clear to you? You may turn around and ask me to define each word in the definition. It is not an impossible expectation by me that you will, because if you don't know what "passed" means, then there are very likely a lot of other things you don't know.
Quoting Amalac
I actually said, if you would kindly check, that an infinite number of years passed, not an infinite amount of time.
I understood this question by you, and I answered this way:
Quoting god must be atheist
I appreciate that my composition is awkward. So please consider this. It has your point you insist on, it has infinity, and it has the years. It's all in there. Please read carefully.
"A year passed after a point in time that marked the end of the previous year, in an infinite series."
You are forcing me to mince words, and you know that; it's fine, I can do with some English construct exercises. Thanks.
Quoting god must be atheist
As it's commonly used, “passed” or “elapsed” implies a beginning and an end.
This sort of definition is the one I have in mind:
That definition doesn't assume that the universe must have had a beginning in time, for if the universe has no beginning in time, I can still say for instance: 13.8 billion years have elapsed since the Big Bang happened to today. But I can't say: infinitely many years have elapsed since ??? happened to today.
If you say that time doesn't have to pass or elapse “since” some moment, then you are using the term in a way that's different from how it's usually used, hence why I ask you to tell me what you mean by that.
Quoting god must be atheist
Isn't an infinite number of years an infinite amount of time? I don't see how that distinction is important.
Quoting god must be atheist
Surely, this doesn't answer the question: “Since when did infinitely many years pass up to the present?”
If I asked someone: “since when have 5 years passed? I expect them to simply answer: “since 2016”.
So if I asked you “since when have infinitely many years passed?”, I expect you to answer “since year X”.
So what's the value of X?
Perhaps you just mean that if the universe has an infinite past, then an infinite amount of time “exists” or “It is the case that the past is infinite”, which is fine by me, and doesn't fall prey to Kant's criticism.
Quoting Amalac
You're right. And this is why I paraphrased it. And I assure you I did not use it differently from you. You can live with that definition, as long as you are able to comprehend my paraphrasing the concept.
Watch this carefully:
I use the same term in the same way and in the same meaning as you in this:
I will NOT change the meaning or the usage, but you must follow me carefully.
Can a year pass after a year ends? Yes or no. If you answered yes, you were right.
Can you name the end of a year a point? Yes or no? If you answered yes, you were right.
Can you imagine three years in a row, with two occurrances of one year ending, and another beginning at one point in time in the three-year period? If you can imagine that, please continue.
Can you imagine a thousand years in a row, with a thousand minus one occurrences of one year ending, and another beginning at one point in time in the thousand-year period? If you can imagine that, please continue.
Now... take a deep breath... if there are an infinite number of such one points, that each of them are between two consecutive years.... is that hard to imagine? Yes, or no? If no, then forget it, I can't show it to you.
Now... a passing of a year is between two points. Each of the years in the above series passed between two points... and there is an infinite number of them.
Does this make sense to your pedantic insistence on the proper use of "pass", "year", "infinite" and "and" and "you" ... etc. etc.
Exactly. You are absolutely right. But to get the point, as it may be, across to you over the hurdle of pedanteria, you had better accept that the two are equivalent.
If you go back, I did point it out to you that this is the wrong question. Much like asking "how manieth infinitely small point is the end point in a straight line segment consisting of an infinite number of infinitely small points?"
I perceive/sense location and distance, which are different from the located and distant (like objects), and perceiving/sensing this takes time.
My coffee is out in the kitchen, some meters away, not everywhere, anywhere, nowhere, but somewhere.
I perceive/sense change when fetching it (and that I do, consistently).
None of this is the coffee, and neither is it existentially mind-dependent (no more than the coffee, if you really must).
Spatial differentiation is perceivable/sensible, yes? (hm not sure "sensible" is the right word here)
Or at least so it seems? :)
I had a couple of references, but they keep moving around...
• James Harrington
• Craig Skinner
Don't think it's contradictory (implies a contradiction, p ? ¬p), but it is counterintuitive.
Why would the backward recitation end at one time and not another, any other?
A definite earliest time means a definite age (at any time), so why this age and not another, any other?
Weird.
What's violated here seems to be the principle of sufficient reason.
Skinner writes "Take your pick"; maybe "Pick your poison" is better?
Quoting jorndoe
What you say here reminds me of David Hume's view (as Bertrand Russell interprets him) that we percieve relations of time and place, although we do not perceive causal relations.
According to Kant, it can be proven that space is a necessary pre-condition (“anschauung”) of all perception. One of his arguments (though a dubious one) is that we can't imagine anything as not being in space, but can imagine empty space (space with nothing in it). Bertrand Russell interprets this as implying that Kant's space is absolute, not relational.
So, if we suppose that Kant managed to imagine absolute empty space, then it would seem that space could be perceived in the mind's eye, though not perceived in the world. But as Russell pointed out, it is hard to see how one could imagine space with nothing in it.
I diverge from Kant here, and adjoin Schopenhauer, re: the world as “will and representation”, in that I consider the world to be the immediate unity of phenomena, that which directly appears to my representational faculties, a much narrower view of experience proper. All else, being possible experience doesn’t change the my idea of world, but rather, enlarges its content and thereby its limits. As such, the boundary of my world is the totality of my possible experience, and, because of that restriction, the CMB is irrelevant.
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Quoting Amalac
I think more the simultaneity of the initiation of phenomena, with the possibility of the representation of them, by an eventual intellect equipped with a cognitive system predicated on it. Within such a system, time is not an object so doesn’t depend on the ontology of objects, but it is used by the system in referencing objects to the system or to each other, so as soon as objects become possible, so too does the possibility of referencing them. Time is therefore irrelevant if there are no objects and if there is no system.
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Quoting Amalac
Again, he doesn’t maintain it, he supposes it in order to have something to debunk. There is a world in existence, therefore an infinite time is impossible, for that world. There may be an infinite time regressively from the beginning of the world, but not from an infinite time progressively to the beginning of the world. There is no present for the world from a progressively infinite time makes no sense. From the progressively infinite time point of view, to ask what time elapsed to what time, makes no sense. What is there to reference it to?
If you read the antinomies, you should have found he did the same thing in the antithesis. In the thesis he supposed the world had no beginning then proved it did, in the antithesis he supposed the world had a beginning and proved it didn’t. They are called conflicts of transcendental ideas for just that reason; either can be proved in its own way.
Didn’t I do exactly that? Dunno what else you want.
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[quote="god must be atheist;545868"]If the infinite is an adjective as you say,
— Mww
you are using it as a noun. You used it as a noun when you quoted Kant.
Are you referencing this: “Now, just as the unit which is taken is greater or smaller, the infinite will be greater or smaller”?
Ehhhh....that just means regardless of how many minutes there are in an infinite time, there will be more of them than an infinite time composed of hours.
Easy peasey
I might be thinking wrong, though.
[sub](I guess Hume, Kant, Russell left some imprints decades after reading and mostly forgotten.)[/sub]
Yeah, my bad. I saw it, but couldn’t fix it without starting over. Compromised between making an effort and taking the heat.
