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.

This doesn't follow, unless by "limited" you mean just that: being limited by something else. — SophistiCat

By limited I mean restricted in size. Think of spacetime for example. If spacetime is restricted in size then we can reach its edges by moving in straight lines (of course if spacetime is not a closed manifold). The problem is what is beyond the edges. It cannot be nothing since nothing does not have any geometry and occupies no room. So, whatever is the beyond edges of spacetime is something. Therefore, what I said follows.

The problem I'm seeing with your approach is that you don't identify the whole as a concept. Its origin is a mental abstraction. — Mark Nyquist

By the whole, I mean whatever that exists, spacetime, material, etc.

Limits are mental definitions. — Mark Nyquist

No, it can be physical as well.

If you apply limits to infinity you no longer have infinity. — Mark Nyquist

Correct. But what is the implication of this to my argument?

I covered this in my Universal Form post not long ago if you want to understand why I object to your method. — Mark Nyquist

Could I have a link to your post?

If the whole is limitless it has no bounds. Then you introduce bounds and impose limits. What?
Maybe I can get it on a second try but why?

Nope, not getting it. W1 is no longer the whole you started with. — Mark Nyquist

What I am trying to show is that there are two cases where what you consider as the whole is either limited or limitless. If $W_1$ is limitless we reach our goal otherwise $W_1$ is limited and it is bounded by something else, let's call it $B_1$. Etc.

No, we are dealing with an infinite regress in cases where we have to posit an infinite number of past causes for something. E.g., X began because of Y and Y began because of Z and Z began because of... etc. The statement that "X exists without begining or end," does not require an infinite regress because X never begins to exist. There is nothing to regress to. — Count Timothy von Icarus

I should have said that we are dealing with an infinite regress in time if something exists eternally ("in time" was missing). By infinite regress in time I mean for any chosen time, t, there exists another time, t', where t' is before t.

This is precisely why Aristotle decides that the world must be eternal, and why so many cosmologists, even those embracing versions of the "Big Bang," theory nonetheless claim that elements of the universe must be eternal. — Count Timothy von Icarus

To the best of my knowledge, there are two arguments against the eternal universe: (1) Infinite regress in time and (2) Heat death which is the unavoidable ultimate fate of the universe if the universe is old enough.

You might attack to coherence of something existing "without begining or end," but it doesn't require a regress of explanations.

For example, you might consider the following proposition: Given we accept Euclid's axioms, it follows that all triangles will have angles that sum to two right angles (180 degrees).

Did this fact have a begining in time? Did it start to exist when Euclid developed his postulates? Or did it not exist until he had completed a proof for this proposition for each type of triangle? If the latter, and Euclid completed the proof of right triangles first, is it a true statement that at that time "given Euclid's axioms, it is the case that right triangles, but not other triangles have angles that sum to two right angles."?

Or, prior to Euclid, when earlier mathematicians empirically observed this fact about triangles, did the fact begin to exist then, even though Euclid's axioms has never been written down?

The problem here is that it seems like it will always be true that, given Euclid's axioms, this fact holds. It never begins to be true and under no conditions does it seem to become false.

Maybe we might think Euclid's axioms are rubbish, but it won't change the status of facts of the sort of "If A and I → B," where A is a set of axioms and I are inference rules, and B is a conclusion that follows from A and I.

Things like "if A = B and B = C, then A = C," do not seem to require any sort of infinite causal regress. Being logical truths, they do not require an infinite series of deductions either. Circularity is not infinite regress, we are not always going back to new reasons, but looping. — Count Timothy von Icarus

To me, the truth is objective, by objective I mean it does not depend on the mind so mathematical theorems are valid even if there is no man who could deduce or know them.

What's the alternative? An infinite past? That has its own problems. If the past is infinite then as of now an infinite period of time has completed, which seems nonsensical. — Michael

Correct. The infinite past makes no sense.

So I think that the past must be finite. — Michael

Correct.

I'm unsure if that entails that something came from nothing or if something "already" existed when time started – but then how did time start? — Michael

Spacetime simply has existed since its beginning. Spacetime could not begin to exist. That is true since otherwise we are dealing with nothing to spacetime. Nothing to spacetime is a change. Spacetime is needed for any change. Therefore, spacetime is needed for nothing to spacetime. This leads to an infinite regress.

