And that shows that only a finite amount of time has transpired. However, the number of “events” is infinite.
I think we can be agnostic about that. In fact, I must say that because there can be such a thing as a number of events, that therefore each event must be distinct, and one distinction is it lasts from such a time to another such time.
Events in time are a great deal more complicated than abstract numbers; not all events in time are a progress (unless the Ice Age, or the “Dark Ages”, may be considered “progressive” to you. I know the Enlightenment is a regress in my mind). In my mind, an “event” is more like an equation than a number. It is true that the infinite contains it. But I would not say that the preceding was always less than the greater.
And I suspect that this is what Chainbreaker meant all along, that there are no infinite “physical” quantities. But the OP seems to be rejecting all infinite regressions, and my example contradicts this provided that we agree motion is continuous.
Hmmm. That is food for thought. Yes, I think, considering the laws of physics, not to mention matter itself, an infinite regress is not possible. IIUC, I think that was the regress which Thomas Aquinas spoke of as being an absurdity. And that makes sense.
But temporal infinity - in past and future - that is one of the qualities of God, at least as Aquinas put it. But, then, this temporal infinity could not be bound by physics; it’s the other way around.
I disagree. The infinity that Archimedes invoked was indeed quite infinite. In modern terms, the method of exhaustion he used to find areas under parabolas leads to an infinite sequence, with the true area being the limit of that sequence. The area is finite, but the sequence is indeed infinite. So, once again, I think what you mean to say is that there are no infinite “physical” quantities such as surfaces of infinite area. But there are certainly infinite sets, and partitions of finitely large objects into infinitely many pieces.
I am not saying the sequence is finite. But it can be represented in a finite quantity. You are correct in saying there are infinite sets. But they are not physically infinite (which you also agree with). And I do not think these sequences are infinite in motion, either, simply because motion is a matter of physics, not merely of time.
To go back to Achilles, let’s say he was in Athens in 240 BC and Sparta in 239 BC. If the motion of physical sequences were infinite, he would be in both at the same time for eternity. In fact, Achilles and every person and thing that could be conceived of would exist everywhere and at all times, with no limit in time or space. In short, Achilles and everything would be God. That would be a real (and real strange) pantheism.
And just to clarify, I am not splitting hairs here.
Oh, I know.
The fact that the universe has no infinite “physical” quantities is, as far as we know, coincidental–a synthetic rather than analytic truth.
I would say, unlike geocentrism, tectonic plates, and evolution, the evidence for the physical world being finite is tremendous. Nothing - at least nothing natural - mankind has observed thus far is infinite, and mankind has witnessed much. The claim that physical things are finite is almost as unchallengeable as the axiom that “from nothing comes nothing”. In fact, were it not for both axioms, it seems to me science would not be possible if we held agnosticism about the measurability of a thing. An infinite thing and an immaterial thing both share the trait of immeasurability.
Not that I think all extant things are finite. But all things typically bound by the laws of nature must needs also be finite, else it would be difficult to see how they are bound by the laws of physics, or of any other science, since all the natural sciences depend on measurable qualities (i.e, quantities).
A universe with infinite physical quantities may be logically possible, which means that you cannot argue against infinite regressions through deductive reasoning alone.
I plead ignorance to the “physically infinite”, whatever that is supposed to mean. I only know that what we do know exists is certainly finite. And how we go from the certainly infinite to the certainly finite is a very interesting and difficult to account for question, at least within science.