I apologize for butting in but I want to run something by you.
There are three parts to time - past, present, future.
The future presents no problems as regards it being an infinity for the simple reason that it doesn't, in a sense, violate our mind's "integrity" which seems to, in this particular case, hinge on the Aristotelian distinction between actual and potential infinity - that the former kind is ontologically suspect while the latter kind is acceptable.
The past, however, is treated as something complete - done with so to speak - and thus, any talk of the past being an infinity immediately sets off alarm bells inside our heads.
It might be of some help hsre to look at the definition of infinity. I visited the Wikipedia page on infinity and among the various meanings of infinity, I find this:
[quote=Wikipedia]but infinity continued to be associated with endless processes[/quote]
Concentrate all your fire on the nearest starship...er...I mean focus your attention on "endless". Infinity, it seems, is defined in terms of an end, to be precise, endless. There simply is no talk of the corresponding concept of an end viz. the beginning.
Could this mean we can't, shouldn't, apply the idea of infinity to beginnings? If yes, then infinity and a beginning to time or anything else for that matter can't be harmonized in a way that we can grasp.
Why, you may ask, is it that people (philosophers/scientists/theologists/etc.) continue to investigate this matter as if it makes sense?
For my money, this is the situation because we're reversing the arrow of time i.e. we're looking at the past as a time traveller. When we do that the past flips in a manner of speaking and morphs from an actual infinity to a potential infinity. How you look at the past (normally or as a time traveler) will cause it to flip-flop between an actual infinity and a potential infinity. This, in all probability, will play havoc with our minds. My puny brain at least is baffled beyond measure.
Quoting TheMadFool
Is the series of negative integers, ordered from smallest to biggest (ascendingly), complete? Yes, in the sense that it ends with its last element -1. That’s true in spite of the fact that it has no first term.
Likewise, if the universe had an infinite past, the temporal series would “end” in the present moment.
My view is that the concept of time passing or elapsing is only applicable to finite intervals of time, so I disagree with Kant when, paraphrasing, he says: “If the universe had an infinite past, that implies that an infinite amount of time has elapsed“, I don’t think an infinite past would imply what he says it implies.
I just don’t see why we would want or need to say that an infinite amount of time elapsed, if the past were infinite.
Quoting Mww
Hmm, ok.
Quoting Mww
Ok, that makes sense (I guess?)
Quoting Mww
Well that's what I meant, it seems I expressed myself poorly (english is not my mother tongue).
Quoting Mww
If the past is infinite, then there would be an infinite amount of time regressively from the present moment, right? You say, it seems, that there is no “present moment”. But how, then, do you define “the past”, if not as the time previous to the present moment?
Quoting Mww
Yes, I know how his antinomies work, but if one of the arguments for a thesis is fallacious, then one can't even say that you can “prove it in its own way”.
Quoting Amalac
Actually, never mind: going back to that post you're refering to, what I said was that he maintained that if the past were infinite then that implies that an infinite amount of time has elapsed.
I'm not saying Kant maintained that the universe had an infinite past, I'm doubting the truth of that hypothetical proposition.
That is how I would define it, but I didn’t use “past” in my statement. You transcribed the term into it.
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Quoting Amalac
Hence, the antithesis. Or in your case, a possible antithesis, upon your presentation of a thesis self-consistent and necessary in its own right, but constructed with different initial conditions than he used.
As long as the Kantian antinomies are the ground of the discussion, best to keep in mind.....
“....Thetic is the term applied to every collection of dogmatical propositions. By antithetic I do not understand dogmatical assertions of the opposite, but the self-contradiction of seemingly dogmatical cognitions (thesis cum antithesis), in none of which we can discover any decided superiority. Antithetic is not, therefore, occupied with one-sided statements, but is engaged in considering the contradictory nature of the general cognitions of reason and its causes. Transcendental antithetic is an investigation into the antinomy of pure reason, its causes and result. If we employ our reason not merely in the application of the principles of the understanding to objects of experience, but venture with it beyond these boundaries, there arise certain sophistical propositions or theorems. These assertions have the following peculiarities: They can find neither confirmation nor confutation in experience; and each is in itself not only self-consistent, but possesses conditions of its necessity in the very nature of reason—only that, unluckily, there exist just as valid and necessary grounds for maintaining the contrary proposition....”
....so if you’re going to argue the falsity of all or parts of the series of antinomies, you should stay in the context provided by the section in which they are found.
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Quoting Amalac
So you’re doubting the truth of the hypothetical proposition that the universe had an infinite past. Regardless of what that has to do with Kantian antinomies, and best you refrain from referencing them when expounding on how you conclude the fallaciousness of that hypothetical, what truth contained in it is doubtful, and how is it doubted?
On the other hand, if you insist on referencing the antinomies, perhaps start with this.....
“.....Now the infinity of a series consists in the fact that it never can be completed by means of a successive synthesis. It follows that an infinite series already elapsed is impossible...”
......which, while having nothing to do with the universe, does.....er....maintain....that no infinite series can have a past, an “already elapsed”, so the truth of the hypothetical proposition “the universe had an infinite past”, is already refuted, so you are correct in doubting it.
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Quoting Amalac
So is this where you’re coming from? And by association, is this the hypothetical proposition the truth of which you find doubtful?
“....up to every given moment of time, an eternity must have elapsed, and therewith passed away an infinite series of successive conditions...”
You’re equating your “if the past were infinite” with his “an eternity must have elapsed”, probably, which is fine. Close enough. As well, your “an infinite amount of time must have elapsed” is close to his “therewith passed away an infinite series of successive conditions”.
So why are you doubting the truth of what he says given you are saying practically the same thing?
The problem arises upon recognition that his hypothetical proposition is prefaced by granting there is no world. You can find the truth doubtful in his hypothetical proposition, just as he himself does, from the excruciatingly sufficient reason that there is a world.
All I can do now, is grant I got the hypothetical propositions mixed up, and that’s not what you’re talking about at all. If so, you’ve successfully confused the hell outta me, and I’m at the end of my dialectical rope. So fix the confusion, or forget the whole thing.....up to you.
Quoting Mww
Then what did you mean when you said “there is no present”?
Quoting Mww
The hypotetical I'm refering to is “If the universe has an infinite past, then an infinite amount of time has elapsed up to the present”.
Quoting Mww
No, I don't think those two mean the same thing, I'm saying: The past is infinite ? an infinite amount of time has elapsed, because to say that time has elapsed implies that it elapsed since some moment in time to some other moment in time, and hence the notion of time elapsing is not applicable to infinite amounts of time, but only to finite intervals of time.
For example: 20 years have elapsed since I was born, up to the present. But you can't say: infinitely many years elapsed since ???, up to the present day.
If one can't say since when the infinite amount of time elapsed, then I maintain that it couldn't have elapsed, but that a universe with an infinite past does not rest upon the supposition that an infinite amount of time has elapsed up to the present day.
