Proof Infinity is Impossible

[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 - 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. But such a brick cannot possibly exist - if it has no right end, it has no middle (because the middle would count as the right end) and if it has no right end, it cannot have a left end either (as the left end would also count as the right end) - so the brick cannot exist.

Reenforcing this, a brick with a left end but no right end obviously has an UNDEFINED length and all objects must have a non-zero, positive length to exist.

We can then take our finite brick with a left end but no right end and lengthen it back to an infinite length brick and use again exactly the same argument as above - the infinite brick would have no right end so it could not have a middle or left end - such a brick is in general a physical impossibility. In general all objects must have a start and end to be viable objects that could exist - objects simply cannot go on ‘forever’.

Returning to the ‘set’ of natural numbers:

{1, 2, 3, 4, 5, 6, 7, 8, … }

If something existed in reality with the entire structure of the natural numbers, then like the brick, it would have no right end. If it has no right end, then it has no end-1 (because that would count as the end). If it has no end-1, it cannot have an end-2. If it has no end-n, it has no end-(n+1). We can then use mathematical induction to work backwards through all the natural numbers to show the sequence has no start either. So anything with the structure of the entire natural numbers (IE actual infinity) cannot possibly exist in reality, or even logically - it would have no end; therefore no start and so it would not exist at all.

So (actual) infinity appears logically impossible?

[Present awareness]

An infinite brick, if such a thing were possible, would not have an end, but would stretch out in both direction for an infinite amount of time. An infinite amount of time would have no past or future, but would be infinitely the present moment. The present moment, does not begin because it is already here and it does not end, because it is still here.

[devans99]

An infinite brick, if such a thing were possible, would not have an end, but would stretch out in both direction for an infinite amount of time. An infinite amount of time would have no past or future, but would be infinitely the present moment. The present moment, does not begin because it is already here and it does not end, because it is still here.

I was imagining an infinite brick with a concrete left end but that stretched forever to the right.

That all takes place in THE PRESENT - IE the whole brick exists at one moment of time.

My proof in the OP indicates such a brick is impossible - which implies actual infinity is in general impossible.

Time based infinities (potential infinities) are a separate subject; probably best to leave them to another thread.

[Marvin_Edwards]

An infinitely long brick has neither a left end nor a right end. And, every point is precisely in the middle of the brick. As to the numbers, there is a special symbol for the number that represents infinity.

As to whether such a brick exists someone out there in space, we'll never know. However, we can be fairly certain that a brick that was infinite in three dimensions does not exist. If it did then we wouldn't have room to discuss it.

[devans99]

An infinitely long brick has neither a left end nor a right end. And, every point is precisely in the middle of the brick. As to the numbers, there is a special symbol for the number that represents infinity.

As to whether such a brick exists someone out there in space, we'll never know. However, we can be fairly certain that a brick that was infinite in three dimensions does not exist. If it did then we wouldn't have room to discuss it.

Please kindly read the OP again - it shows that nothing withe the structure of the entire set of natural numbers can actually exist.

What you are describing with a brick with no left or right end is more like the structure of the entire set of integers.

The naturals are a subset of the integers.

So if the naturals can't exist, the integers cannot either, so a brick with no left or right end cannot exist either.

[Marvin_Edwards]

An infinitely long brick has neither a left end nor a right end. And, every point is precisely in the middle of the brick. As to the numbers, there is a special symbol for the number that represents infinity.

As to whether such a brick exists someone out there in space, we'll never know. However, we can be fairly certain that a brick that was infinite in three dimensions does not exist. If it did then we wouldn't have room to discuss it.

Please kindly read the OP again - it shows that nothing withe the structure of the entire set of natural numbers can actually exist.

What you are describing with a brick with no left or right end is more like the structure of the entire set of integers.

The naturals are a subset of the integers.

So if the naturals can't exist, the integers cannot either, so a brick with no left or right end cannot exist either.

The OP doesn't prove anything of the sort.

Infinity is what it is by definition. The set of any numbers proceeds from the infinitely small to the infinitely large. And every number in the set is precisely in the middle, because it has an infinite set of numbers on each side. That is the nature of the concept of infinity.

[MAYA EL]

Yes you are correct an "infinite brick" under the conditions you have stated cannot exist physically.

But are you trying to state that infinity doesn't exist at all and is just a concept of the mind?

[devans99]

[quote=Marvin_Edwards post_id=361186 time=1593203069 user_id=4952
Infinity is what it is by definition.
[/quote]

The definition is the axiom of infinity from ZFC. It states that there exists a set with a greater than finite number of objects.

You can arrange sets of object linearly. Then the number of objects is just:

END - START
=
UNDEFINED - START
=
UNDEFINED.

IE the infinite set of naturals, if they existed, would have an UNDEFINED size, but things need a non-zero size to exist.

Hence infinity is impossible.

[devans99]

Yes you are correct an "infinite brick" under the conditions you have stated cannot exist physically.

But are you trying to state that infinity doesn't exist at all and is just a concept of the mind?

The concept of infinity exists in our minds at a high level, but as soon as we intellectually delve into it, we find it is impossible, as with the infinite brick example.

[Terrapin Station]

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?

[devans99]

An infinite brick could simply have no end period.

Hello Terrapin!

By 'no end', that's exactly my argument:

LENGTH = END - START

And by 'no end' we 'no end' IE end=UNDEFINED.

Thats means length is UNDEFINED. But if any of the dimensions of an object are UNDEFINED, then that object can't exist.

Hence something that goes on without end is impossible.

IE infinity is impossible.

[Count Lucanor]

A circular brick will have no end and it can exist.

[devans99]

A circular brick will have no end and it can exist.

But it is finite. You can choose a point on the brick to be start/end and measure the circumference from there - and it will be finite.

[Something_Different]

all objects must have a non-zero, positive length to exist...

the infinite brick would have no right end so it could not have a middle or left end - such a brick is in general a physical impossibility...

objects simply cannot go on ‘forever’...

Hi Devan!

I like the proof, but I fear it might be undermined by a small logical issue. Your goal is to prove that infinity is not physically possible, but in the three statements quoted above it seems that you are appealing to the fact that "infinite objects cannot exist" as a basic intuitive fact. Thus your premise contains your conclusion, and the argument is tautological.

In any case, I don't grant this premise, so you'll have to find another way to convince me. I *can* imagine the existence of an object which "goes on forever" --- the universe itself might be one of them. I don't think that an infinite brick like you describe actually exists, but there's no contradiction in its definition, and humanity certainly doesn't have enough experience with the cosmos to rule out the existence of similar objects.

[Terrapin Station]

An infinite brick could simply have no end period.

Hello Terrapin!

By 'no end', that's exactly my argument:

LENGTH = END - START

And by 'no end' we 'no end' IE end=UNDEFINED.

Thats means length is UNDEFINED. But if any of the dimensions of an object are UNDEFINED, then that object can't exist.

Hence something that goes on without end is impossible.

IE infinity is impossible.

Frustrating that you're not even understanding my comment.

You initially wrote:

"An actually infinite length brick would have a left end"

I'm saying that an infinite brick wouldn't necessarily have a left (or right) end.