I understand that the volume of existing reality—that is, the relations between celestial bodies, etc.—is indeed increasing.
But the concept of growth or expansion logically (or at least a priori) compels the existence of a substrate relative to which this process takes place.

Of course one can do a thought experiment and try to deny the existence of that “empty” substrate within which space (and time?) supposedly expands, but if you negate that substrate you paradoxically come back to assuming that it “exists” (as a possibility without which the expansion could not even get started).

Do you see a way out of this thought experiment?

I can only repeat what I wrote. I see no necessity for this at all (that there is some substrate, empty or otherwise, at whose expense space expands).

Okay. I can’t understand your reasoning for the claim, but I’m not interested in continuing this discussion.
I have a related question: would you agree that Newton’s bucket argument, insofar as it is meant to prove the existence of absolute space (separate from man and his knowledge), is also aimed at proving the existence of that same “empty” substrate that existed “before” the Big Bang (according to his view)?

How does Newton relate to the Big Bang? I don’t see any connection to the question of a substrate.

Newton assumes that space is an entity separate from man and therefore absolute, and he uses the bucket argument to demonstrate this (and ties it to his discussion of motion). His position is opposed to that of Leibniz, for example (with whom he argued over this question), because he rejects the assumption that space is an “abstraction” from the relations among the objects located in space.
So far it seems to me that you understand and agree.

From this it seems to me that Newton opens the door to the idea that space was never “created,” and therefore it cannot expand. In other words, his argument implies that space is a necessary and permanent substrate (“an eternal substrate”).
Admittedly, Newton could insist and argue (according to his religious belief) that God created everything ex nihilo, meaning that He also “created” space. It seems to me that this insistence—if indeed it would come from him—is arbitrary.

That is how I understand the bucket argument and its connection to my question.

The dispute between Newton and Leibniz about the bucket argument deals with the question whether there is absolute space in the sense of empty space (devoid of objects), and whether motion—linear or rotational—can be defined in empty space. It has nothing to do with the question of the Big Bang and the expansion of space. Whether space expands into a substrate or without a substrate, one can still ask whether it is absolute or not (in the bucket sense).

I don’t understand. After all, space also moves. At least in the sense that its edges keep moving farther away from the point of departure at the beginning of the process (the start of the Bang).
And in any case I can’t understand what motion is that does not require a spatial substrate standing in relation to it.
As I understand it, the bucket argument tries to prove exactly this: not only that space is absolute, but also that it is a necessary substrate relative to which alone the concept of motion can be conceived.
Can you give me an example of the motion of an object that does not require a spatial substrate?

The universe is everything.
This universe has volume, and the volume increases.
What exactly happens in practice? That’s not clear. It’s not clear what space itself is made of.
For example, if space is a lattice structure with a fixed distance between points, then one can imagine more and more points being added to the lattice throughout all of space, and that is how its volume grows.

I can’t give an example, and that’s exactly why it’s hard to imagine. You have to think about it non-visually. You’re talking about the expansion of everything, and every example I give could be the expansion of something. The closest is inflating a balloon, if we look only at the surface (and not the volume). The parts added to the area of the surface do not come out of some two-dimensional edges. But I don’t see the point of dealing with an example, because one can quibble over it. Think conceptually (not visually) and you’ll see there is no problem at all.

Maybe it would help to think about the formation and development of a language. The addition of words does not come at the expense of something. And again, there’s no point quibbling over the example.

Doron,

You should first learn what a metric is. It’s very hard to imagine the concept of expansion without knowing what a metric is. Really the example of the surface of a balloon is the best one, but it’s not all that successful because the balloons you know live within a three-dimensional world and expand within it (though conceptually it can also expand without such a world).

Precisely because no example can be given, I conclude from this the special and necessary status of space—that is, that it cannot expand. In fact, the claim that it can expand seems meaningless to me. The concept of expansion compels a substrate in the background, and in the end this substrate must itself be space (and that is how a regress of space within space within space is generated…).
Nor does an appeal to a metric seem relevant to my question. A metric does not deal with an a priori metaphysical conception like the one in my question.

The proper Hebrew term to describe what happens with the universe is “inflate.”
The universe inflates.

Inflation, unlike expansion (and even enlargement), does not include something external outside the inflating object.