Quoting Amalac
Man, this hypothetical’s got a farging mind of its own donnit? Seems “up to the present” makes an appearance in this current iteration, which changes the entire proposition.
Anywhooo.....so you doubt the truth of the proposition that if the universe has an infinite past then an infinite amount of time has elapsed up to the present.
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Quoting Amalac
Neither do I. I was guessing you were equating them because that’s all I could find that was even close.
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Quoting Amalac
I am vindicated!!!! No where in this: If the universe has an infinite past, then an infinite amount of time has elapsed up to the present, is to be found this: The past is infinite ? an infinite amount of time has elapsed. YEA!!!
Quoting Amalac
OK.....
Quoting Amalac
Hmmm......and what of the idea of a succession of a series of times that never completes? Isn’t a succession in a series of times the same as an elapse of time? A succession in a series makes no need of an amount for each time of the series. Even so, isn’t an infinite series of successive finite intervals of minutes, still an infinite amount of time?
“....up to every given moment of time, an eternity must have elapsed, and therewith passed away an infinite series of successive conditions....”
Quoting Mww
Well, the first time I thought the “up to the present” part went without saying, but seeing how that lead to misunderstandings, you are right that I should have been more careful and should have stated it explicitly.
The Popper quote in the OP does mention it though, so I thought the “up to the present” was implied:
Quoting Mww
I guess you meant to say “Isn't a succession in a series of time the same as a lapse of time?”
Quoting Mww
Not quite sure what you mean by this, but if you mean that it doesn't need to have an interval with an infinite amount of time elapsing, then that is my point, since an interval must, by definition, have a beginning and an end, whereas a universe with an infinite past doesn't have a beginning, although it would have an end (the present moment/ the “now”). An interval of time must have both a beginning and an end in order for time to elapse in it.
Quoting Mww
In a universe with an infinite past, one could say that there would be infinitely many finite intervals of time, which, when added, make up an infinite amount of time.
But if that's all that Kant meant when he said that:
Quoting Mww
... then I don't see what the supposed contradiction is, he says (in my translation of the Critique):
To make things clearer: if we were talking about an infinite future, and modify what Kant says so as to apply to a universe with an infinite future, then we could interpret what Kant says in a way that makes sense: time could never, going forward in time, be “finished”, in a universe with an infinite future time. What would follow from that is: therefore, the infinite future temporal series of finite intervals can never be completed (forwards in time) since you will never arrive at a final interval of time, and therefore it would be contradictory to hold that in such a universe we could arrive at a final moment/interval of time in the timeline, since that would imply that it both can and cannot be completed.
However, when saying that the infinity of a past temporal series consists in it never being finished/completed, what would be meant, it seems to me, is: If you start from the present moment/the “now”, and go backwards in time, then you will never arrive at a moment in time that is the beginning of time/ a first finite interval of time, therefore the infinite series of finite temporal intervals can never be completed (backwards in time).
And so, if that is what is meant by “completed”, then there is no contradiction in holding that a universe with no beginning in time would not be completed backwards in time, but would be completed forwards in time, since it would be completed/finished by the “now”/ the present moment, in the same way in which the series of negative integers cannot be completed towards the left direction of the x axis if you start with any particular negative integer/ any particular interval between two integers, but can be completed towards the right direction of the x axis if you start with any particular negative integer/any particular interval between two integers, since it is “completed” by its last interval from -2 to -1.
So, to make the mathematical analogy clear:
-1= the present, the last element of the series, which finishes/completes it .
The x axis in the cartesian plane, ending/ being completed with -1= the timeline of the universe.
- infinity/ the three dots to the left of the timeline= The infinite past.
The series of negative integers is “completed”, forwards from any particular negative integer/ interval (so to speak) between integers by its last interval from -2 to -1 (which represent the moment exactly one year before the present moment, and the present moment, if we use years as our units of time) ; but is not completed backwards from any particular negative integer.
Hopefully now I made things clearer.
If complete means finite, then we've just shown what we assumed.
It's not difficult to derive counterintuitives.
Deriving a contradiction (p ? ¬p) is the task, though, at least it is if an infinite past is claimed impossible.
But I think there is no problem with an event becoming ever more past for infinity. For that's a potential infinity, not an actual one.
The mistake most make when it comes to time is to conceive of it as a kind of extended stuff, and that immediately generates actual infinities. For now any region of time, like any region of space, can be infinitely divided. And thus we have to posit actual infinities. Which can't exist.
One also gets other absurdities, such as a past-most event that nevertheless cannot become any more past (even though clearly all past events are getting more and more past all the time).
Intuitively it seems like there is no limit to how past an event can become, and no limit to how far in the future an event can be. Time is boundless.
What this teaches us is that time is not an extended substance. It's a category error to think of it that way.
Another quite different way of thinking about time is to think of it as a set of attitudes. As an analogy, take hate. It is impossible to hate an infinite amount of things. But there is nothing impossible in one hating something more and more without limit. There seems no upper limit to how much one can hate something, yet we do not have thereby to suppose the existence of some kind of infinitely extended stuff - hate - that we acquire ever more of. It's just an attitude. And though attitudes cannot be divided, they can be of infinite potential intensity.
Thus for an event to be past is for it be being 'past-ed' more and more intensely. In this way the first event or events can 'recede' forever into the past, for the past is no longer a strange endless zone, but an attitude that is growing in intensity.
I'm aware that you used Kant in the discussion. I'm more interested in the thought experiment itself of time going "back" infinitely. It's been in the back of my mind recently and I was going to start a thread on the topic, but then saw this one.
Maybe this is cheating and is probably also quite ignorant but I'd like to put aside what physics says and just take the topic as is, meaning, if time is infinite and had no beginning, how could we be here?
Let's me take a stab at your argument, for my own benefit. As I understand what you're saying: even if time had no beginning it would not matter because we are finite, so we can place ourselves anywhere on the timeline and no be bothered about how we got here.
Isn't the counterargument here that in order to get to now, we had to begin somewhere. But if time is infinite, how could we place ourselves here? An infinite amount of time has gone on before we got here.
Either a part of infinity is finite or if not, it is also infinite. If a part of infinity is also infinite, regardless of not having starting conditions, we could not be here.
But this raises more problems, if a part of infinity is finite, wouldn't we have to go through an infinite amount of time to reach a portion of infinity which is not. How's that possible?
Unless I'm stuck with a linear idea of infinity.. Sorry for the length, but I'm curious about a reply. It's likely muddled thinking on my part.
Quoting Manuel
Well, my view is not that we don't need to be bothered about how we got to the present, but rather that we should not (and need not) say things like “an infinite amount of time has elapsed up to the present” when we examine the consequences of assuming that the universe had no beginning in time, we should only talk about time elapsing when talking about particular intervals of time. In fact, the very notion of time "elapsing" implies a beginning and an end of an interval in which it elapses (most definitions of the word I have seen do assume that, anyway).
If the word “elapsed” does not imply a “since X point in time to Y point in time”, then it means something different from what it means in a statement such as: “5 years have elapsed since my birthday 5 years ago up to now”, since otherwise necessarily one must be able to answer the question: “infinitely many years have elapsed since (when?) up to now”.
