Proof Infinity is Impossible

[devans99]

Is this last sentence a claim or a question?

I fairly sure the proof is correct - nothing actually infinite can exist. But I might be wrong. Hence posting it here so you good folks can take a look at it.

[devans99]

If something exists in our minds and not in reality, it can't be said to exist.

If that's the narrow definition of the word "exists" that you want to use, no problem. But remember, others will not stick to it. The people who wrote the Wikipedia article that you cited did not stick to it. I did not stick to it when I said:

"Verbs exist in the English language".

So when you said "it can't be said to exist", that wasn't quite true. What you should have said is: "I personally don't use the word 'exist' in that sense."

The dictionary definition of 'Exists' is 'have objective reality or being' - IE exist in reality - so I not think it is a narrow definition.

Also consider that the proof in the OP says that infinite objects (eg with a left end but no right end) are just illogical - you can say infinite objects exist in our minds, but they exist in a illogical way in our minds: infinite objects, talking trees and fairies all have the same intellectual existential type of existence - things that cannot be.

[Steve3007]

For reference, the first post which pointed out the first serious error in the OP was the second half of this one:
viewtopic.php?p=361192#p361192

You didn't address that.

[Steve3007]

The dictionary definition of 'Exists'...

Okay, it's dueling-dictionaries time again. I'm out.

[devans99]

I'll first explain how this proof works with the analogy of a brick:

A finite brick with left and right end is the type of brick we are used to. An actually infinite length brick would have a left end but continue forever to the right

This is the first thing that doesn't make sense. An infinite brick could simply have no end period. (Also, if there's an end, it doesn't matter if we say it has no left or right end; that would just be a matter of observational orientation).

- IE it would have no right end - if it had a right end it would of course be a finite length brick.

If we reduce the length of our actually infinite brick to finite length, then we have a finite length brick with a left end but no right end.

I'm completely lost by this point, and it seems like you're contradicting what you just said above. If it has a left end (per the observational orientation) but no end on the other side, then it's not finite (it hasn't been reduced an finite length). Rather, it's infinite.

Can you clear up these points before we move on?

The whole point of the proof is to demonstrate that nothing can exist if it has a left-end but no right-end.

Objects needs a non-zero length to exist. Length=right-end - left-end.

If the object has no right-end, its right-end is UNDEFINED, so its length is UNDEFINED, hence it can't exist.

[Terrapin Station]

This is the first thing that doesn't make sense. An infinite brick could simply have no end period. (Also, if there's an end, it doesn't matter if we say it has no left or right end; that would just be a matter of observational orientation).



I'm completely lost by this point, and it seems like you're contradicting what you just said above. If it has a left end (per the observational orientation) but no end on the other side, then it's not finite (it hasn't been reduced an finite length). Rather, it's infinite.

Can you clear up these points before we move on?

The whole point of the proof is to demonstrate that nothing can exist if it has a left-end but no right-end.

Objects needs a non-zero length to exist. Length=right-end - left-end.

If the object has no right-end, its right-end is UNDEFINED, so its length is UNDEFINED, hence it can't exist.

Ah--the problem there is that just like infinity isn't literally a number or quantity, there wouldn't be a number that we could say is the length of an infinite spatial extension. That doesn't imply such a thing couldn't exist. It's just that it wouldn't have a length aside from "unending."

"Length=right-end - left-end" would be a mathematical convention re finite lengths.

[devans99]

The whole point of the proof is to demonstrate that nothing can exist if it has a left-end but no right-end.

Objects needs a non-zero length to exist. Length=right-end - left-end.

If the object has no right-end, its right-end is UNDEFINED, so its length is UNDEFINED, hence it can't exist.

Ah--the problem there is that just like infinity isn't literally a number or quantity, there wouldn't be a number that we could say is the length of an infinite spatial extension. That doesn't imply such a thing couldn't exist. It's just that it wouldn't have a length aside from "unending."

"Length=right-end - left-end" would be a mathematical convention re finite lengths.

Space is expanding and ‘nothing’ cannot expand, so space must be something (substantivalism) rather than nothing (relationism).

So we are talking about an object (an infinite brick or space if you prefer) with a left-end but no right-end - that sort of object cannot exist - if it has no right end, that implies it has no middle (because the middle would count as the right end) and no left end (because the left end would count as the right end).

Infinity is literally a number in set theory:

Aleph-naught - is defined by Cantor as the cardinality (size) of ‘set’ of natural numbers. This definition itself leads straight to a contradiction:

1. Aleph-naught is the size of the set of naturals
2. Sets contain a positive number of whole items only
3. So Aleph-naught must be a natural number
4. But there is no largest natural number
5. So Aleph-naught cannot exist

[Terrapin Station]

Space is expanding

So the first problem with this post in my view is that space is not a thing in itself that's expanding.

Space supervenes on the extension and extensional relations of matter. The reason that we say that "space is expanding" is because per what we can observe, the extensional relations of matter--in particular, of galaxies, is expanding, at least per how we interpret the data with respect to spectrum shifts.

[evolution]

Is this last sentence a claim or a question?