I’m not a professional physicist, but it seems to me that the claim is a bit different. The claim about the expansion of the universe should be understood in light of Einstein’s special relativity. According to this theory, the presence of mass curves space and as a result causes light rays to move in a curved rather than straight way. Think of it as a small pit created by something with mass. Every such factor creates a pit in which the waves cannot move straight but must move according to the shape of the pit.

When we say that the universe is expanding, what we are really saying is that the initial point of mass that created a shell of space around itself, within which light could move in a limited way, gradually expanded and began to move in a way that enlarged the universe—that is, the region of space within which the light waves moved. That is the meaning of the expansion of the universe. Different mass factors moved away from one another in a way that enlarged the space within which light rays move, and thus the universe expanded. What lies beyond the boundaries of the space in which light rays move? We have no idea. Our information is based on light rays, and light rays too are limited by the space of mass. It may be that if there were something with mass beyond the region of mass, space would expand to include it and then light rays would provide us with information about it. But for now it seems that mass is limited to our universe.

So what is the space within which the universe expanded? I don’t know, and apparently we have no way of knowing. But when people say that the universe expands, they mean the expansion of the space within which light rays move.

Decisor,
The concept of “inflation” is logically bound up with the relation of the inflating object to some substrate relative to which it inflates. In the final analysis, that substrate is infinite space. Otherwise the concept has no meaning at all. If you think otherwise, I challenge you to give me an example of something inflating without “something external.”

Y.D.,
First of all, it seems to me that you are mistaken on the factual level about the role of special relativity. Special relativity does not deal with the question raised here concerning the structure of space, its existence, or gravity’s effect on it, but rather with ways of measuring velocities, distances, and intervals of time. Let physicists come and correct me if I’m mistaken.

As to the substance of the matter, my claim about the concept of space is not about whether something about it can or cannot be known. I am making a more radical claim: there is no meaning to the assumption that space was “created,” and therefore there is no meaning at all to the claim that it expands. The fact that the balloon analogy does not work, in my opinion, is not because analogies are by nature partial and problematic. That is almost always true. The reason it doesn’t work is that, in my opinion, this analogy proves the opposite of what the person proposing it intends to say.
Therefore your appeal to the information brought to us by light rays also does not seem relevant to me. This is not a matter of data that one day we might perhaps obtain, and then be able to reform our opinion on the matter.

The concept of inflation describes something happening to an object, without reference to the thing at whose expense it inflates, and therefore it is the closest to what happens with the universe.
But clearly, in all the examples we know from within the universe, inflation in practice does come at the expense of some other space.

This conceptual problem will not be solved through words, but through understanding that the examples you know from within the universe will not help you understand the subject.

The change has to be a change in thought, not a verbal change.

Doron,
I think your question is not about expansion but about the meaning of finite space.
Expansion assumes some kind of finitude, but finitude does not necessarily assume expansion.
If in your view one can understand what a limited, finite, bounded space is even without expansion, then the concept of expansion is self-evident: now the distance measured within the boundaries is greater. Until now we could fit four one-meter sticks between the boundaries, and now we can fit five one-meter sticks there. But you are saying that non-infinite space must be situated within an infinite space, because one cannot define a boundary without referring to what is outside it. Agreed?

Witztum, a very nice point.

Decisor,
You are pointing to the built-in limitation of language in describing the concepts we are discussing, and in that you are right.
But if we have already chosen to express ourselves, and we believe that our words nevertheless carry some weight, it still does not follow that all claims are equivalent.
Your original claim was that the more precise verbal description is inflation. Now you are changing your position. Apparently you too think, like me, that there is nevertheless value in more precise verbal claims.

Witztum,
I didn’t understand most of what you said, except for the last sentence, which sums up my position well. Indeed, I claim that the concept of finite space—which it seems to me we all believe in—conceptually implies the existence of infinite space. Such a space cannot come into being “out of nothing” or pass away.
If I am right, that sheds light in this way also on scientific theories such as general relativity and the Big Bang theory.

Doron,

Remarkably, it was דווקא the first part of Witztum’s comment that you didn’t understand—the part that shows how the concept of expansion does not require space to be situated within some other space—and the second part (which you say is what you were saying), that you do understand. So you basically understand yourself… but in the end you are still wrong. This is a philosophical discussion, but the fact is that relativity works and explains reality, and it does not require a more external space in which space-time resides. So maybe there is a larger external space, or maybe there isn’t, but there is no need for it in order to explain our reality. And in such a case we say, paraphrasing Laplace: “External space? I have no need of that hypothesis…” (he was talking about God in physics). That is, the monastic approach of minimizing unnecessary assumptions has proved to be the more fruitful approach in physics.