Quoting Manuel
Why is it that we had to begin somewhere?
Doesn't that beg the question by already assuming that there must have been a beginning in time?
Quoting Manuel
If by “an infinite amount of time has gone on before we got here” you mean “ if the universe had no beginning in time, then an infinite amount of time would have elapsed before we got here”, then I have already said why I think that's not the case. Time can only elapse since some moment to some other moment. It is clear, therefore, that the idea of time elapsing only applies to finite intervals of time.
Kant therefore can't use the idea that if the universe had no beginning in time then that logically entails that an infinite amount of time would have elapsed, to show that a universe with no beginning in time would imply a contradiction, since such a universe doesn't logically entail what he says it entails.
Such is my current view on the matter anyway.
Quoting Manuel
A part of “infinity” can be infinite, yes. In the set of all positive integers, the set of all even numbers which is part of the set of all positive integers is also infinite. But of course a part of infinity could also be finite, for instance the set of all integers bigger than 0 and smaller than 5, which is also part of the set of all positive integers.
So, when talking about the timeline of the universe, which part of it are you saying would be infinite, and how would that imply that “we could not be here”?
Quoting Manuel
Again, when saying we would have to “go through an infinite amount of time”, you must specify since when we would supposedly have to “go through” an infinite amount of time, since in the very definition of time elapsing, a beginning and an end of the lapse of time are pressupposed.
So no: if the universe had no beginning in time, it's not the case that that would necessarily entail that we would have to go through an infinite amount of time to get anywhere.
I'm not sure I follow completely, I may be, but I may not be. I think that part of the problem may be that there's our innate conceptions of space and time, or spacetime if we are to incorporate modern physics and spacetime outside our conception of it.
This may be the wrong way to state this...
I think that by now, we should try to distinguish our conceptions of spacetime with spacetime in the universe. Absent human beings, strictly speaking, yes, we can't speak of time "elapsing" or as I prefer to say "passing", as these terms must imply our conceptions of them.
But if there is spacetime outside our conceptions of it, as appears to be the case then I think that in order to speak at all, we are forced to use our human vocabulary. Perhaps we can speak of one infinite span of time, or an infinite number of events, this would go on "backwards" forever.
The time in the universe, on this thought experiment, goes back forever. If it does, how can we get to any point at all, given that an infinite time preceded our species?
Quoting Amalac
We as a species evolved at some point in evolutionary history. It's from that perspective that we began as a species. It does not presuppose a beginning of time in the universe, but it does presuppose a beginning of time as we conceive it. In that respect I'd stick my neck out and say that we "began" once we had our conception of time.
Quoting Amalac
In our conception of time yes. I think it differs in the external world.
But I could be way off. Again, just throwing out ideas.
If the Big Bang is true and complete, how can we speak of time before that? It would be analogous to saying what's a feature of Earth that is higher than Everest.
What did you have in mind with time dilation?
Ever onward......
Quoting Amalac
Kant is working onward, you are working backward. Referencing your universe with “past” presupposes a regression in time from some other given time, otherwise “past” is irrelevant. His “up to every given moment” presupposes a progression in time from every other time, so it makes no difference what that some other time is. They are indistinguishable. Kant is working with time alone, you are working with something existing in time.
The contradiction resides in your inclusion of the universe as an uncompleted series. If it was, then the elapsed time of the universe, your “infinitely many finite intervals of time” for the universe is impossible, therefore there could be no universe, a contradiction. The universe would never be “finished by means of successive synthesis”, from which follows necessarily that talk of “in a universe with an infinite past”, is meaningless. Even if you think the universe the same as Kant thinks the world, it is still to be treated an a completed series of times, from which there arises a present condition of that which is called “universe”.
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Quoting Amalac
The set of negative integers is an uncompleted series, in which the last member is impossible to represent. Even so, the conception of integers remains. In the case of the universe, given its existence, which is the equivalent of zero for the reference of infinite negative integers, it is merely the infinite set of constituents of the universe that cannot be represented, while the conception of the universe itself remains. This shows the compatibility of arguments with respect to integers, with arguments with respect to the infinite series of times for an existent whole.
Nevertheless, while it is possible to think the infinite past of the universe in which it has no beginning, such thought is necessarily contradicted by experience. It is at the same time possible to think the infinite series of negative integers, and forever be safe from contradiction by experience. So the arguments are not compatible.
Hence.....the conflicts of pure reason, the antinomies.
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Quoting Amalac
No, I said what I meant to say. Time can contain nothing but intervals of itself. Things are in time, but time is not in the things. Ultra-modernists posit time as a property, such that time can be in things, but then they cannot explain how empirical things can have an infinite property.
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Quoting Amalac
It is clear, but I don’t think it sufficient to support the OP, which asks “can the universe be infinite towards the past”, and, of course, has nothing whatsoever to do with the antinomies.
Metaphysics.....the most fun to be had without paying for it.
Quoting Mww
And why would there being infinitely many finite intervals of time be impossible given a universe with no beginning in time/ infinite past, exactly?
Like I said, those infinitely many intervals (or “syntheses”) go backwards in time since the “now”, or since any other particular moment in time before “now”, so the only thing those intervals make impossible is for there to be a beginning moment which completed the series backwards, which is what is entailed by the definition of a universe with no beginning in time, they don't render the series being completed forwards by the “now” impossible.
Quoting Mww
I'm not sure how that follows:
1.In a universe with no beginning in time, there would be infinitely many finite intervals of time.
2. Those intervals or synthesis could never end (backwards in time)
3. Therefore, given that 2 is true, a universe with no beginning in time would not have a present moment, a “now” which completed the series (forwards in time).
4. The actual universe does have a present moment which completes its temporal series (forwards in time).
5. Therefore, the talk of “in a universe with an infinite past..." is meaningless.
The jump from step 2 to step 3 is what seems like a non-sequitur to me. That, or equivocation of the idea of a series being “completed”, which can have 2 different meanings.
When the natural thing to infer would be rather:
1.In a universe with no beginning in time, there would be infinitely many finite intervals of time.
2. Those intervals or syntheses could never end/ be finished (backwards in time)
3. Therefore, a universe with no beginning in time would not have a beginning in time, since that
would imply that the temporal series would be
completed (backwards in time), which necessarily can't be the case given 2.
And yes, that's just how a universe with no beginning in time/ infinite past is defined, 3 is an analytic truth and therefore contains no contradiction.
Quoting Mww
Again, if by “infinite elapsed time” we mean that in such a universe there would be infinitely many finite intervals/syntheses of time, then I don't see why its contradictory with the premise of a universe with an infinite time, for the reasons given before.
Quoting Mww
If you sort the series in descending order, then there is no last member indeed.
But if you sort the series in ascending order, then its last member can be represented, its -1.
I'm refering to that series sorted in ascending order, and in that series the correct statement would be: “The set of negative integers is an uncompleted series, in which the first member is impossible to represent”.