You need the beginning of spacetime for the Big Bang to happen, I think.

You think there was spacetime before the Big Bang? — Quk

The beginning of spacetime lay either before or at the Big Bang. The material either popped into existence after or at the beginning of time or it was caused or simply existed.

Either there was never a time when there was nothing, or there was nothing and something came into existence uncaused. — Patterner

Nothing to something is impossible. This is discussed here. There are two arguments for this one from Bob Ross and another from myself.

Bob Ross's argument:

P1: If an entity is the pure negation of all possible existence, then it cannot be subjected to temporality.
P2: ‘Nothing’ is the pure negation of all possible existence.
C1: Therefore, ‘nothing’ cannot be subjected to temporality.

P3: Change requires temporality.
P4: ‘Nothing’ cannot be subjected to temporality.
C2: Therefore, ‘nothing’ cannot be subjected to change.

P5: ‘Nothing’ becoming ‘something’ requires change.
P6: ‘Nothing’ cannot be subjected to change.
C3: Therefore, ‘nothing’ cannot be subjected to becoming (something).

My argument:

P1) Time is needed for change
P2) Nothing to something needs a change in nothing
P3) There is no time in nothing
C1) Therefore, change in nothing is not possible (From P1 and P3)
C2) Therefore, nothing to something is not possible (from P2 and C1)

Time is treated differently in these arguments, in my argument time is a substance whereas in Bob Ross's argument is not.

Neither seems possible, but at least one is the case. — Patterner

There is another case in which spacetime exists and then either things pop into existence or thing is caused by an agent, the so-called God.

I think this topic has nothing to do with logic but with causality. To think that every event has to have a cause is just a human intuition, in my opinion, or, according to Kant, a category "a priori". Space and time are another "a priori" category. Our senses cannot detect space and time, nor causality. Our senses can just detect things. Space and time, and causality are not things. — Quk

Causality is not a thing. Whether spacetime is a thing or not is still subject to debate. You might like to read this article.

They are the prerequisite in our own transcendental mind that makes the detection of things possible for us. Just because this is the case here and now, doesn't mean that causality is everywhere all the time. Aside from that, there are acausal events in quantum physics. — Quk

I think you are talking about virtual particles. Virtual particles however pop into existence from the quantum vacuum. Quantum vacuum is different from nothing.

Also, assuming the big bang theory is correct, the bang occured without a cause as there wasn't even a time period before it. — Quk

You need spacetime for the Big Bang to happen.

Agreed, nothing cannot create anything. Nothing is nothing. It is not a 'thing'. There is a question of whether something can be uncaused, a topic I cover here if you're interested. https://thephilosophyforum.com/discussion/12098/a-first-cause-is-logically-necessary/p1 — Philosophim

Oh, thanks for the reference to your thread. I will read it shortly.

Hmm, interesting hypothesis.

However, I do believe something can come from nothing in quantum physics (believe it is called the Schwinger effect, but I'm no physicist). That would mean there is a possibility of creation out of nothing. I can't logically explain why, but in rare cases something just is, without a cause (or maybe without a cause yet or without a cause knowable by us). — Double H

I think you are talking about virtual particles that pop into existence from the quantum vacuum. The quantum vacuum refers to space that is devoid of matter whereas nothing is a condition that there is no thing, no spacetime, no material,...

We have had a great many threads on this topic. In general, I think your line of reasoning works. However, proponents of uncaused existence generally argue that they do not need to claim that something ever "came from nothing." Rather, they must simply posit that something began to exist, or if positing eternal entities, that "something exists (without beginning or end)." — Count Timothy von Icarus

We are dealing with an infinite regress if something exists eternally. Infinite regress is not acceptable. Therefore something cannot exist eternally.

Beginning to exist, uncaused, does not imply "coming" from nothing. It implies that something began to exist, and that prior to its existence it did not exist. — Count Timothy von Icarus

Well, this statement is valid if spacetime exists.

Yes, you were misunderstanding. Your conception of spacetime is metaphysical, but what I was trying to explain is it is more than metaphysical -- in fact, we should start with Einstein's spacetime continuum, which consists of the three dimensions of space and the fourth dimension which is time. He posits that spacetime can shift shape.