In any case, it really is strange and hard to get used to such a thought, but apparently it is true. What happened here is that an auxiliary concept (space), which helped us describe motion (change of place) of physical entities (matter), that is, the changes in reality, became a reality (physical) in itself. A kind of mathematical object that became physical. (There are more examples of this in physics—the vector potential of the magnetic field; the Aharonov-Bohm experiment.) Of course, naturally, as a physical object one immediately asks where it lives—that is, one asks for a new space in which it will reside (and in which it will move). But there isn’t one. It itself is what it is (it resides within itself). By the way, this also causes physical phenomena that seem to us to contradict the laws of nature. For example, the speed of expansion of this space in certain places in the universe (in galaxies sufficiently far from us, according to Hubble’s law) is greater than the speed of light. In fact, nothing else in nature (including light and other various force fields) can move faster than the speed of light. According to your method, space too could not move faster than the speed of light within the larger space (although this is not entirely necessary).

By the way, time has a similar problem. People speak of motion in space-time—a four-dimensional space, time being one of its axes. And motion in time requires a new time (here one cannot evade it; people use a concept called proper time, but it is not really “time” as we think of it), and this too causes a conceptual problem. And in general one can ask about the Big Bang that occurred 14 billion years ago (in which our time too was “created”): what was before? And the answer is that before it there was nothing (because before it there was no time either). The word “was” does not apply before the Big Bang. That is, the question cannot even be asked in the first place (it’s not only that there is no answer to it; it is not defined at all).

I haven’t changed my position.
The word inflation is more suitable for describing what happens. Imagine you are inside a balloon that is inflating. All you see is that the balloon’s volume is growing. That is the meaning of inflating. When that happens you do not need to think about “where the balloon is inflating to,” but about the fact that its volume grows over time.

The concept of expansion is not suitable for such a situation. It includes in the concept that there are certain regions into which it expanded—that is, previously it was not there and now it is. And that does not fit what happens with the universe.

What happens with the universe is that its volume grows. Space itself inflates.

Immanuel,
With all due respect, your argument is confused.
At the beginning you note that I myself distinguish between the scientific claim about space and the philosophical claim about it, and that I am referring only to the latter.
But then, when you are called upon to tell me where I erred on the philosophical level, you suddenly slip back to an argument in the name of science—a pragmatic argument according to which relativity “works” and we “have no need” for that assumption (that space is infinite and does not expand). What relevance is it that it works? Quantum mechanics also works (big time), and we still argue about its philosophical meanings.
In any case, insofar as we discuss the topic from a philosophical angle, we absolutely do need the assumption of the existence of such a substrate.

And again: if you want to expose my mistake/fallacy, you have to show why it is not plausible conceptually in principle—in other words, philosophically.

Doron,

That is exactly the point. Philosophically, nothing can be decided, because nothing stands to experiment. Science is “philosophy that has reached maturity.” Other than self-contradiction (or absurdities—something that directly contradicts our experience, though then it is also a kind of science), you won’t find any mistake in any philosophical claim. And my argument is not pragmatic; it is entirely theoretical. I am talking about fruitfulness. Fruitfulness is an indication of truth. That is exactly the mistake in the “God of the gaps” approach, for example. It was not fruitful, unlike the other approach (that is, closing the gaps by means of further scientific research, and if necessary finding new science in order to explain the gaps).

Just to sharpen the point: the fruitfulness I am talking about is theoretical and explanatory fruitfulness, not technology. That is, the ability, by means of a certain claim, to explain additional phenomena that until now had no explanation (or that we had not even imagined ought to have one)—that is what I mean by what I call the fruitfulness of a claim.

Fine, I’ll say a few marginal things and one more important one. What you are presenting here is scientism, which in my view is naive and confused: a paradoxical philosophical position that comes to undermine all philosophy as such in the name of science. It is a self-defeating position.

