I'm not getting this at all. Whether the universe is limited or unlimited is a matter of physical state. If we conclude that its state is unknown then this discussion is just an attempt at a mental overlay that has no bearing whatsoever. Seems like any mental model we can contrive would be the same. Just a speculation.

So the best we can do is examine the universe we do know and base our models on the known. That could lead to reasonable projections of some of unknowns but still would have a physical basis and not mental abstractions.

Wouldn't a continuous area that is unoccupied be 'nothing' though?
— Philosophim
No, nothing is the absence of space, physical objects, etc. — MoK

You need to redefine space as being something then. An 'unoccupied' area is seen as 'nothing'. Things occupy. Nothing does not.

I am ok with the idea of simply stating, "space is a substance" as a start.
— Philosophim
That is alright. Saying that space is a substance does not resolve any issue here nor it helps us to prove the argument. — MoK

Its fairly important here because most people see space as 'nothing'. There is an old term for the idea that there really is no emptiness, and that all of space, or nothingness, is filled by a substance called "Aether". Aether was eventually debunked by science, but for your purposes the idea of space being 'something' instead of nothing, can be helpful here.

That is what I am trying to show in OP. is either limited or limitless. W1
is either limited or limitless. If it is limitless then we reach the conclusion otherwise it is surrounded by something else, B1. Then the whole is W2 =W1+B1. W2 again is either limited or limitless. Etc. — MoK

Oh, I see what you're doing here now! Clever! The only problem is you have necessitated that something always be bounded by something else, when it is commonly known that things are not bound by other substances, but the mass of their own matter. So while clever if things were bound by other things, its just not the case that they are. Further, that's not really the definition of "the whole" but really, 'a thing'. The whole is generally considered 'everything' which of course is bound by the entirety of its internal parts, and can have no other thing outside of itself.

I mean if space is open is limitless otherwise it is closed which means that it is limited. — MoK

No disagreement here, you just have to demonstrate that space is limitless or limited.

I'm not getting this at all. Whether the universe is limited or unlimited is a matter of physical state. If we conclude that its state is unknown then this discussion is just an attempt at a mental overlay that has no bearing whatsoever. Seems like any mental model we can contrive would be the same. Just a speculation.

So the best we can do is examine the universe we do know and base our models on the known. That could lead to reasonable projections of some of unknowns but still would have a physical basis and not mental abstractions. — Mark Nyquist

As I discussed we cannot have physical access to the whole but a very small part of it. So the only way to understand what its size is is through reason.

You need to redefine space as being something then. An 'unoccupied' area is seen as 'nothing'. Things occupy. Nothing does not. — Philosophim

Well, that is a matter of definition of things. Could we please agree that the condition in which there is no thing, namely no space, no material objects,.... is nothing?

Its fairly important here because most people see space as 'nothing'. There is an old term for the idea that there really is no emptiness, and that all of space, or nothingness, is filled by a substance called "Aether". Aether was eventually debunked by science, but for your purposes the idea of space being 'something' instead of nothing, can be helpful here. — Philosophim

I still think that that is irrelevant but we can think of space as substance if you wish.

Oh, I see what you're doing here now! Clever! The only problem is you have necessitated that something always be bounded by something else, when it is commonly known that things are not bound by other substances, but the mass of their own matter. — Philosophim

Well, if that was the case, namely if the whole was limited, then it has an edge or it is closed. We already discussed the case the whole is closed. The question which is relevant then is what is beyond the edge if the whole is open. What is beyond the edge cannot be nothing as we discussed so it is something. This means that what we call the whole is not whole but something else.

So while clever if things were bound by other things, its just not the case that they are. Further, that's not really the definition of "the whole" but really, 'a thing'. The whole is generally considered 'everything' which of course is bound by the entirety of its internal parts, and can have no other thing outside of itself. — Philosophim

The whole does not have an outside.