In that case, the series of negative integers would be an uncompleted series descendingly since it has no first term, but not ascendingly since it has a last term (-1).
All in all, I just don't see how Kant's argument is that much different from the argument of the first cause of, say, Aquinas, if one just replaces “causes” with “syntheses” ( I mean besides the fact that Kant does not continue to deduce the existence of God from that beginning in time he got from this thesis, which is understandable given that the antithesis can be “proven” as well).
[quote= Bertrand Russell]
(...)take again the arguments (of Aquinas) professing to prove the existence of God. All of these, except the one from teleology in lifeless things, depend upon the supposed impossibility of a series having no first term. Every mathematician knows that there is no such impossibility; the series of negative integers ending with minus one is an instance to the contrary.[/quote]
So if one argues that Kant's argument “proved” that the temporal series of the universe must have had a beginning in time, by the same reasoning one could also prove that the series of negative integers must have a first term, a smallest negative integer, since otherwise the series could not end with -1, which is clearly not the case.
Quoting Mww
Sorry, that was a typo, I meant to write “a succesion in a series of times” with “times” in plural, what I was trying to ask was if by “an elapse of time” you meant to say “a lapse of time”.
Quoting Mww
Well, I hope you are at least having some fun, and not losing your patience despite my obstinance in trying to understand Kant's argument (if indeed I misunderstood him and am just hopelessly confused).
Again....forward vs backward. The infinite series of negative integers doesn’t end with -1, it begins with it. The smallest negative integer is -1, in that it is the least distant from its referent. The universe, conversely, is the absolute furthest from its referent, which is its non-existence, made explicit by the consideration of its infinite past.
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Quoting Amalac
That there are an infinite amount of intervals of time of the universe is not contradictory, for any given whole is infinitely divisible, and the universe is itself a given whole. But how can there even be a universe with no beginning in time?
No beginning in time does not carry the same implications as an infinite past of time. Past implies backward from original present, so an infinite past just means backwards indefinitely from the present. In both of these, the present is given. But for a universe with no beginning, there cannot be a given present, hence the absurdities in connecting a non-existent, re: the universe, insofar as that which does not begin does not exist, with its past, infinite or otherwise.
To think the infinite intervals of times of the universe, does not contradict itself. To think the infinite past of the universe, from its present, does not contradict itself, but experience does show its contradiction in fact. To think the universe as having no beginning contradicts everything about the universe. To say there is an infinite time lapse before the beginning of the universe just makes the universe impossible.
Infinite time, in itself, and the universe, by itself, are incompatible. Metaphysically, this is a legitimate thesis if time is only a condition of all things and the universe is a thing. Or, it is equally legitimate if time is meaningless unless it relates things, and the universe is a thing.
You probably can't. The question then becomes, Is it possible that time evolved in a way that conflicts with current analysis and provides a path back in time that is unbounded, even to the moment of the BB?
I know, sounds absurd. But I have been looking at a dynamical system in C in which, starting at a particular past moment, one analyzes a sequence that begins at n and devolves to 1, then begin at a larger n at the same starting point, etc.
Just musing.
I would actually phrase it a little differently. For me, time is the display of an imaginary clock. After all, it is not possible to place a clock inside the sun. Would someone claim in the inside of the sun there would be therefore no time?
One must distinguish simply between events and the time itself. The events play no role for the abstract time, also not the Big Bang. I can imagine a clock, which survives all events and therefore this clock can indicate any time (it would have to be able to indicate however arbitrarily many digits).
This clock could have shown any time back to negative infinity.
And others like Smolin say time is emergent.
If Smolin is correct, it's very hard - if even possible - to think of anything "before" the emergence of time. But one must assume that there wasn't nothing in the sense of absolutely nothing: no energy, no quantum vacuum, etc, prior to the emergence of time.
But if Hawking is correct, then at least time "remains". Though it's very hard to make any sense of any of this.
Sure. Just trying to use words to try and make some minimal sense of the things "out there", well aware of the myriad of complications attached to doing this.
? <--------------A-------------> ?
That’s not an infinite line.
You must have known that, so what did you think you actually proved?
ETA: Maybe this could be useful: Kant’s problem is thinking of time the way flat-Earthers think of space. What is the Earth resting on? What is that resting on in turn? And that? Do we need a stack of turtles “all the way down”? Or is it instead a misapprehension of space to think that something can’t just be here, and there’s infinite room to look further down as far as we want, with no need for a stack of things “from the bottom” to hold “here” up.
In contemporary physics, the Big Bang is understood not as the total beginning of everything, but as the end of the inflationary epoch... which may have been going on for infinite time beforehand (or may not have, there’s no scientific evidence either way as of yet). But at some point (according to the latest models) the universe was mostly empty space expanding absurdly fast, we don’t know for how long, and then suddenly it stopped (at least in the part we can see) and all that expansion energy got dumped into all of the other fields, exciting them immensely, leaving an absurdly hot and dense (patch of the) universe, still expanding but less rapidly. That transition is what we now think of as the Big Bang.
Thanks for the info, some clarification:
So empty space contracted into the big bang?
Is this connected to some of these cyclic big bang theories in which it is postulated that the universe expands and contracts many times?
As I understood it, and apologies if I state it incorrectly, the Big Bang was a moment in which everything in the universe was compacted in a very small point of very high energy.
"Before" that moment, there either was nothing or it's part of a cycle.
Sorry if this question sounds stupid, but when it comes to math, I'm really mentally challenged.
This type of system you are describing, it's a kind of recursive system or a "loopy" system, but it has a "starting point". Is this roughly what you have in mind?
[math]{{F}_{n}}(z)={{f}_{1}}\circ {{f}_{2}}\circ \cdots \circ {{f}_{n}}(z)[/math]
In this instance where [math]{{f}_{n}}(z)\to z[/math]. If it has a bearing here or for time dilation at the event horizon of a black hole is problematic. :chin:
:scream:
That's brutal.
But I saw the word "recursion".
Imagine an infinite grid that you’re zooming out from, and that gives you a picture of what rewinding time looks like: you never run out of grid to zoom out from, even when the “whole screen” has been zoomed down to a single pixel; and when you cross that point, it all starts zooming out even faster.
We posit that inflationary (rapidly-expanding) period before the “hot Big Bang” to explain some observations about the early state of the universe, but we have no evidence suggesting anything about how long it had been going on beforehand.
The theory of eternal inflation posits that that breakneck rapid expansion of mostly empty space is actually the normal state of the infinite (in size) and eternal (without beginning or end) universe, and the part of that universe we can see is just a (part of a) comparatively tiny part that randomly and temporarily slowed down; and the current acceleration of the expansion of space is the process of our part gradually returning to that normal state of absurdly fast expansion.
If that theory is true, there are constantly “big bangs” going off all across the infinite universe, but they’re all so far apart and being accelerated away from each other so rapidly that none of them will ever have any chance of seeing each other, and the space between them is still mostly empty. So on a large enough scale view, whole lifetimes of “universes” like ours are just sparkling briefly all over space and time forever and always, and there always have been.
