Be careful with Wolfram, I think he is a bit of a crank. At best, he is the proverbial man with a hammer who sees nails everywhere.

I would rather recommend John Norton articles, such as What Can We Learn about the Ontology of Space and Time from the Theory of Relativity?

We observe change and we attempt to model that change. Then you can model that change however you like, — leo

You can't exactly model it "however you like", as some models work better than others. It is difficult, for example, to understand why interference patterns develop on the screen in the double-slit experiment if you model everything as particles.

I appreciate what you are saying though, and I am familiar with this sort of thinking. But it seems to me that at some point, if a model works well enough, it is sensible to just accept that that's how things are.

Consider that in the end, everything we understand about the world amounts to models. The idea of a round Earth, for example, is just a model, and is subject to your criticism every bit as much as the idea of bending spacetime. Is there actually a round Earth out there in the objective world? Going along your lines, all we can say is that this model has a lot of explanatory power, but in the end, it's just a model. It allows us to make successful predictions about what we'll see next when we fly in an airplane or launch a rocket, but this never demonstrates that the Earth is actually round. There could conceivably be a another model that explains all that we observe equally well, one that paints quite a different picture of what's out there. A round earth could be like epicycles. There might even be a simpler but much different model, one that we just haven't thought of yet.

You get my point. Strictly speaking, round earth is just a model, but I think we can all agree that the model works so incredibly well and is so parsimonious and elegant an explanation for what we observe that it is probably how things actually are. Earth probably is actually round (well, not exactly spherical). Consilience might be the best indicator here that we are on the right track. Many independent lines of evidence lead us to the idea of roundness.

Your objection is something we ought to keep in mind much more when we are dealing with the barely known, like the very, very small, the very, very large, the deepest fundamentals of nature, and so on. This is so especially when consilience is low.

I hear you. Your criticism of Wolfram might be valid, and I am not devoted to any of his ideas. That article I linked to, however, is rather interesting! But I am partial to modeling space as a network, so I like his thinking there. I'll take a look at your Norton article.

If you want to know how space bends, drive down the street in a Mercedes and turn the corner. Space curves the same way as a Mercedes Benz.

You can't exactly model it "however you like", as some models work better than others. It is difficult, for example, to understand why interference patterns develop on the screen in the double-slit experiment if you model everything as particles. — petrichor

Well you can, it's just some models are simpler than others. But "simpler" is subjective, and it doesn't mean "closer to truth". The double-slit experiment can be understood in terms of particles, for instance with the pilot wave theory in which particles are guided by a wave. Yes there is a "wave", but a wave can be seen as made of a lot of smaller particles, so that experiment and others can be explained purely in terms of particles. I was working on something like that, I will publish it some day when I get the time to finish it, the upside is that you can explain experiments much more intuitively than the usual interpretations of quantum mechanics, you don't have to talk of a thing going through both slits at the same time or not having a definite location or trajectory and all that quantum weirdness. To me, more intuitive is "simpler", while for some other people neat and elegant mathematical equations are "simpler" even if they imply a completely non-intuitive picture of the universe. In the end what matters is whether the model works.

Is there actually a round Earth out there in the objective world? Going along your lines, all we can say is that this model has a lot of explanatory power, but in the end, it's just a model. It allows us to make successful predictions about what we'll see next when we fly in an airplane or launch a rocket, but this never demonstrates that the Earth is actually round. There could conceivably be a another model that explains all that we observe equally well, one that paints quite a different picture of what's out there. A round earth could be like epicycles. There might even be a simpler but much different model, one that we just haven't thought of yet. — petrichor

Yes precisely, this is actually an example I mention every now and then, it's possible to come up with non-round Earth models that work just as well and allow to fly an airplane or launch a rocket successfully because they make the same observable predictions. For instance these models would predict that the Earth would appear round from space (same observable prediction) but they would treat it as an optical illusion (one doesn't have to assume that light travels in straight lines in space, it's not something that can be proven without making other unprovable assumptions).

Strictly speaking, round earth is just a model, but I think we can all agree that the model works so incredibly well and is so parsimonious and elegant an explanation for what we observe that it is probably how things actually are. — petrichor

I agree that it is the simplest we have, but I wouldn't go as far as to say that it implies it is "probably how things actually are". Could be that "how things really are" is something that would appear very complicated to us, or could be that there is no such thing as "how things really are" independently of us.

