Is Infinity Real?

Arguments for a "First Cause" presented by philosophers from Aristotle to Jaki are that infinite regression is not possible. Hilbert, the great 20th Century mathematician, produced the infinite hotel paradox to show that infinity is not real. I am enough of a mathematician to understand how limiting processes can use infinity in looking at convergent series, the calculus, and so forth, and I appreciate Cantor's arguments about the cardinality of infinity. What is of interest are arguments (pro and con) about whether infinity "really" exists and, therefore, whether the universe might be finite or infinite.Edited by anselm, : plurality didn't agree

Is this proposed topic somehow related to the creation/evolution debate?

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--	Percy
	EvC Forum Director

If you're not sure which forum to put this topic in, I'd suggest "Cosmology and Big Bang". The point here is that if you want to posit cyclic universes, then you have to show that infinite regress is a valid philosophical concept. And insofar as cosmology and the Big Bang are relevant to EvC, then so is the suggested topic.
Thank you.
Anselm

Thread copied here from the Is Infinity Real? thread in the Proposed New Topics forum.

What does reality have to do with philosophical concepts?

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Anyone so limited that they can only spell a word one way is severely handicapped!

I don't think that's what the hotel paradox shows. Can you run me through that one? I thought the best current model of the universe is one that is finite, yet unbounded.I think the simple answer is that we don't know if the universe is infinite or not. I don't think arguments are going to settle whether infinity really exists or not. What? Fuck philosophy. Science doesn't have to cater to philosophy! Besides, the maths will speak for themselves.Further, a finite universe can still exist without a First Cause so this whole thing is even more pointless, no offense.

Is infinity real?
Does infinity really exist?Isn't this like asking "Is a kilometre real?" or "Does large really exist?"'Infinity' is a human mental construct to either i) describe a object without limits or ii) represent a mathematical concept.
You cannot physically interact with it.

well the problem with infinity is that we cannot precive it.example there is no number infinity because you can always add one so technically the argument that he had a full hotel with infinite number of rooms cannot be ever full because you can always add one.our minds do not work that way they work infinity = infinity and we use the same logic as 100 = 100 so if you have 100 guests and 100 rooms the hotel is full. But if you have an infinite number of guests and an infinite number of rooms that does not mean that every room is full because there is no finite number of rooms you can always ad one and if a new geust shows up you added one guest and one roomso infinity +1 is still infinityinfinity is an imaginary number never obtainable because you can always ad oneAs for the universe if it is infinitively large we do not know and we never will know if it is infinite we may one day know if it is finite.

And then there is the Zeno's paradox argument, which purports to show that motion is impossible.We should be skeptical of all such arguments.Is reality infinite? I don't see how we could ever determine that.It is best to think of infinity as a human idealized concept. The way that the infinite works in mathematics seems to be mostly not a problem, though some people have conceptual struggles over, say, the Banach-Tarski paradox.

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Jesus was a liberal hippie

...but even more powerful than Infinity is NaN. Anything that comes into contact with a NaN becomes a NaN."Inside the museums Infinity goes up on trial.
Voices echo 'this is what...salvation must be like after a while'.
But Mona Lisa musta had the highway blues -
you can tell by the way she smiles...."

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- xongsmith, 5.7d

LOL.For those not familiar, "NaN" stands for "Not a Number", and is defined in the IEEE standard for floating point arithmetic.

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Jesus was a liberal hippie

But Zeno's paradox is only called so because it is counter-intuitive (veridical paradox), since it is solved through Calculus in Mathematics.I think the paradox of infinite regression not being possible falls into the category falsidical paradoxes.I don't really know the outline of the argument so I can't really know for sure. But if the premises are true and no fallacy is involved, then there is no place for skepticism, unless you put into question the laws of logic.At first glance I see no reason why the universe couldn't be spatially infinite. Past time being infinite, however, I do have some problems with.

Why? Do you have a problem with future time being infinite? If not, and you believe in CPT, then where's the issue?

I can certainly without contradiction describe a universe infinite in space and time. Consider a universe with one spatial dimension, and let it contain a single object which is at point x in space at time t (and hence has a velocity of 1 in appropriate units). Here we have infinite space, infinite time, infinite causality --- and no internal logical contradictions.It follows, does it not, that these infinities cannot be disproved a priori, since that could be done only by identifying a logical contradiction existing within all such hypothetical systems. So that removes such questions from the domain of philosophy and puts them in the domain of science --- which is not to say that scientists can or ever will answer them, only that if they can't it's no use asking a philosopher.