And if that is the case, then if you look far enough back in time — really incomprehensibly far — whatever tiny speck of space expanded into the universe as we know it was at one point a tiny empty part of some other “universe”, which in turn began as an empty speck that some time incomprehensibly further in its past had been a tiny empty part of an even earlier “universe”, etc. And the empty space that will someday be all that’s left of the universe as we know it will be littered with uncountably many empty specks of space that will, incomprehensibly far in the future, each become a “universe” like ours themselves.
Very interesting and many thanks for the detail and the visualization aspect, helps a bunch. I recall reading some of this in Hand's Cosmosapiens, but you're wording of it makes it "easy" to picture.
The thing is, if this is true, it looks to me as we're just pushing back the origins question. That is, we have no possible conception as to why any universe began, or if it even makes sense to think so far back to a "first universe" - if it ever existed. But, if the theory is true - which I think it's safe to assume we just don't know - then too bad for our comprehension. It looks to me like Many Worlds on steroids, which would have to be accepted as fact.
I suppose one question that lurks here, which philosophers could comment on a bit, is the idea of causality. I tend to like Galen Strawson's view on this, in which he rejects the regularity theory of causation: that things just happen, for no reason.
I know "reason" is a loaded word, but what he has in mind is, there should be a regularity or a habit for which things happen as they do and not some other way. If there are no "reasons" why, then why have any laws at all? We could say that the next universe over is just a lump of green clay. If things just happen nothing is prevented, I guess. Obviously I'm speaking crazy here, but why does the universe(s) behave in this way?
It's really mind-boggling. I mean, we already have more than enough figuring out stuff here on this tiny planet, to think that there are many universes, well damn. Fascinating.
Quantum mechanically, that’s pretty much the case, and such quantum randomness is the posited mechanism that spawns new “universes” on an eternal inflation model.
One last question:
Sure. But I mean, there's a bound to what can and cannot happen, right? It's not as if an elephant will pop in to existence. Maybe a particle or some small thing pops in for discernable reason, but there's a range of things which are expected within the randomness, or that's not the case?
It's a diagram of a segment of an infinite line.
What I said, in other words, if we can exist in infinite space, so too present time can exist with infinite past. Do you think space could be infinite?
Ahhhh....ok, then. A symbolic proof. Thing is....that little squiggly thing at each end of the representational dotted line segment presupposes the very thing you’re using to prove something about it. “A” could be located at that point, or any other point, whether or not the line is infinite. Denying the antecedent comes to mind. Actually, there’s no point “A” could not be found on an infinite line, so it says nothing at all about the line itself, to say where “A” is found.
—————-
Quoting Zelebg
Sure, it could be. I also think it could be bounded by the current universe. Six of one, half dozen of the other. Mathematical/logical proofs for both, empirical proofs for neither.
My point was mainly to introduce an analogy, to look at the problem from a bit different perspective in hope it might shed some new light and open alternative way to look at it. Although the question is whether spatial analogy to temporal infinity is indeed adequate, but it seems to me that it is.
In any case, I think this problem, as many other philosophical and problems in general, is heavily burdened by semantics, that is incomplete definitions, mixing, conflating and inappropriate application of concepts.
For example, the concept of infinity is inherently an abstract concept, which, it seems, just simply cannot be applied to reality, and so this and similar discussions necessarily lead us to some kind of paradox, one way or another.
Basically, I think we cannot find satisfying resolution to this question until we first do something with our vocabulary, perhaps make definitions of concepts involved more robust or restrictive, or maybe come up with some new concepts and definitions, don't know. Who knows? Who knows!
As an abstract concept, yes, by definition space is infinite. But what is our working definition of "space" concept in reality?
For example, does "time" make any sense if nothing moves, if there is no change, and similarily, does "space" make any sense if there is nothing in it?
How about this one?:
...here there's an "object" (blue line) aligned with two rulers. Per the top ruler, it extends backwards from 0 to -1, but keeps going. Per the bottom ruler, that point measured at -1 by the top ruler has infinite measure. It's kind of irrelevant that our numbering system along that bottom ruler "never ends"... that line segment certainly has a point on it.
My point here is that at least in some of your discussions you're confusing the measurement with the thing you are measuring.
Good.
Quoting Zelebg
Better.
My vote for Best......maybe we cannot find satisfying resolutions until we first do something with our metaphysics.
All I’ve contended here, is the notion of proof. I’m ok with your general thinking....and it wouldn’t matter even if I wasn’t....but I categorically reject the possibility of any proof for your original proposition, other than logical syllogism.
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Quoting Zelebg
This, buried back in this maze of comments, is pretty much what I said. Just maybe with a couple additional reductions.
This is going on, and it is what the fighting’s all about, as my ol’ buddy Roger Waters would have you know.
Misplaced concreteness writ large, and I’m trying to demonstrate the futility of it.
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Quoting InPitzotl
Sure it does. It has an infinite number of them. Do you see this doesn’t relate to my arguments with respect to the thread’s original proposition? It is not contested that, given an origin, an infinite regression from it is logically possible. It follows that an infinite number of points are given by that possible infinite quantity which contains them. What I am saying, is diagrams do not prove the case, but merely represent that logical possibility. So neither of these two pictorial renditions prove the absolute necessity, of that which is grounded only in a mere possibility.
It is impossible to prove there is a point on an infinite line, if there is no possibility of an infinite line. This is a perfect example of reason in conflict with itself.....substituting what is legitimate in thought, with what is illegitimate in experience. Still, all that in itself is utterly irrelevant with respect to the thread, in which there is given the origin of a completed whole......the universe. The universe as a whole is the logical equivalent of your pictorial representation. As such, there is an infinite quantity of constituency in the universe, just as there is an infinite number of points on the line segment, 0 through -1. But the other diagram is bounded by infinity itself, no beginning and no end, which makes it absurd to locate any point on that line. I mean.....where is the access point?
Anyway.....metaphysics. Can’t prove it, can’t refute it. Best to discover the limits of what can be done with it.
From reading your reply it appears you don't understand the diagram. Let's imagine the units of the above ruler is hours; and the unit of the below ruler is also hours. -1 by the above ruler means one hour ago. -1 on the below ruler also means 1 hour ago. -2 on the below ruler means two hours ago; -3 three hours ago, and so on. By the above ruler, there's a point in time one hour ago. By the below ruler, that point in time is in the infinite past.
Quoting Mww
Sure, ...
Quoting Mww
...but proving the possibility is equivalent to disproving the impossibility. The original post is about challenging Popper's proof of impossibility.
Quoting Mww
To what does the phrase "illegitimate in experience" refer?
Quoting Mww
If Sam falls into an eternal black hole, and I watch, Sam would experience nothing unusual when he falls into the event horizon. His watch just ticks along as usual. There it goes... tick tick tick. I, on other hand, will never see him fall into the black hole, because time dilation is so extreme that Sam asymptotically never goes in, on my ruler. So where is the exit point? Why, it's the event horizon. This time reversed illustration is simply meant to convey that your question, whereas it may at first appear to have no answer, might have the simplest of them... the access point is simply an hour ago by the top ruler and is a type of horizon by the bottom one.