Your objection is something we ought to keep in mind much more when we are dealing with the barely known, like the very, very small, the very, very large, the deepest fundamentals of nature, and so on. — petrichor

I think we ought to always keep it in mind, for instance I see people getting attacked harshly for believing that the Earth is flat or that the Sun revolves around the Earth, well their beliefs aren't proven false, they can be made compatible with observations, yet these people are treated as heretics by the scientific establishment.

I don't mind that most people use some model, but they ought not to treat it as truth and dismiss other models that can explain the same observations differently. And in the case of the model of space curving and expanding, I actually think that focusing on this model alone while dismissing alternatives has prevented a lot of progress, as it created numerous misconceptions and put physics on a path of ever-increasing complexity privileging mathematical elegance at the cost of intuitiveness. I strongly believe there is a lot to gain by allowing alternative models to flourish, instead of presenting one model as "truth" or as "closest approximation to truth" and having everyone work on it or believe in it.

Physics has become more focused on the realm of theoretical entities than on actual observations. Again look at the example of space curving and expanding, instead of seeing it as a tool of thought people have come to see it as an actual thing that was observed or detected in experiments, and then through that reification they reach conclusions that contradict what the theory actually says. That hinders progress in many ways.

I find that attempting to understand a theory to understand how the universe works is doing it backwards. The theory didn't come out of thin air, it stemmed from observations and experiments, and it makes assumptions that aren't necessarily true. There is more to understand in learning how the theory was developed than in learning the theory itself. Then when you do that you realize that things could have been done differently, different paths could have been explored and weren't, while the succeeding generations only learnt the theory and built on top of it. In my view physics and science in general would be more effective if scientific education was more focused on learning about observations and experiments that were made, and how theories were developed to account for them, rather than on learning the theories and how to apply them. And then physicists would be more open to alternative models and not so dogmatic about the one that they use.

You can have contact action without assuming space to be a concrete substance. As an analogy, if I throw a ball at you and it hits you there is no spooky action-at-a-distance, the contact action occurs when the ball hits you. In the case of gravity we can assume there are things traveling between bodies attracting one another, which have an influence when they reach the bodies. — leo

The problem is not so simple though. One object hitting another is nothing but a transferal of force or energy from on solid body to another. But when we look at what constitutes a solid body, it is tiny parts, with space between them. So we need to account for how the tiny parts of one body interact with the tiny parts of another body, as if the two bodies are each a coherent, massive whole, instead of the tiny parts simply interacting with each other, as independent bodies.

Now, since the space occupied by a massive whole is mainly empty space, with tiny parts precisely positioned to make a whole massive body, all that "empty space" must be modeled as part of the body. This is why the centre of gravity (or, centre of mass) is an important concept in physics, it allows that numerous particles with various spatial relations, can be treated as one cohesive body. However, this way of modelling things necessarily reifies the space within that body, as part of the body. and clouds the issue of how the parts of the body interact with the parts of another body, in the transferal of force. The concept of placing the force at a point has literally been abused by physicists to produce nonsensical things like point particles.

But it is wrong to say that just because we can model what we do observe as perturbations of an underlying space, then that implies that space really is a substance curving or expanding or stretching, it's a theoretical model out of many possible, it's not something we actually observe or detect, and it's not the only way to explain what we do observe. — leo

I believe that this is an incorrect assumption, and that there is really no way to adequately or accurately model motions and interactions of bodies without representing "space" as a real underlying substance. As described above, there is no way to even account for the existence of a body without representing its internal "space", as part of the body, and therefore substantial.

One object hitting another is nothing but a transferal of force or energy from on solid body to another. But when we look at what constitutes a solid body, it is tiny parts, with space between them. So we need to account for how the tiny parts of one body interact with the tiny parts of another body, as if the two bodies are each a coherent, massive whole, instead of the tiny parts simply interacting with each other, as independent bodies.

Now, since the space occupied by a massive whole is mainly empty space, with tiny parts precisely positioned to make a whole massive body, all that "empty space" must be modeled as part of the body. This is why the centre of gravity (or, centre of mass) is an important concept in physics, it allows that numerous particles with various spatial relations, can be treated as one cohesive body. However, this way of modelling things necessarily reifies the space within that body, as part of the body. and clouds the issue of how the parts of the body interact with the parts of another body, in the transferal of force.

there is really no way to adequately or accurately model motions and interactions of bodies without representing "space" as a real underlying substance. As described above, there is no way to even account for the existence of a body without representing its internal "space", as part of the body, and therefore substantial. — Metaphysician Undercover

You can also talk of the center of gravity of two distinct bodies such as binary stars, and treat them as one cohesive body, but it's not necessary, you can simply model the motion of each star individually without referring to a center of gravity, which is a tool of thought and not a tangible thing. So I don't agree that talking about the center of gravity of a body implies that space is a tangible substance that can curve or expand, in principle we could also model each part of the body individually and never talk of a center of gravity.

