Actual Infinity in Reality?

[polymath257]

And, so, if no one can prove that actual infinities exist, that makes their existence "impossible"??

Yes, because then we are left with things like:

1. The knowledge that you cannot get to an actual infinity by successive addition,
2. You cannot have an infinite series of events in the past because we could never count down from 5, 4, 3, 2, 1...Now because there would still have to be an infinite amounts of events that still need to happen, and 
3. Thought experiments like Hilbert's Hotel which give you a series of absurdities when dealing with actual infinities. 

With nothing on the other side to even balance out the question (let alone be convincing), it would seem that even with these 3 reasons, we find an actual infinite of a real object to be metaphysically impossible.

As at least partial answers,

1. All this means is that we won't be able to verify an actual infinity by just counting. It must take some *other* method (for example, using geometric considerations). This is, at least, the most serious of your objections: the possible  inabillity to verify an actual infinity. 

2. This is one that I still don't understand what you are attempting to say. Once we are *anywhere* in the sequence, there is only finitely far to go in the sequence (I assume you meant, by the way, ...., -5,-4, -3, -2, -1.. and not what you wrote. If you did mean what you wrote, I understand your objection even less). So, if you are at -100, there are only 100 more places to go to get to 0. At no point do you have an infinite time to wait. It is simply that every event has a previous event. THERE IS NO START. If you thing there is an infinite wait from some point, please let me know where it is.

3. Exactly which of the results for the Hilbert Hotel are *absurdities*? Every single one is a logical possibility. For example, if there is an infinite amount of time up to now, then there will be also an infinite amount of time up to a minute from now. If there are an infinite number of seconds previous to now, there are an infinite number of half-seconds previous to now. I don't see how the cardinalities being the same is in any way a problem with this being a reality. If anything, the Hilbert Hotel shows there is always room for 'extra time' even if time is infinite. Where is the *absurdity*?

So, exactly what do you mean by the phrase 'metaphysically impossible'? I understand an issue if there is an actual contradiction. But you have shown none. At worst, you have shown where infinities act different than finities. I hope that it isn't a surprise that they do.

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Bold mine.

I think what Steve means is, if we have time moving in a forward direction, how do we get to that one point in time from an infinite past?  How do you get to that single event in time without beginning somewhere?  If events are happening in succession, and time is infinite into the past, how would we ever arrive at a singular point in time?  Wouldn’t you have to start somewhere to get there?   I’m confused! Lol

And the answer is that nothing was ever in the *infinite* past. Everything is finitely far in the past. But different things are different amounts in the past and there is not a bound to how far in the past they are.

So, take the progression that Steve seems to have problems with

...., -6, -5, -4, -3, -2, -1, 0, 1, 2, 3,.....

Show me two of those points that are infinitely far away from each other. You won't be able to: every distance between points is finite. And that is true even if the past goes infinitely far back. Those ellipses are NOT numbers. Any *actual* number will be only finitely far back.