I fairly sure the proof is correct - nothing actually infinite can exist. But I might be wrong. Hence posting it here so you good folks can take a look at it.

What "proof" are you actually talking about here?

Just because of the obvious fact that an object, like a brick, cannot go on infinitely, then this is NOT proof that infinity itself is not possible.

Remember the Universe is NOT an object like a brick is, nor like EVERY other bounded object is. The only boundaries the Universe has are the ones that human being conceptualize.

Also, numbers, themselves, are just a human only made up concept as well.

[devans99]

So the first problem with this post in my view is that space is not a thing in itself that's expanding.

Space supervenes on the extension and extensional relations of matter. The reason that we say that "space is expanding" is because per what we can observe, the extensional relations of matter--in particular, of galaxies, is expanding, at least per how we interpret the data with respect to spectrum shifts.

We observe that distance galaxies are receding from us faster than the speed of light. That is only possible is space itself is expanding. Nothing cannot expand, so space is something.

Anyway, it does not matter - even if space is not 'a thing', it still can't be infinite: Think of space being measured by a ruler which goes on forever - every possible finite number x is inscribed on the ruler and it goes on forever - so the ruler must be longer than all finite numbers x, but finite numbers go on forever, so that’s impossible.

But space is a thing - it has dark energy associated with it. It has quantum fields associated - it is plainly not 'nothing'.

[devans99]

What "proof" are you actually talking about here?

Just because of the obvious fact that an object, like a brick, cannot go on infinitely, then this is NOT proof that infinity itself is not possible.

Remember the Universe is NOT an object like a brick is, nor like EVERY other bounded object is. The only boundaries the Universe has are the ones that human being conceptualize.

Also, numbers, themselves, are just a human only made up concept as well.

The proof I am talking about is in the OP - infinite objects are impossible. Maths claims that infinite objects are possible (axiom of infinity), hence raising this post.

Space is expanding and ‘nothing’ cannot expand, so space must be something (substantivalism) rather than nothing (relationism).

So if space is something, the it is a object, then it must be finite too.

Numbers are a human concept but there is a correspondence between numbers and physical quantities like distance. If numbers can't be infinite, neither can distances. Besides, my proof does not purely rely on numbers - a geometrical argument (the endless brick) is given too.

[evolution]

What "proof" are you actually talking about here?

Just because of the obvious fact that an object, like a brick, cannot go on infinitely, then this is NOT proof that infinity itself is not possible.

Remember the Universe is NOT an object like a brick is, nor like EVERY other bounded object is. The only boundaries the Universe has are the ones that human being conceptualize.

Also, numbers, themselves, are just a human only made up concept as well.

The proof I am talking about is in the OP - infinite objects are impossible. Maths claims that infinite objects are possible (axiom of infinity), hence raising this post.

Space is expanding and ‘nothing’ cannot expand, so space must be something (substantivalism) rather than nothing (relationism).

But, from my perspective, 'space' is NOT something that itself could expand.

So if space is something, the it is a object, then it must be finite too.

What is the 'it' in reference to here?

Numbers are a human concept but there is a correspondence between numbers and physical quantities like distance. If numbers can't be infinite, neither can distances.

Does this mean that if numbers can be infinite, then so to can distance?

Besides, my proof does not purely rely on numbers - a geometrical argument (the endless brick) is given too.

Did you actually read what I wrote above in regards to a 'brick'?

If yes, then what did you actually get, from what I actually wrote?

[Terrapin Station]

We observe that distance galaxies are receding from us faster than the speed of light. That is only possible is space itself is expanding.

Stopping at the first problem again. No. That's not only possible if space is itself a thing and is expanding. And space definitely is NOT itself a thing that can be expanding. The idea of that is ontologically incoherent.

[devans99]

But, from my perspective, 'space' is NOT something that itself could expand.

So if space is something, the it is a object, then it must be finite too.

What is the 'it' in reference to here?

Numbers are a human concept but there is a correspondence between numbers and physical quantities like distance. If numbers can't be infinite, neither can distances.

Does this mean that if numbers can be infinite, then so to can distance?

Besides, my proof does not purely rely on numbers - a geometrical argument (the endless brick) is given too.

Did you actually read what I wrote above in regards to a 'brick'?

If yes, then what did you actually get, from what I actually wrote?

Space itself is expanding - distance galaxies recede from us at faster than light speed - that's only possible if space is expanding.

So space is something, so space is an object, so space must be finite too.

Numbers can't be infinite. Infinite means larger than finite, but finite numbers go on forever - so its not possible for a number to be larger than finite - so there are no infinite numbers.

Space is just like the brick example I gave in the OP - it has to be finite.

[devans99]

Stopping at the first problem again. No. That's not only possible if space is itself a thing and is expanding. And space definitely is NOT itself a thing that can be expanding. The idea of that is ontologically incoherent.

What is 'nothing'? It is the complete lack of matter/energy, space and time - its dimensionless if its nothing. But space:

1) It has energy associated with it (see quantum fields and dark energy)
2) It has dimensions associated with it

So space must be something.

Betides I already gave you another argument that space is finite - and that argument does not even rely on space being 'a thing'.