Proof Infinity is Impossible

[Atla]

But "where" does this five-meter cube exist?

If there is no-"where" for this five-meter cube to exist, then it does not exist. And if this five-meter cube does not exist, then there is no-"where'" for the one-meter sphere to exist. And if there is no-"where" for the one-meter sphere to exist, then it does not exist.

So again, 'finite' objects are proof of an 'infinite' universe (space).

You seem to be assuming linear dimensions, I doubt that your objection works when the dimensions are "circular" (when they are folding back upon themselves / looping back into themselves). Such a universe simply doesn't need to have an outside, it doesn't have to be situated "in" anything.

[Terrapin Station]

But "where" does this five-meter cube exist?

If space isn't your "where" then what is it?

If you're saying that "Just in case space is finite, it needs a 'where' that's not itself" then that would have to be part of your argument. It wasn't part of your argument as stated.

[RJG]

P1. If space were not infinite, finite objects would have no 'where' to exist.
P2. Finite objects exist.
C1. Therefore, space is infinite.

You seem to be assuming linear dimensions, I doubt that your objection works when the dimensions are "circular" (when they are folding back upon themselves / looping back into themselves). Such a universe simply doesn't need to have an outside, it doesn't have to be situated "in" anything.

But "where" does this circle (or sphere) exist?

If there is no-"where" for this circle/sphere to exist, then it does not exist. And if this circle/sphere does not exist, then there is no-"where'" for finite objects (within this non-existent circle/sphere) to exist. And if there is no-"where" for the finite objects to exist, then they themselves do not exist.

So again, 'finite' objects are proof of an 'infinite' universe (space).

But "where" does this five-meter cube exist?

If space isn't your "where" then what is it?

I am simply asking where this "five-meter cube exists". If it exists no-"where", then it doesn't exist, ...right?

[Terrapin Station]

P1. If space were not infinite, finite objects would have no 'where' to exist.
P2. Finite objects exist.
C1. Therefore, space is infinite.

You seem to be assuming linear dimensions, I doubt that your objection works when the dimensions are "circular" (when they are folding back upon themselves / looping back into themselves). Such a universe simply doesn't need to have an outside, it doesn't have to be situated "in" anything.

But "where" does this circle (or sphere) exist?

If there is no-"where" for this circle/sphere to exist, then it does not exist. And if this circle/sphere does not exist, then there is no-"where'" for finite objects (within this non-existent circle/sphere) to exist. And if there is no-"where" for the finite objects to exist, then they themselves do not exist.

So again, 'finite' objects are proof of an 'infinite' universe (space).

But "where" does this five-meter cube exist?

If space isn't your "where" then what is it?

I am simply asking where this "five-meter cube exists". If it exists no-"where", then it doesn't exist, ...right?

Again, isn't space the where? And what would you give as an answer to any "where" question in this vein? For example, "Where does your computer exist?" What's the sort of answer that you'd give to that?

[Atla]

P1. If space were not infinite, finite objects would have no 'where' to exist.
P2. Finite objects exist.
C1. Therefore, space is infinite.

You seem to be assuming linear dimensions, I doubt that your objection works when the dimensions are "circular" (when they are folding back upon themselves / looping back into themselves). Such a universe simply doesn't need to have an outside, it doesn't have to be situated "in" anything.

But "where" does this circle (or sphere) exist?

If there is no-"where" for this circle/sphere to exist, then it does not exist. And if this circle/sphere does not exist, then there is no-"where'" for finite objects (within this non-existent circle/sphere) to exist. And if there is no-"where" for the finite objects to exist, then they themselves do not exist.

So again, 'finite' objects are proof of an 'infinite' universe (space).

I just told you. The sphere is part of the universe I just described, and that universe has no outside, so that's the only "where" there is.

[RJG]

But "where" does this five-meter cube exist?

If space isn't your "where" then what is it?

I am simply asking where this "five-meter cube exists".

Again, isn't space the where?

A finite "five-meter cube" is a 'what', not a 'where'.

But "where" does this circle (or sphere) exist?

I just told you. The sphere is part of the universe I just described, and that universe has no outside, so that's the only "where" there is.

You are saying this universe is "finite", and exists within itself?? Can you not see the logical contradiction? -- Finite objects cannot exist inside/within themselves [X<X is logically impossible]. -- Either finite objects exist some-"where", or they don't exist!