Stuff like this:
Quoting InPitzotl
————
Quoting InPitzotl
It wasn’t Popper’s, it was Kant’s. And it wasn’t a challenge as much as a misunderstanding by the thread’s author, of the original argument logically proving the impossibility of the world having no beginning. Still, you are correct, insofar as proving the possibility of an infinite line would at the same time prove one and all points on the line. To prove a possibility, one must prove a necessity, and to prove a necessity one needs prove an existence. Otherwise, all that’s proved is sufficiency. To prove the possibility of an infinite line one must show the existence of one. Which is impossible. So all that’s left is to represent an infinite line sufficiently, using those little dots after the uncompleted series of whatever’s. Or maybe something like “n + 1”.
In the case herein being senselessly beaten to death, the existence is given, re: the world, so the need to prove its possibility is negated, as is for the equivalency in disproving the impossibility that the world had a beginning, or, which is the same thing, that the beginning of the world is in the infinite past. The common rejoinder is, of course.....why not both. A beginning for the world and that beginning infinitely long ago. The contradictions so blatantly obvious, the counterarguments so lackluster......eventually regressing into such modern conceptual monstrosities as (gaspsputterchoke) “spagettification”
(Sigh)
Sort of; it's "Kant's argument as Popper presents it" (see below).
Quoting Mww
The one does not preclude the other:
Quoting Amalac
There is definitely a challenge here ("isn't that as fallacious as"...).
Quoting Mww
We seem to have vastly different views of modality. One need not prove a necessity nor an existence to prove a possibility. I can prove it possible for me to run from A to B by running from C to D, or running on a treadmill. Or, I can prove a wooden floor can hold 500 pounds by analysis (I need never put a 500 pound weight on it). In this case, the impossibility argument is based on an alleged absurdity; showing the alleged absurdity viable suffices to undermine the argument.
Or we can phrase it another way. The challenge is that the argument is fallacious. A fallacious argument is an invalid argument. But arguments can be invalid even if their conclusions are true. To show an argument invalid, one simply needs to show the conclusions don't follow.
Quoting Mww
Sure, that's possible too. Per the illustration, it's even possible that there was a prior to the infinitely long ago, as illustrated by the line. I drew this diagram intentionally depicting such a prior, and intentionally making it ambiguous whether there was a beginning or not. But the infinitude nevertheless demonstrates the argument invalid by undermining the alleged absurdity; even if the universe in fact turns out to have a beginning.
Quoting Mww
Obvious does not entail correct. The counterarguments do exactly what was intended... they undermine the alleged absurdity. Undermining the alleged absurdity suffices to undermine the argument. Your confusion that the burden must be way higher is just your confusion.
By my reading and treatment, this thread is more about an argument's validity than about time's actual beginning or lack thereof. To me, it's unknown whether time had a beginning. But it's certain that argument is invalid.
Agreed. I don’t care about time in and of itself. That which it conditions, or is the condition for, interests me.
Quoting InPitzotl
To everyone, I would think.
Quoting InPitzotl
There have been a few. Which one, please? Popper’s? “That argument” denotes specificity, so....
Fair question. Here I was referring to the argument Amalac quoted in the first post ("Kant's argument as Popper presents it").
. There is no past ...
. Past ... as such ... is a myth ... so you can be entangled with and towards that ... which is not ... so you can be dreaming while alive ... so you cannot be in here ... which is the only place ... and now ... which is the only time.
. The society creates guilt ... the priests and the politicians ... towards that you've done ... at a remote past ... so you cannot live in the here-now ... so you can be an efficient machine ...
a beautiful machine ... a flesh and blood machine ...
. When I say ... that ... you must die to that which is not ... but you think it is ... I don't mean that you will not be able to remember it. It does not mean that all your memories will be dissolved or destroyed. It only means that now you don't live in those memories. You're free from them. They will remain, but now they will be just a part of your brain, not part of your consciousness.
. The brain is a mechanism ... a beautiful mechanism ... yes ...
. But ... it is just like a tape-recording machine. The brain goes on recording everything. The brain is the physical part. It will go on recording, and your memories cannot be destroyed unless the brain is destroyed. But that is not the problem. The problem is that your consciousness is filled with memories. Your consciousness goes on identifying itself with the brain and the brain is always stirred by your consciousness - and memories go on flooding you.
. So your question ... must ... do a eighty hundred degree turn ...
. Can the universe be FINITE towards the past?
. The beggining and the end are ... the whole ... of it ... They are one ... an oneness ...
. There is no past ... therefore ... it can be finite ...
. How can the universe be infinite towards that ... which ... is not ... whose existence ... is not ... ?
. In order to exist ... you must be ... you must exist ... you must be a being ...
. That's why you're a human being ... you're constantly ... being ...
Two things, both of which have been covered in these comments:
One thing.....
Your diagram represents a given present, called “0”, initiating a regression of quanta, such that one of the infinite quanta is included in the totality of them. As such, three hours ago is a member of the set of all hours regressing from zero, which is the same as being included in the infinity of such hours, which is the same as being included in infinity of past hours, which is the same as being included in the infinite past. And you thought I didn’t get it. Shhheeeesh......gimme some credit, huh??
I grant the present represented by zero is synonymous with the beginning of negative hours, just as Kant’s argument stipulated the beginning of the world. It follows that there must be a time where negative hours did not exist, just as there must have been a time when the world did not exist, for that which has a beginning must have a time relative to it necessarily.
Nevertheless, do you see that these two are not compatible? And therefore cannot be used to argue that one invalidates the other? In the case of the numbers, the non-existence of negatives is subsequent to them; the non-existence of the world, is antecedent to it. Therefore, that past consistent with each, isn’t consistent with itself, insofar as the infinite past of negative numbers is yet to be past, but the infinite past of the world has already past. Now it is clear that given an infinite already past of the world, the beginning of it has no referent, hence the existence of it cannot be said to have ever occurred. But no matter its beginning, it did have one, therefore it could not have had an infinite past in which no beginning is to be found. Hence, that the world has an infinite past, is self-contradictory.
The other thing....
Your diagram represents exactly that which resides in the accusation of “confusing the measurement with the thing you are measuring“. The concept of negative hours included in an infinite past, is very far from the existential reality of the world as it was, and must have necessarily been, three hours ago. Again, Kant’s remark, that do so is “mere subterfuge”.
Your turn. How is the argument invalid?
—————
On modality.
Whatever steps are taken, it must be possible to take them. Given it is possible to take them, something must existent in order to take them. Given that steps are taken, it must been necessary for that which takes them, to exist as something capable of taking them.
“......It is to be added, that the third category in each triad always arises from the combination of the second with the first. (...) necessity is nothing but existence, which is given through the possibility itself....”.
This is not to say we cannot have different notions of modality. On such occasions where it is questioned, the above is my answer.
