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]

[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.