Actual Infinity in Reality?

[SteveII]

I am not asking if there is a concept in mathematics that deals with infinity or if there exists sets with an infinite number of members (although you might use the concept in a larger argument). I am not asking if we can theoretically divide something an infinite amount of times (although you might use the concept in a larger argument). I am not asking about a potential infinite. 

I am asking about an actual infinite of something concrete (not abstract). Can it logically exist? Why or why not? 

No mention of God either. Philosophy subforum--let's stick with pure metaphysics.

[Angrboda]

I provided my answer in another thread before I saw this thread. So I'll simply cut and paste that response here. Unless I've missed something, it does not appear that there are any logical contradictions to my conclusion here. If someone has one, please provide it. To sum up, it doesn't appear to be impossible for the universe to be temporally infinite. On less certain ground, I don't see anything immediately contradictory to the notion that the universe may be spatially infinite.

It is typically argued that the universe can't be past eternal because there would be no way to traverse an infinity of time. However, such arguments about being unable to traverse an infinite past up to the present, as implied by such arguments as the one that says you can't count successively to infinity, rely on the A theory of time. The idea of "traversing" an infinite past is incoherent on the B theory of time. If the B theory of time is correct, and the universe is infinite in time, such arguments do not apply and you have the case of an actual infinite existing. This leads to attempts to show that the universe is not past eternal by attempting to directly demonstrate that the universe's past is not infinite because the universe had a beginning. This is done by invoking things such as the Borde-Guth-Vilenkin theorem and the standard interpretation of the big bang model which supposedly indicates that the universe has a beginning. However there are theories such as Penrose's Conformal Cyclic Cosmology (see below) in which neither of these objections apply. Conformal Cyclic Cosmology explains why we would find points "in time" that have the appearance of resulting from a universe that had a beginning in a universe which does not in fact have a beginning. So, to the best I can tell, the idea that the universe is temporally infinite is consistent with a B theory of time and with some models of cosmology. So, ultimately, it doesn't appear that the case that you can't have an actual infinite has been made. (Regarding Hilbert's hotel, supposedly the results are absurd. This can mean several things. It can mean that the result is counter-intuitive, or it could mean that the result is logically impossible. I don't off-hand see that Hilbert's exercise demonstrates anything about logical impossibility so much as it is just showing that such things seem to defy our normal intuitions. I don't see the latter as any kind of argument that actual infinities don't exist so much as a demonstration that we aren't natively well equipped to think about such things. That latter fact is of little consequence. Quantum mechanics presents results that are equally absurd in that sense, that doesn't make quantum mechanics wrong. If you think Hilbert's hotel demonstrates something more substantial than this, I'd appreciate someone drawing out the relevant connections, because I don't see them.)

The conformal cyclic cosmology (CCC) is a cosmological model in the framework of general relativity, advanced by the theoretical physicists Roger Penrose and Vahe Gurzadyan. In CCC, the universe iterates through infinite cycles, with the future timelike infinity of each previous iteration being identified with the Big Bang singularity of the next. Penrose popularized this theory in his 2010 book Cycles of Time: An Extraordinary New View of the Universe.

Wikipedia || Conformal Cyclic Cosmology

The basic point is this. The very early universe is smooth. The universe right now is lumpy, with stars and galaxies and black holes all over the place. But the future universe will be smooth again — black holes will evaporate and the cosmological constant will disperse all the matter, leaving us nothing but empty space. (Just wait about 10100 years.) So, Penrose says, we can map the late universe onto a future phase that looks just like our early universe, simply by a conformal transformation (a change of scale). Do this an infinite number of times, and you have a cyclic cosmology — the universe goes through a series of “aeons” that start with a smooth Big Bang, get lumpy as structure forms, smooth out again, and then gets matched onto another smooth Big-Bang-like phase, etc.

Penrose’s Cyclic Cosmology

[BrianSoddingBoru4]

The number of cat hairs in the universe is an actual infinity.  I know this because:

1. We keep hoovering the settee and it never gets any better.

2. Our cats have not gone bald.

Boru

[brewer]

What do you think Stevie?

(this feels like a gotcha attempt, therefore god)

[Whateverist]

This is all to argue that the past can't be infinite, therefore God made it on His cosmic watchmaker's bench.

[BrianSoddingBoru4]

This is all to argue that the past can't be infinite, therefore God made it on His cosmic watchmaker's bench.

It'll all fall apart once we establish that God is made of cat hair.

Boru

[Whateverist]

This is all to argue that the past can't be infinite, therefore God made it on His cosmic watchmaker's bench.

It'll all fall apart once we establish that God is made of cat hair.

Boru

In the beginning all was null and void.  Then God coughed up a giant hairball, and He saw that it was good.

[pocaracas]

I am asking about an actual infinite of something concrete (not abstract). Can it logically exist? Why or why not? 

No mention of God either. Philosophy subforum--let's stick with pure metaphysics.

Unfortunately, our metaphysics is bound by our experience and intuitions.
Intuitively, the Universe is finite. Huge, but finite. To the best of our knowledge, it has some 10^9 galaxies each with some 10^9 stars, leading to, according to some estimates, 7.1×10^79 atoms in the whole Universe.
This concerns the observable Universe.
Is there Universe beyond the observable Universe? Cosmologists typically say that there doesn't seem to be.

Is the space-time in our Universe all there is? who knows...
Could the space-time out of our Universe be infinite? Sure, why not?
If it's infinite, then it could hold infinite Universes... some smaller than ours, some larger, some roughly the same.

Of course, once we leave the threshold of our own Universe, the question becomes: does our Physics still apply? If not, then any intuition needs to go out the door. If yes, Jorm's answer becomes appropriate.
Heck, our intuition needs to check out when we go very fast or look at the very small within our Universe. I don't imagine it would stand if we carry on outwards.


This all then hinges on what you mean by "exist". Exist in our Universe? Exist in any form?

[polymath257]

Yes, of course, it is *logically* possible. There is no internal contradiction to the concept of an actual infinity.

Now, I don't know if you consider time to be abstract or concrete, but there is certainly no internal contradiction to the concept of an infinite time.

There is also no contradiction in the possibility of an infinite number of stars in our universe if the universe is infinite in spatial extent.

[GrandizerII]

Steve, it doesn't work this way. If you see something is not logical, the burden is on you to show that it is not.

And no, forget Hilbert's Hotel because all it demonstrates is that we're not dealing with a number, but rather with several concepts that we mistakenly refer to as the same thing but are not. The infinity encompassing all positive integers is not the exact same as the infinity encompassing all even positive integers, and definitely not the same as the infinity of all real numbers (which remarkably is greater in size than countably infinite sets).

So it's not like you have shown that infinity is self-contradicting, but that infinity is used as the same label for multiple concepts. And that is why with your misleading handpicked equations (assuming they were even correct and derived logically from the problem described), we get results that don't occur when we're doing numbers instead.