But time exists if space exists independent of whether change exists or not.

You mentioned that time does not exist if change does not exist.

And sometimes those limits are determined by the way in which we choose to assemble the language.

For example, one could just as well say: time is the measure of change rather than a pre-requisite for it. There would be no time in the absence of change. Time is not in the nothing anymore than time is in the something.

And of course we would have a different set of logical implications. — Arne

Time and space are twisted and are parts of a single manifold called spacetime. This means that you have time if you have space.

Spacetime doesn't really exist. It isn't real, in the way matter and energy are. It is theory. It's a mathematical model.
"Spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects such as how different observers perceive where and when events occur." (Wikipedia) — Alkis Piskas

Unfortunately, the wiki references in some cases are not good enough or may be misleading. You will enjoy this article if you want to get involved in the debate of whether spacetime is a substance or not. I am a physicist and cannot understand the article well since it is very technical.

Well, this is debetable. Anyway, it refers to a specific theory: the energy wave theory, where it is considered a medium that allows the transfer of energy of its components. But I believe it is used for descriptive purposes, as I mentioned.
In reality, space and time cannot be perceived as physical things, as matter and enery can.
Neither can space or time produce change or movement. Rather the opposite: change and movement produce the notion of space and time. — Alkis Piskas

Spacetime can affect the motion of objects and light. Massive objects can change the curvature of spacetime as well.

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.

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.

Or maybe rather, "we could determine that AI was thinking if we knew how we thought?" But we don't, and therein lies the massive hole at the center of this debate.

But for those who deny the possibility... — Count Timothy von Icarus

Correct. Unfortunately, we don't know how we think so we cannot design an AI that can think.

Yes, AI can think if we know how we think. We can simulate the brain if we know how it works when it comes to thinking. There are three questions that we need to answer before we can design an AI that can think. These questions are:
1) How the new information is classified in the brain?
2) How the related information are linked in the brain?
3) How do we find new information from the linked information?

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.

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.

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.

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.

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.

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.

I think I see what you mean here. There is always a whole larger than and surrounding sub-wholes. E.g. W2 = W1+B1. And that this goes ad infinitum. Right? — Alkis Piskas

Yes.

But this is not exactly what you said in the OP. You said that "This means that the whole is not W1 but W2 where W2=W1+B1". But W2 is simply a different, larger whole, including W1. W1 is still W1. It has not changed. It has not become W2. This is what I discussed in my previous comment. — Alkis Piskas

Yes, $W_1$ stays the same and does not change. I mean what we consider as the whole $W_1$ which is limited is not the whole but something bigger $W_2$ where $W_2$=$W_1$+$B_1$.

Now, about wholes --or the whole as you say-- going ad infinitum, i.s. being limitless.
If this were the case, then the Universe itself --which includes all the "wholes"-- should be also surrounded by something larger than it. E.g. there could be another Universe, larger than our known Universe .But we don't and can't know that. Or there can be the case of parallel universes. Which remains still to be proved. With our present knowledge the Universe includes everything. (Except if this knowledge has changed and I don't know it.) — Alkis Piskas

Yes, we cannot have physical access to the whole so we can never physically confirm that is limitless. But my argument shows that the whole is limitless.

Wouldn't a continuous area that is unoccupied be 'nothing' though? — Philosophim

No, nothing is the absence of space, physical objects, etc.

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.

In principle, perhaps. But the entire point you're trying to make is that the whole is limitless. If space is the whole, we have to prove that, not declare it. If I'm trying to prove that cheese is a moon rock, I can't just say, "Cheese is a moonrock" as one of the arguments. This is a 'begging the question' fallacy. — Philosophim

That is what I am trying to show in OP. $W_1$ is either limited or limitless. If it is limitless then we reach the conclusion otherwise it is surrounded by something else, $B_1$. Then the whole is $W_2$=$W_1$+$B_1$. $W_2$ again is either limited or limitless. Etc.

Alright, lets look at hyperspace then. Doesn't he same question about space and the grain of sand apply here as well? — Philosophim

You mean hyperspace? Hyperspace is either closed which mean it is limited or it is open which means that it is limitless.

