isn't that as fallacious as arguing that the series of negative integers cannot be infinite because otherwise it could never reach -3? — Amalac
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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my point is that the argument he used to prove that the universe cannot be infinite to the past doesn't appear valid. — 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.