Well, that is a matter of definition of things. Could we please agree that the condition in which there is no thing, namely no space, no material objects,.... is nothing? — MoK

As long as you view space as a substance, this is fine. This is why it is not irrelevant. If space is not a substance, it is usually synonymous with 'nothing'.

The question which is relevant then is what is beyond the edge if the whole is open. What is beyond the edge cannot be nothing as we discussed so it is something. This means that what we call the whole is not whole but something else. — MoK

I still don't see why there cannot be nothing beyond the edge of something. I get that you want to define the whole as bounded by something else, but you've given no reason why that necessarily must be. Try to disprove the scenario I'm going to put in front of you. Referring earlier, I have a grain of sand with nothing else in the universe existing around it. Why is that a contradiction under your viewpoint?

The whole does not have an outside. — MoK

I also do not understand this. Are you saying that the whole is infinite? That seems to be the conclusion, so once again we're begging the question. I think what would really help to flesh out your definition of the 'whole' is to give an example of what that would be.

As long as you view space as a substance, this is fine. This is why it is not irrelevant. If space is not a substance, it is usually synonymous with 'nothing'. — Philosophim

I don't agree with you that space is synonymous with nothing but for the sake of argument, we can assume that space is a substance. One problem is resolved.

I still don't see why there cannot be nothing beyond the edge of something. I get that you want to define the whole as bounded by something else, but you've given no reason why that necessarily must be. Try to disprove the scenario I'm going to put in front of you. Referring earlier, I have a grain of sand with nothing else in the universe existing around it. Why is that a contradiction under your viewpoint? — Philosophim

Well, this we discussed it. Nothing has no geometry nor can occupy a room therefore nothing cannot surround a thing.

I also do not understand this. Are you saying that the whole is infinite? — Philosophim

The whole is larger than any infinity that you can imagine.

That seems to be the conclusion, so once again we're begging the question. — Philosophim

It is not the begging the question. If the whole has an outside then there is something outside of it therefore what we consider as the whole with an outside is not the whole.

Hey Mok, been away a few days. :)

I don't agree with you that space is synonymous with nothing but for the sake of argument, we can assume that space is a substance. — MoK

As long as we're identifying space as 'something', that's fine by me for this argument.

Well, this we discussed it. Nothing has no geometry nor can occupy a room therefore nothing cannot surround a thing. — MoK

Lets make sure we're not making 'vocabulary reality', a common thing we can do in philosophy. Vocabulary is used to describe reality, it does not create reality.

Nothing does not 'surround' anything in a substantive sense. But if there is a limit to something, does nothing surround it in a directional sense? Yes. Its just words to describe the idea that beyond something, there is nothing. The only way this cannot be is if the entire universe is a thing without limits. This is what we're trying to prove by your philosophy, so it cannot be part of the premises.

I also do not understand this. Are you saying that the whole is infinite?
— Philosophim
The whole is larger than any infinity that you can imagine. — MoK

This doesn't make any sense. Infinity means 'uncountable', or 'without end'. How can something be larger than something without end?

That seems to be the conclusion, so once again we're begging the question.
— Philosophim
It is not the begging the question. If the whole has an outside then there is something outside of it therefore what we consider as the whole with an outside is not the whole. — MoK

No, if the whole has an outside, that outside can be something, or it can be nothing. I get the feeling what you really want to prove here is "Nothing is impossible". Maybe that would be a better tactic?

Lets make sure we're not making 'vocabulary reality', a common thing we can do in philosophy. Vocabulary is used to describe reality, it does not create reality.

Nothing does not 'surround' anything in a substantive sense. But if there is a limit to something, does nothing surround it in a directional sense? Yes. Its just words to describe the idea that beyond something, there is nothing. The only way this cannot be is if the entire universe is a thing without limits. This is what we're trying to prove by your philosophy, so it cannot be part of the premises. — Philosophim

What do you mean by directional sense?