. There is no present too ... friend ...
. Present ... as such ... is ... just a bridge ... a temporal bridge ... connecting the past and the future ...
. If there is no past and future ... necessarily ... the bridge disappears ... exists not ...
. For the sake of language ... you must ... call it so ... but ... existentially ... present exists not ...
. You try to say the word NOW ... the moment you say it ... it's already past ... it's already ... past experience ...
. That's the reason why ... only ... a meditative being ... can Live totally ... can be fully in the present ... because ... he's fully aware of this truth ...
. You're always being rejuvenated ... not only you ... the whole existence ...
. The quantum physics ... at the 20th century ... arrived ... to this conclusion ... that ... in an ultrasonic speed ... all the existence disappears ... and ... appears again ... as a new phenomenon ... as new reality spectrum ...
. So ... it's not just ... spiritually portraying ... it's ... also ... physically saying ...
. In Yoga ... this knowledge ... for thousands of years ... at least ... 5 thousands of years ... have been known by the mystics ... but ... then ... thousands of years later ... the physics arrived to this truth too ...
Apparently not, because you keep saying something follows that doesn't follow.
Quoting Mww
"Negative", "zero", and "positive" are classes of numbers. In terms of ordering, 0 divides the classes; greater numbers are positive, lesser are negative, and 0 per se is in neither (in the typical scheme). By beginning we usually talk about the lower end; so in this case, that would be discussions about horizons. This refocus on the upper end "to make a point" doesn't seem to make it pretty well. Even so, nothing meaningful is entailed on that side either, so let's talk both.
Nothing about the extent of that blue line follows from the extent of the ruler. Be it horizon or origin, the line may not reach it, may reach it exclusively, reach it inclusively, or may go beyond it. I cannot rule in or out any of those things on the basis of pontificating on the nature of the number classes.
Quoting Mww
Not sure what you're saying here. 0 is the beginning of the negative numbers by your scheme, but 0 is not negative; so the beginning point is exclusive.
Quoting Mww
...I've discussed the number cases above. We have classes with inclusive and exclusive endpoints and classes with no endpoints.
Quoting Mww
No, that does not follow. The horizon can be an exclusive endpoint or an inclusive endpoint (or a non-endpoint). We can have a future horizon just like that as well. There is no meaningful restriction to the extent of that blue line that you can infer from any infinitude of a ruler.
That settles it. I guessed wrong, I didn’t get it, which just goes to show....you’re way too smart for me.
What does one mean by past? Elapsed time ending in the present (now).
So, if the past is infinite, an infinite amount of time must've elapsed. You can't accept one without accepting the other. It's like someone saying, "I've arrived in Paris". Well, if fae's arrived somewhere, for certain he was travelling.
Ok, so let's suppose all that Kant/Popper meant when saying that an infinite amount of time passed/elapsed up to the “now” was to say that it is the case that the universe had no beginning in time.
What then is the alleged contradiction about that with the fact that time in the universe ends in the “now”? It is maintained by Kant that a universe with no beginning in time would never be “completed”/ would never “end”.
If all he means by that is to say that time would never end towards the past, then obviously yes, that's entailed by the very definition of such a universe, and there's no contradiction about that, since one cannot maintain that it must end towards the past in some beginning moment of time, without also rejecting/contradicting the definition of a universe with an infinite past, unless there's a reason why it must have had a beginning in time, which is what Kant had to prove and didn't prove.
But if Kant means that such a universe would also never “be completed/end” in the “now”, then that seems like a non-sequitur.
Again, one cannot use the claim that it could never end in the “now” because that would imply traversing an infinite amount of time in order to get to the “now”, because:
a) The assumption that it would necessarily imply that, as I said before, is false, and there's no reason for someone who held the universe to be infinite towards the past to make that assumption.
b) The models of a universe with an infinite past/ no beginning in time do not logically depend upon the claim that in such a universe one would have to traverse an infinite series of syntheses of time in order to get to “now”.
(Also, see my replies to Mww)
If, on the other hand, we take that word “elapsing” to have its usual meaning, then time “elapsing” necessarily implies a beginning and an end of an interval of time. In fact, a lapse of time is the same thing as an interval of time.
But intervals, by their very nature, must be of finite amounts of time, not infinite ones (otherwise you can't even construct the interval, since you would be missing at least one of the limits that define the interval/lapse of time).
So if that's what you mean by “an infinite amount of time elapsing up to the present", then I disagree with:
Quoting TheMadFool
That definition would only be adequate if the past was finite, not infinite.
All “a universe with a finite past” means is: a universe with a beginning in time. Likewise, all “a universe with an infinite past” means is: a universe with no beginning in time.
That doesn't mean the same as “a universe in which an infinite amount of time elapsed ending in the present”.
So what one means by past is simply: the time before the present. With this definition, no assumption about time “elapsing” is required.
The only thing needed to make that universe consistent is to drop the false assumption that in such a universe necessarily an infinite amount of time must have elapsed up to the present, since such a claim implicitly assumes, for no reason, that a universe with an infinite past both had and didn't have a beginning, so obviously, as I said before, there's no need for one to assume that that must also be the case in a universe with no beginning in time.
If thats the case how so we hear a piece of music as a unity? We would only know each present note but not the previous flow of notes that creates the mellody. This was a problem for the old model time as punctual now points. The solution, offers by William James, Husserl
and others , was that we experience the just past note in the present alongside the current note. It is not. past that is gone but a past simultaneous with the present , appearing alongside it in the same moment.
Quoting TheMadFool
That's just a figure of speech, obviously.
Quoting TheMadFool
Did I ever say such a thing?
Quoting TheMadFool
Something can't end before starting (if it started), obviously. A universe with an infinite past would not end before it started, it never would start in the first place (by definition), but that doesn't mean it can't end in the "now", or at least that needs to be proven first.
Perhaps there's a grain of truth in it. The expression, "my career ended before it even started" does make sense, right? The way I parse it is, that which has no beginning [before it even started] has terminated [ended]. My career was over before it even began - notice a reversal, a complete volte face as it were in the sequence of events, the events being start and end. The usual way these two happen (temporally) is start first and end second. The phrase "my career ended before it even started" flips this order and end comes first (before) the start which is second; don't forget that it says, "before it even began" i.e. there was/is no beginning. Isn't this exactly the same problem we're facing - a beginningless time that has an end (now) which is the infinite past conundrum we've trying to get a handle on.
By way of trying to get a fix on, zero in on, the intuition that makes the statement, "my career ended before it even began" slip through the logical checkpost with such ease we can again revisit the fact that the order of start and end has been reversed, "my career ended before it even started" In other words, there's an ambiguity - the end is first but that's a start's position and the beginning is second and that's the end's position. While we attempt to wrap our heads around this fine piece of linguistic cum logical gymnastics, what happens is the end and start are swapped because of the ordering and our minds don't feel violated in the slightest way - the end that was before the start is treated as the start and the beginning that never was is the end - a normal state of affairs for a potential infinity which our minds seem to have little trouble accepting.