Isn't hyperspace bound by its own self? — Philosophim

What do you mean by is bounded by its own self?

This is a contradiction though. Something cannot be both limitless and limited. — Philosophim

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

The figure is a 2d representation of space-time distortion. These several people I quoted are not wrong about physics, you are.

So how do you discover intrinsic geometry empirically? You measure angles, you measure dot products and you see what the values are. If those values are what you'd get with flat space, you're in a flat space. If they're what you'd get in curved space, well, you're in a curved space. You can consider this the definition of a curved space. You don't have to envision space bending into some other space. Just that in our space, we measure dot products of basis vectors to have some non-zero value.
— https://physics.stackexchange.com/questions/547140/what-is-intrinsic-curvature

We call it "curvature" because it works exactly like curvature. Angles and distances measured are exactly what they would be if the space was curved. We don't assume an embedding space because we don't need to to get the right answers. So why add something to the theory that cannot be observed?

Unless you can observe the embedding space, then no, you cannot deduce that you exist embedded in a higher space. That's an assumption that cannot be tested.

If your reply does not address these quotes directly, I will move on. — Lionino

Ok, so I have to draw a figure to show what I mean. Here is the figure: https://ibb.co/09dXsQH . As you can see the curvature on each point of this surface is zero. Why? Because the angle between each pair of immediate lines is constant regardless of whether you are close to the center or not. If you however draw the same picture on the surface of a balloon then you observe that the angle between lines changes as you get close to the center. If you don't have a ball or balloon then please check this figure:
https://en.wikipedia.org/wiki/File:Cassini-science-br.jpg.
It is clear in this figure that the angle between each pair of immediate lines increases as you get closer to the center therefore you have a positive curvature.

So, to sum it up, the existence of a curvature in space means that the space must bend inside a hyperspace as the 2D space in the figure of wiki bends toward the third direction.

Ok, I see. So if I have your idea right, you believe that space is a thing. — Philosophim

If by "space is a thing" you mean that space is a substance then that is still the subject of debate. If by space you mean a continuous area that is unoccupied then we are into business.

If this is the case, and space is an actual thing, then just replace my example of 'a grain of sand' with 'a section of space'. — Philosophim

Cool, that works.

Once again, wouldn't the bounds of space be the internal limitations of space itself? — Philosophim

Space in principle could be limitless. A section of it is however limited.

I agree with you that nothing cannot bind space, but if space is limited, how is it bound by something outside of itself then? — Philosophim

Space in principle could be limitless if it is flat. Space however could be a closed manifold. In this case, the space is limited but it is surrounded by something else, let's call it hyperspace.

How is the limitation of space not bound by its own internal volume? — Philosophim

Space is bounded by its own volume which is limitless if it is flat otherwise it is limited. Space then is surrounded by something else in the second case so-called hyperspace.

What do you mean by "bounded by"? — Alkis Piskas

To explain that I need to explain what I mean by limited. By limited I mean restricted in size. By "bounded by" then I mean that there exists something that surrounds the limited thing.

It normally means having something as its edge or simply an edge around something. What edge do you have in mind? And why that edge is part of W1, in a way that W1 is actually W1 + edge (B1)? — Alkis Piskas

Think of a ball in a room for example. The ball is restricted in size so the room surrounds it. So in this case the ball is $W_1$ and the room is $B_1$.

All this is too abstract. In such cases it is always recommended to give some example(s). — Alkis Piskas

OK, I try my best to give good examples.

Maybe you can use this: Water in a glass. W1 is the whole (quantity of) water. And we have two kinds of "edges" or boundaries: the glass --around and at the bottom of the water (B1)-- and the air above the water (B2). According to your argument, W1 is actually W1+B1+B2. Right? Can this be considered a valid case? — Alkis Piskas

No, $B_2$ is what surrounds $W_2$ where $W_2=W_1+B1$. In the example of the ball, $W_1$ is the ball, and $B_1$ is the room. $B_2$ is what surrounds the room, the rest of the building for example. So, $W_3$=$W_1$+$B_1$+$B_2$. $B_3$ then is for example the city which surrounds the ball $W_1$, the room $B_1$, and the building $B_2$. So, $W_4$=$W_1$+$B_1$+$B_2$+$B_3$. Etc. This chain as you can see is ongoing unless there exists $B_i$ such that $B_i$ is limitless. Either way, the chain where all $B_i$s are limited is limitless because there is no end for the chain or there exists a $B_i$ that is limitless which makes the whole limitless.