This doesn't make any sense. Infinity means 'uncountable', or 'without end'. How can something be larger than something without end? — Philosophim

Georg Cantor showed that there is an infinity of infinities.

Good point about not making vocabulary reality.
There are also infinities and mathematical models that are not physical objects but only mental objects.

The thing is..... physical and mental are both handled with our brains/minds so they get commingled.

What do you mean by directional sense? — MoK

Imagine a grain of sand. Outside is nothing. "Outside" is the direction.

This doesn't make any sense. Infinity means 'uncountable', or 'without end'. How can something be larger than something without end?
— Philosophim
Georg Cantor showed that there is an infinity of infinities. — MoK

I think you need to go into the specifics of how Cantor's theorem applies to the argument. This doesn't explain anything by itself.

Imagine a grain of sand. Outside is nothing. "Outside" is the direction. — Philosophim

Please check the following figure:

https://ibb.co/nj94LtJ

If by nothing you mean the black area then that cannot be nothing since nothing cannot have a geometry, property, and occupy room.

I think you need to go into the specifics of how Cantor's theorem applies to the argument. This doesn't explain anything by itself. — Philosophim

This was an answer to you when you asked whether the whole is infinite. I answered that the whole is bigger than any infinity you can imagine.

If by nothing you mean the black area then that cannot be nothing since nothing cannot have a geometry, property, and occupy room. — MoK

No, I'm not saying there exists a black area, I'm saying there's nothing. It is the logical consequence of there being a limit. To state there is a limit means there is an end. What is beyond the end? Nothing. The only way to avoid this is to state that the whole is limitless. But this has to be proven, and I'm not seeing anything but a conjecture here.

This was an answer to you when you asked whether the whole is infinite. I answered that the whole is bigger than any infinity you can imagine. — MoK

I understood that was your answer, but your answer doesn't explain itself well. I am familiar with Cantor's theory and I still don't see how this applies to what you stated.

No, I'm not saying there exists a black area, I'm saying there's nothing. It is the logical consequence of there being a limit. To state there is a limit means there is an end. What is beyond the end? Nothing. The only way to avoid this is to state that the whole is limitless. But this has to be proven, and I'm not seeing anything but a conjecture here. — Philosophim

I know but the very existence of a limit means that there is nothing beyond it! What is beyond the end? It is either something or nothing. Take your pick.

I know but the very existence of a limit means that there is nothing beyond it! What is beyond the end? It is either something or nothing. Take your pick. — MoK

If 'the whole' is everything and the whole has a limit, then by consequence there is nothing past that limit. If the whole is limitless, then there is no end, thus 'nothing' cannot exist. But one has to prove that the whole of existence is limitless, which we cannot do.

If 'the whole' is everything and the whole has a limit, then by consequence there is nothing past that limit. If the whole is limitless, then there is no end, thus 'nothing' cannot exist. But one has to prove that the whole of existence is limitless, which we cannot do. — Philosophim

You cannot draw a figure in which the whole has a limit and there is nothing beyond its limit.

You cannot draw a figure in which the whole has a limit and there is nothing beyond its limit. — MoK

Correct, because you cannot draw 'nothing'. This doesn't negate what I've stated. If you have limits, nothing must be beyond those limits. The only way to avoid there being 'nothing' is if everything is infinite and eternal.

Correct, because you cannot draw 'nothing'. This doesn't negate what I've stated. If you have limits, nothing must be beyond those limits. The only way to avoid there being 'nothing' is if everything is infinite and eternal. — Philosophim

It negates what you have said. I am afraid that I don't see any point to repeat myself.

Correct, because you cannot draw 'nothing'. This doesn't negate what I've stated. If you have limits, nothing must be beyond those limits. The only way to avoid there being 'nothing' is if everything is infinite and eternal.
— Philosophim
It negates what you have said. I am afraid that I don't see any point to repeat myself. — MoK

I disagree, but we've both said our piece now. :) Good chatting with you again MoK,