So with that under consideration, space and time are, in fact, a physical reality. My starting point that human cognition is temporal (as well as spatial) is well within the dimensions of spacetime. — L'éléphant

It can be shown that we are living in a block universe once we accept the special relativity. You might be interested to read this.

Naturally. If your definition of nothing includes that it has no property, there are only two scenarios, it either stays as nothing (no change), or acquires a property (change), becoming something (creation ex nihilo). The first possibility is analytic because it purely follows from your definition. — Lionino

Nothing stays as nothing. But we need to show this. Bob Ross elegantly put this in an argument:

P1: If an entity is the pure negation of all possible existence, then it cannot be subjected to temporality.
P2: ‘Nothing’ is the pure negation of all possible existence.
C1: Therefore, ‘nothing’ cannot be subjected to temporality.

P3: Change requires temporality.
P4: ‘Nothing’ cannot be subjected to temporality.
C2: Therefore, ‘nothing’ cannot be subjected to change.

P5: ‘Nothing’ becoming ‘something’ requires change.
P6: ‘Nothing’ cannot be subjected to change.
C3: Therefore, ‘nothing’ cannot be subjected to becoming (something).

Now your argument is morphing from "nothing to something is impossible" to "spacetime cannot begin to exist", which would be an argument for eternalism of spacetime. — Lionino

Spacetime has a beginning for two reasons, the current state of the universe is not heat death and infinite regress in spacetime is not acceptable. Spacetime however as you said cannot begin to exist.

P1 was just my best guess at what you were trying to convey in the OP—but it may not be. The reasoning behind P1 would be that something that is the pure negation of all possible existence would be, as per its nature, NOT something that exists and time only affects things that exist; therefore, if there is nothing, which is the negation of all possible things (hence the ‘no’ + ‘thing’), then there isn’t anything to be subjected to time. — Bob Ross

I see what you mean and I agree with you. Time simply relates different states of affairs temporarily when there is something. I think the rest of your argument follows then.

Oh, well, then, your argument would need to clarify your metaphysical position on time and space; which sounds a bit like you believe (1) time and space are substances (which I deny), that (2) they are united (which I deny), and that (3) nothing be subject to space-time (which I agree with if I grant the previous two).

The problem, though, is that this doesn’t negate the possibility of things that ‘pop into’ existence with no reason behind it. This just implies that there isn’t anything a part of nothing. — Bob Ross

Well, that is the subject of debate to the best of my understanding. So let's put it aside for now as your argument follows so we don't need my old argument.

That is fair. I would say, more generally, that there’s nothing incoherent with positing the actual temporal sequences of things as simply the form or mode by which one experiences and thusly they are not substances in reality. — Bob Ross

I see.

Then I don’t see how your argument holds: a change from nothing but not a change in nothing does not violate that “there is no spacetime in nothing” because the change is ‘outside of’, or ‘beyond’, the nothing—it is in something that the change occurs: there exists something in which there is no X, and then X poofs into existence out of thin air. — Bob Ross

Correct. I agree with you.

Yeah, it’s a real pickle. Honestly, I lean back and forth between block universe and transcendental idealism style nihilism on time and space; and both are subjected to your worry here.

If we are representing reality to ourselves via our representative faculties, then doesn’t that imply a temporal process? I would say no, and this leads me to a much stronger agnosticism on the ontology of reality than I would suspect you are willing to accept.

Take traditional transcendental idealism (i.e., Kantianism): if space and time are purely the modes by which we intuit and cognize objects, then it necessarily follows that however we are representing, truly as it is in-itself, objects to ourselves is completely unknown to us other than indirectly via our [human] understanding of that process (which is inevitably in the form of space and time). — Bob Ross

I see. Thanks for the elaboration.

Just for background on this topic:

Mathematical theories are supported by mathematical proofs.

Physical theories are support by the preponderance of the physical evidence and are subject to revision.

I'm just pointing out a tricky situation you need to think about. The known end point is that physical matter does exist (now). So does some start point of nothing existing have any basis in physical evidence?

As I said, as mathematical objects something does not equal nothing. — Mark Nyquist

As I discussed this before considering that something exists right now implements that the initial condition cannot be nothing. One however needs to prove change in nothing is not possible as I did. We also can conclude that nothing to something is not possible as well once we conclude that change in nothing is not possible.