I hope things are clear now.

Being and Time is his most noted work. I highly recommend. — Arne

Thank you very much for the reference to the book.

Nonetheless, my primary area of philosophical interest is ontology (the nature of being) and my primary ontological disposition is Heideggerian. — Arne

Cool. I didn't know about him. I am not a philosopher by education. Good to know about him because I have something extra to read.

By saying "perhaps the whole is limited by time" I mean perhaps the whole is limited by time. It is an idea that emerged shortly before I said it and I suspect I am not the first person to consider something to that effect. I have not thought it through to the point of making it a proposition. Thus the word "perhaps." — Arne

What do you mean by "limited" in this case?

I have no doubt.

I was joking. — Arne

I know. :wink:

I agree that the whole includes "all". I neither agree nor disagree that the whole is "limitless." — Arne

Well, if by "all" you mean "everything that exists" then following my OP I can show that the whole is limitless.

I suspect "all" and "limitless" have different implications regarding ideas such as finite/infinite. — Arne

I agree.

Similarly, perhaps the whole is limited by time. — Arne

What do you mean?

how newtonian of you. :-) — Arne

Actually, I am very open to changing my mind if I am shown to be wrong. :wink:

I state unequivocally that the whole cannot be limited by "thingness." How you interpret my statement is on you. — Arne

I didn't say that your statement is on me. I mean, we both conclude that the whole is limitless so we agree on the conclusion.

Exactly. The flaw in the notion of a limited whole is our obsession with "thingness. By definition, a limit to the whole cannot be a "thing" or it would be included in the whole.

If there is a whole, then it includes all. If it does not include all, then it is not the whole. Beyond that is philosophy as industry. — Arne

That was my reply to Philosophim. Lionino thinks that the whole could be a closed manifold. I am trying to show that any closed manifold is embedded in hyperspace. He does not agree so the discussion is ongoing.

By the way, glad to see that you agree that the whole is limitless.

And therein is your flaw. Considering the whole to be limited is simply a mistake in logic. And we already knew that. — Arne

Lionino does not think so. He thinks that the whole can be limited. Please see my discussion with him.

And that argument was already refuted. — Lionino

Where? I already argue that a flat manifold with a boundary cannot represent a closed manifold.

The counter-example I am giving is exactly where space is not flat, where it has positive curvature. — Lionino

How the lines could deviate towards or away from each other if the space does not bend? Here is the figure that illustrates what I am trying to say:

https://en.wikipedia.org/wiki/File:Cassini-science-br.jpg

It doesn't.

No, general relativity is based on something called "intrinsic curvature", which is related to how much parallel lines deviate towards or away from each other. It doesn't require embedding space-time in a higher dimensional structure to work.

In summary, it is important to distinguish between extrinsic curvature, which involves bending through an additional dimension, and intrinsic curvature, which is directly visible on a surface without reference to an extra dimension. — Lionino

He is wrong. Please see the above figure.

Until physics tells us that our human-made logic is not absolute and that we may have to reframe, as modern physics may make us do. — Lionino

I don't think that time ever comes.

"(◇¬p → ¬□p)". — Lionino

What does that mean?

Hello again MoK! — Philosophim

Hello Philosophim!

Let me take your abstract into a thought example for a minute. Lets say that in the universe, only a single grain of sand exists. Now we claim that is the whole, but what is the definition of the whole? Usually 'the whole' is seen as 'everything'. But then you add in something outside of the whole as binding the whole. I'm confused here. What is outside of the grain of sand that is binding the sand?
It would seem that the bind to me is the internal limitation of the sand's matter. — Philosophim

First, you need a space as large as the size of the sand to embed the sand within. Now, the question of what is outside of the space is valid.