Your odd determination that philosophical questions cannot be decided (except for certain reservations you set) is also factually mistaken. The history of ideas in general, and of philosophical ideas in particular, is full of decisions regarding countless questions, theoretical and practical. The decisions are not always justified, but factually there is no principled problem in “deciding” in a reasoned and systematic way.

As for fruitfulness, I do not understand how a sharp distinction between philosophical discussion and scientific discussion (as I make) could suppress fruitfulness in either of these fields. If you bring an example, maybe there will be something to discuss.

But all that is marginal to the main point of our discussion.
The main point is that even you yourself admit, despite your scientism, that philosophy has value in the realm of identifying contradictions or absurdities. It seems to me that this is exactly what I tried to do here with regard to the concept of space and its accepted interpretation in Big Bang theory. It is not clear to me why you “allow” this discussion in principle, but in practice refrain from addressing the concrete claims that appear in it.

Decisor,
I think you’re playing with words. In the balloon example, you insist on claiming that one need not think “where” the balloon is inflating to, but only observe it from within, subject to what I actually see. And so too with your claim about space.
Witztum already wrote here (and Hegel said it before him) that once you have the concept of a boundary, you have already crossed it in your thought. The example of the balloon’s shell is, in the end, an ostrich maneuver—as if, if I do not relate to something, it does not exist. But even that does not work. Even the ostrich burying its head in the sand does so in the context of an external reality that it assumes and that it wants to “erase.”

First of all, I suggest that you stop using words like “odd,” “naive,” “confused,” “scientism,” “paradoxical,” “self-defeating.” Those are a lot of empty words that I’m used to seeing in use among fake and empty intellectuals—words that cover up a lack of content. I don’t believe in scientism, or in nonsense-ism, or in any other -ism. Those labels are meaningless.

I am also not conceding anything. From the outset, my whole discussion is philosophical. I don’t think there are no decisions in philosophy, because there really are decisions, only they are made on the basis of observation that is every bit as scientific—observation of the subject being discussed. And that is what I am talking about when I speak of absurdities, for example (which are not paradoxes—contradictions—but situations that common sense—the observation of the mind’s eye—rejects). When I speak about the lack of decisions in philosophy, I mean either metaphysical disputes that lack information (airy disputes), or cases where it is clear that the disputing sides (or at least one of them) lack information, or situations in which all sides of the argument have been exhausted and from then on people remain in their positions forever. In such a case there really will be no decision because information is lacking. And in the end I claim that science is part of philosophy itself—only it is philosophy that works. I don’t understand what is unclear. In my opinion, this approach of space within additional space is barren. That is my basic feeling. If you show interesting implications for it, then it won’t be. There’s nothing more to argue here. You think there’s something here—go with your strength and save the scientific world. Show that there is something here and we’ll continue talking.

Fine, as for your linguistic suggestions (as well as your earlier suggestion that I train myself in “metrics”), I’ll consider them and get back to you. If that’s acceptable to you.

As stated, I think your position is inconsistent, and I brought relevant arguments for that from the relevant field (not from the “sciences”).

In general, I think my claim about space is true, and I’m not interested in whether it has practical implications or not.

That said, I definitely agree with you that a large volume of the history of ideas is hot air.

As for my ability to save the scientific world… well, I do not wish that world any salvation from people like me.

No—that is exactly the point. Something barren means that it is not correct. Like the God of the gaps. There is no proof that it is not correct (that God is responsible for the explanatory gap). The God of the gaps is an approach that has never been refuted. But it was barren. By contrast, the alternative approach—for every gap in science there is an explanation from within science (and not outside it, like God)—proved fruitful. I don’t have an example offhand right now, but there are many. Go ask. (Even Newton sinned in this. Here is an example: how the universe does not collapse into itself because of gravity. He claimed among other things that God holds the stars so that they will not draw near one another. The second approach, by contrast, gave us Hubble’s law and the concepts of cosmological inflation and dark energy.)

Doron,

By the way, not every space can be embedded in a larger space of the kind you know. For example, our space-time (what is called a space of type SO(3,1)) cannot be embedded in any larger space of the kind we know (the n-dimensional Euclidean space R^n). That is a mathematical fact. And that thing is the real physical space in which we live, and it is the one that inflates (not only space inflates; time does too).

Doron,
The problem begins long before your question, and it does not concern words at all.

In your question you assume that you understand what the universe is, what space and time are in essence, and then you ask your question about its expansion.