And what would you give as an answer to any "where" question "Where does your computer exist?" What's the sort of answer that you'd give to that?

My (finite) computer exists in this (infinite) universe. If the universe were not infinite, my computer would not exist (i.e. there could be no finite objects). -- It is logically impossible for a single finite object to contain ALL finite objects.

[Terrapin Station]

A finite "five-meter cube" is a 'what', not a 'where'.

Are you arguing that space is a "where" when it's infinite, but space isn't a "where" when it's finite?

What would be the argument for that (just the claim above wouldn't be enough).

And what would you give as an answer to any "where" question "Where does your computer exist?" What's the sort of answer that you'd give to that?

My (finite) computer exists in this (infinite) universe.
[/quote]

If that's a sufficient answer to a "where" question, why wouldn't "My finite computer exists in this finite universe" be a sufficient answer to "where"?

You'd need to give a response that doesn't just say, "Because the universe isn't infinite," you'd need to give an answer that says why it couldn't be that isn't just a repeat of the previous argument, an argument which I've already objected to in a way that you haven't addressed yet (we're working on you addressing it with the first question I ask you in this post).

[RJG]

A finite "five-meter cube" is a 'what', not a 'where'.

Are you arguing that space is a "where" when it's infinite, but space isn't a "where" when it's finite?

Correct. "Finite" implies an object. An object is a "what", not a "where".

My (finite) computer exists in this (infinite) universe.

If that's a sufficient answer to a "where" question, why wouldn't "My finite computer exists in this finite universe" be a sufficient answer to "where"?

Where does this 'finite' universe exist? If it exists no-where, then it doesn't exist. And if it doesn't exist, then neither does my computer (as it has no-where now to exist!).

X<X is logically impossible.

[Terrapin Station]

Correct. "Finite" implies an object. An object is a "what", not a "where".

Okay, so what would be an argument for that? (It doesn't have to be constructed like a formal logical argument, although if you want to do that, that's fine.)

[Atla]

I just told you. The sphere is part of the universe I just described, and that universe has no outside, so that's the only "where" there is.

You are saying this universe is "finite", and exists within itself?? Can you not see the logical contradiction? -- Finite objects cannot exist inside/within themselves [X<X is logically impossible]. -- Either finite objects exist some-"where", or they don't exist!

You added this contradiction, in the above scenario the universe doesn't exist "within itself". There's nothing outside the universe, it isn't "in" anything, and it exists.

[RJG]

Correct. "Finite" implies an object. An object is a "what", not a "where".

Okay, so what would be an argument for that? (It doesn't have to be constructed like a formal logical argument, although if you want to do that, that's fine.)

I have no desire to play games. If you wish to prove that a "finite object is not an object", then have at it.

You added this contradiction, in the above scenario the universe doesn't exist "within itself". There's nothing outside the universe, it isn't "in" anything, and it exists.

Where then, does this 'finite' universe exist? ...does it exist "no-where"?

[Atla]

Where then, does this 'finite' universe exist? ...does it exist "no-where"?

Where does your infinity exist? Does it exist no-where?

[Terrapin Station]

Correct. "Finite" implies an object. An object is a "what", not a "where".

Okay, so what would be an argument for that? (It doesn't have to be constructed like a formal logical argument, although if you want to do that, that's fine.)

I have no desire to play games. If you wish to prove that a "finite object is not an object", then have at it.

Okay. If providing at least an informal argument for something you're claiming on a philosophy board is "playing games" to you, then you're wasting my time.

[RJG]

Where then, does this 'finite' universe exist? ...does it exist "no-where"?

Where does your infinity exist? Does it exist no-where?

1. Infinity is not a 'thing' that resides anywhere. Only 'things' (finite objects) reside some-where.
2. Infinity (or infinite space) is where finite 'things' exist.
3. A 'finite' thing that exists no-where, does not exist.
4. Without infinity, there could be no finite.

**********
P1. It is logically impossible [X<X] for a finite object to contain ALL finite objects. It cannot contain itself.
P2. If space were not infinite, ALL finite objects would have no 'where' to exist.
P3. Finite objects exist.
C1. Therefore, space is infinite.

[Atla]

1. Infinity is not a 'thing' that resides anywhere.

It's not nothing, so why doesn't it have to be somewhere?