But let me explore your other line of thinking and be charitable where possible. Lets say that the grain of sand is actually bound by 'nothing'. You then note that this binding plus the original whole creates a secondary whole. This doesn't quite work in your variable setup, as W1 and W2 are clearly different concepts here. While a whole indicates 'totality', these are obviously different totalities. So how do I see fixing this?

Perhaps what would make more sense is that some 'thing' is bounded and has limitations where there is 'nothing'. 'Nothing' may bind 'something', but 'nothing' has no limits. Is that more along the line of what you were thinking of? — Philosophim

Nothing cannot have any geometry or occupy any room so nothing cannot bind the space that the sand is within.

I'm still having trouble understanding what you mean by the whole. Is it a philosophy term? As the whole is the sum of its parts, the whole universe in the physical sense, mathematics or what I thought at first, a concept of the whole being something limitless or infinite.

I can make some progress on your argument but then the conversation goes in another direction such as the physical universe which was never stated.

I'm thinking if it's the physical universe we can't impose our own mathematical model on it without knowing what it is. — Mark Nyquist

By whole I mean whatever that physically exist.

Seems to me you have reinvented the universal set. As such what you have shown is that there is nothing outside of W, not that W is limitless. — Banno

But W could not be limited as I argued.

Where did you show that a closed universe requires extrinsic curvature? — Lionino

Here. Moreover, considering that you return to the point you started (if you move on a straight line closed manifold) requires extrinsic curvature. How could you return to the point you started if the global geometry of space was flat? You get a square if you cut a balloon and put it on a flat surface. You reach a dead end if you move in a straight line on the square. So a square is not a proper representation of a sphere.

Whether something is closed refers to intrinsic curvature. — Lionino

Actually, after some thought, I realized that even intrinsic curvature also requires a higher dimension. How the lines could deviate towards or away from each other if the geometry of space is flat. This figure is very illustrative:

https://en.wikipedia.org/wiki/File:Cassini-science-br.jpg

It is a physically-unfounded belief about the empirical world arrived at using a priori syllogisms in a natural language. — Lionino

It is physically necessary if it is logically necessary. Moreover, we don't know what is the right curvature of spacetime. Spacetime could simply be limitless if its geometry is flat globally.

The closedness of spacetime does not require extrinsic curvature. — Lionino

It requires as I illustrated.

If anything, your argument would require infinite dimensions, as each time you evaluate the extrinsic curvature of a dimension another one would be in order. — Lionino

Not all hyperspaces that I am talking about are necessarily closed so we could deal with finite hyperspace dimensions which accommodate everything. You are however right that we need infinite dimensions if all hyperspaces are closed. I don't see any problem with hyperspace which has infinite dimensions though.

What you are saying makes sense, however:
No, general relativity is based on something called "intrinsic curvature", which is related to how much parallel lines deviate towards or away from each other. It doesn't require embedding space-time in a higher dimensional structure to work.
— Does space curvature automatically imply extra dimensions? — Lionino

Here I am not talking about intrinsic curvature in spacetime that is caused by a massive object locally but extrinsic curvature which tells us what is the global geometry of space.

I don't know what hyperspace is, neither how closedness of the universe implies one. — Lionino

By hyperspace I mean a space of more than three dimensions. Why does the closedness of the space imply a hyperspace? Because any closed manifold has a local curvature. To help the imagination think of a closed 2D space, a sphere for example, instead of a 3D one. Each point on this sphere has a curvature at any given point which means that the surface of the sphere bends at each location on the sphere. The fact that the sphere bends at each location on its surface requires a higher dimension space, in this case minimally 3D space, where the sphere is embedded within otherwise the sphere cannot bend at each location on its surface and we cannot have a curvature.

What if space is closed? As in, a loop where going in a certain direction for enough time sends you back to where you started. The world would then not be limitless, but still unbounded.

A mind-boggling property of this universe is that it is finite, yet it has no bounds.
— https://www.astronomy.com/science/what-shape-is-the-universe/ — Lionino

I think if space is closed then it is embedded in a hyperspace.

Oh, I didn't know about him and his argument. I am glad you mentioned it.

Ok, I found the thread. I am however confused with what you are trying to say. I will read it more and post my opinion in the thread if I understand something.