If you are not using the words “world” and “universe” as synonyms, then what's the difference between the two? — Amalac

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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we could deduce the proposition “The universe has a necessary origin in time” without experience, merely by analysis of the concept “world”, right? — 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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show me how that proposition is analytic. — 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.

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. — 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).

How the universe has a necessary origin in time? Hmmmm.....two ways, perhaps. Show the origin of the universe is simultaneous with the origin of time, — 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?

I don't think there are any purely deductive proofs either way.

We could start with an anecdote attributed to Wittgenstein:

Wittgenstein overhears someone saying "5, 1, 4, 1, 3. Done."
He asks what that was about, and they respond that they just finished reciting π backward.
"But, how old are you?"
"Infinitely old. I never started, but have been at it forever and finally finished."

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?

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? — jorndoe

I'd say we should follow Kant's view on this matter:

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. — Karl Popper

Question: is it? Or do they think in terms of unbounded? Or even unending? Or, is the physicist's infinite a term of art that differs significantly from the mathematician's infinity? — tim wood

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.

. . . when physicists talk about infinity they usually mean something entirely different than the way mathematicians use the term. They usually do mean unbounded — fishfry

I side with the physicists on this.

isn't that as fallacious as arguing that the series of negative integers cannot be infinite because otherwise it could never reach -3? — Amalac

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.

SO the question arrises as to how accurately it represents Kant's argument. — Banno

Well, here's Kant's argument from my copy of the Critique of Pure Reason:

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. — Kant

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.

That does follow if 1 and 2 are true. — Amalac

Infinite Regress.

there is nothing logically inconsistent about a universe with an infinite past, — Amalac

:up:

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 — Amalac

Bravo! :up:

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”. — 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:

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. — 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?

Well I cannot find the reference if it exists but I've heard attributed to Wittgenstein this illustration of Kant's idea. Imagine this conversation: "........1,4,1,point 3. There, I've finished." "What are you doing?" "Reciting the digits of pi backwards." (I think we are being invited to consider this project to be logically incoherent; as opposed to merely practically impossible, like reciting the digits of pi forwards. Forwards, you'll never finish. Backwards, you will never have begun.)

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

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? — Amalac

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.

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". — 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?

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? — Amalac

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.

Trivial simplification though this is, I nonetheless can't understand 'spacetime' except in terms analogous to the surface of the Moon or a grapefruit: finite and unbounded. I find the No Boundary / CPT-Symmetrical Universe conjecture compelling in this regard.

I would like to return to the op because I find Kant's argument fascinating. Wrong, but fascinating.

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.

we’ve witnessed it in its entirety from outside its limits — Mww

unknown parts of the world, and parts we have not observed yet or of whose existence we are not even aware at present — 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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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? — 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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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? — Amalac

There is no present. Questions predicated on impossibilities are irrational.

There are two ways of thinking about infinity — god must be atheist

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....”

Well, our difference is that you differentiate between two infinities, whereas I say if you define it one way, and you define it another way, it's still infinity. To you infinity is different from itself depending on how you define it.

I can live with that, if you can.

Now, just as the unit which is taken is greater or smaller, the infinite will be greater or smaller — 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.

therefore he can't equate the two. — god must be atheist

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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Now, just as the unit which is taken is greater or smaller, the infinite will be greater or smaller
— Mww

This is actually not right. There is no such thing as "infinite" other than to describe a feature of infinity. — 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.

There is no such thing as "infinite" other than to describe a feature of infinity. — god must be atheist

adjective, noun? :chin:

Should we just make stuff up? — jorndoe

As long as we're making shit up, go hog-wild, you know — Bill Hicks

I will disagree — Mww

But you don't have to, right?

I would like to return to the op — god must be atheist

Why? Are you expecting a gift?

Witnessing indicates observation. To witness an object from outside its limits merely indicates observing the object’s spatial boundaries. — 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).

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. — Mww

So by simultaneously you don't mean “at the same time”, what do you mean by that then? Logically simultaneous?

There is no present. Questions predicated on impossibilities are irrational. — 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?

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"? — 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?

I think we are being invited to consider this project to be logically incoherent; as opposed to merely practically impossible, like reciting the digits of pi forwards. Forwards, you'll never finish. Backwards, you will never have begun. — Cuthbert

There are rigurous proofs of the irrationality of π, 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 π, 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.

And then it's clear that there are an infinite number of years that have passed already to the present day. — god must be atheist

...since when?

...since when? — Amalac

That is not a valid question. Much like you can't say, "what year will time end?" A question or statement with "since" implies a point in time. The beginning of time does not exist, and therefore there is no point in time that is the beginning.

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.

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.