The truth is that we do not understand at all what the universe is, or what the essence of the fabric of space is.

So after you understand what space is, try asking questions about it. Until then, just as you do not understand the essence of space and yet live with it in peace, do the same with regard to the fact of its inflation.

From the outset it is clear that the concept of a finite universe but without boundaries cannot be illustrated. Illustrations always have boundaries.

Decisor,
I understand.
All of us, including you, make claims (in actual words!) about “expansion” and “inflation” and the differences between them, etc. … but now the great truth has been revealed: all of that is for nothing, because in fact we understand nothing about anything, and our words have no meaning at all.

Are you convinced?

Forget the words. Focus on understanding. The very concept of space is not understood. I wrote this in the first comment.
“What exactly happens in practice? That’s not clear. It’s not clear what space itself is made of.”

Immanuel,
As stated, in my opinion the pragmatist stance you advocate (“the main thing is fruitfulness,” “what works as a criterion for truth,” etc.) is inconsistent, and in practice you smuggle in through the back door theoretical and even metaphysical assumptions. You do so despite yourself. Pragmatism itself, as a philosophical position (and not, heaven forbid, a “scientific” one), rests on a foundational assumption that is not at all pragmatic, even if it also includes pragmatic considerations.

Second, in my opinion you have not succeeded in showing that fruitfulness is necessarily a recipe for the petrification of science (though in practice that definitely has happened and does happen).

Third, you opened here a new and interesting topic concerning the implications of mathematics for the picture of reality. I don’t know whether you were trying to bring proof from mathematics that there is an “other” space that cannot be embedded in infinite space. In any case, I wonder (I don’t fully understand this) how mathematical truths can be translated into philosophical and metaphysical language at all. Since mathematics is to a large extent convention-dependent (and I say this as a Platonist), naturally not every statement in it has a counterpart in the real world. It seems to me that here the test is first of all philosophical (that is, logical): if there is a logical flaw in the translation, then apparently the claim that reality can be derived from mathematics is not correct.

There is no pragmatic stance here at all. Or if you like, it is philosophical pragmatism. But all this is nonsense. There is no need to prove anything here, and there is no back door here. This is how one thinks. Someone who doesn’t understand this on his own doesn’t know what thinking is. If a person is treading water and getting nowhere, he is supposed to understand that he is on the wrong path, that he is not thinking correctly. There is no theoretical assumption here. It is an assumption that is part of our thinking. I didn’t try at all to show anything, and there is no need to prove it either. Someone who doesn’t understand it on his own is simply not sufficiently experienced in independent thought. This is metaphysics that is part of the paradigm of natural philosophers (part of the conceptual infrastructure of scientific thought). It is metaphysics to the same degree that physics itself (the assumption that there is order in the universe) is itself metaphysics. Understanding this is part of philosophical maturity (that is, not something that can be proven. When you grow up, you’ll understand).

Okay, I see we’ve moved to the declaration stage. I’m also happy to discover that you, unlike me, have moved on to the stage of “independent thought.” If only your shining light would illuminate me as well.

With God’s help, speedily in our days. But really, it’s a matter of maturity. It’s not that something is wrong with you (other than that you’re stubborn and think you’ve discovered America. The intuition that when space curves—or expands—there must be a larger space into which it curves was before the eyes of all geometers beginning with Riemann. But it turned out mathematically that from the moment people began speaking in terms of a metric and intrinsic curvature, there was no need for such a space. And that was long before relativity). Keep thinking for yourself and reflect on my words. It’s not a problem not to be mature. And besides—maybe socially what I’m saying is not accepted—that’s also fine; there doesn’t have to be equality between the two of us. That’s no sin on either side.

And the matter of fruitfulness is indeed not trivial. In history there were many times when people faced holes and tried various methods, and there were many philosophical disputes, and it took time before progress was made (the God of the gaps was also one of these; I already mentioned Newton). And it happened only from the moment they tried to be productive—to ask about the implications of the different views. There is the famous story about the dispute around the EPR paradox in quantum mechanics (regarding the interpretation of quantum mechanics), which people said resembled Christian debates over how many angels can sit on the head of a pin. And the discussion was stuck until a physicist named John Bell came and showed a physical practical difference (Bell’s inequality), which indeed was tested experimentally several years later.

Be well.