If we define space as the unoccupied volume between tangible objects, then when the shape of that volume changes it's simply that the tangible objects are moving, we don't need to say that the volume is made of an underlying substance that is changing shape and dragging the objects with it.

You can also talk of the center of gravity of two distinct bodies such as binary stars, and treat them as one cohesive body, but it's not necessary, you can simply model the motion of each star individually without referring to a center of gravity, which is a tool of thought and not a tangible thing. So I don't agree that talking about the center of gravity of a body implies that space is a tangible substance that can curve or expand, in principle we could also model each part of the body individually and never talk of a center of gravity. — leo

As I explained, a body is full of empty space, and that empty space is treated as part of the body, and therefore substantial. You might model the motion of a body without referring to its centre of gravity, but it is implicit within the way that the multitude of parts which compose "the body", is treated as one whole.

If we define space as the unoccupied volume between tangible objects, then when the shape of that volume changes it's simply that the tangible objects are moving, we don't need to say that the volume is made of an underlying substance that is changing shape and dragging the objects with it. — leo

This is not an acceptable definition for physicists though, because physics deals with objects which are very tiny and therefore not tangible. A tangible object is made up of parts which are not tangible. And even if you define "tangible" in such a way that all these tiny parts are said to be tangible, there is the issue of having to deal with the "space" within a large tangible object. The "space" within an object allows its parts to be moving.

The "space" within tangible objects is outside your proposed definition of "space". If we say that when we are talking about its constituent parts, the "space" within the whole is "space", and when we are talking about the object as a whole, it is not "space", then the same area is treated in one context as "space", and in another context not as space, and this is contradictory. So we cannot define "space" in that way without the consequence of contradiction. .

As I explained, a body is full of empty space, and that empty space is treated as part of the body, and therefore substantial. You might model the motion of a body without referring to its centre of gravity, but it is implicit within the way that the multitude of parts which compose "the body", is treated as one whole. — Metaphysician Undercover

And as I explained, that's the same as saying that a binary star is full of empty space, rather than simply saying that it is two stars orbiting one another. Just because we call two stars orbiting one another a "binary star" and can treat it as one whole, does not suddenly imply that space is a substance that can curve or expand and that it refers to anything more than the unoccupied volume between things.

How do you get from "space refers to the unoccupied volume between things" to "space is a substance that can curve and expand"?

The "space" within tangible objects is outside your proposed definition of "space". If we say that when we are talking about its constituent parts, the "space" within the whole is "space", and when we are talking about the object as a whole, it is not "space", then the same area is treated in one context as "space", and in another context not as space, and this is contradictory. — Metaphysician Undercover

Well on the one hand we have the space that we do see, the unoccupied volume between tangible objects, that's where our very notion of space comes from. And on the other hand at some point we come to model tangible objects as having mostly unoccupied volume within them, but that space we do not see. Let's call the first one space1 and the second one space2 if you like.

So what I was doing, is that I used the notion of space1 to explain that when the shape of space1 changes, it's merely that the tangible objects (which define the very shape of space1) are moving, so we don't need to say that space1 is a substance that curves or expands and that is responsible for making the objects move. When we talk of space1 curving or expanding, we're not doing anything more than describing the motions of the tangible objects, there is no need to reify space1 as a substance.

Then usually the notions of space1 and space2 are conflated, that is usually we imagine that the tiny invisible particles that make up a tangible object are real things and not just theoretical entities, so in that context we can apply the same reasoning as in the paragraph above to say that the space between these particles refers merely to the unoccupied volume between them, that it is not a substance that has any causal influence on the motions of these particles.

If you want you can define space in general as the unoccupied volume between things, whether these things are tangible objects or theoretical entities imagined to be real objects.

All it boils down to really is that the space between tangible objects and the space that is imagined to be within tangible objects does not need to be reified as a substance that has any causal influence on the objects. The shape of that space changes because the objects are moving, not the other way around. If we want to say that the objects are moving because space is changing shape, then we would have to show that space is a tangible thing that is dragging or pushing or pulling the objects, but we don't observe that.

And as I explained, that's the same as saying that a binary star is full of empty space, rather than simply saying that it is two stars orbiting one another. Just because we call two stars orbiting one another a "binary star" and can treat it as one whole, does not suddenly imply that space is a substance that can curve or expand and that it refers to anything more than the unoccupied volume between things. — leo

That analogy doesn't provide a solution to the problem. The problem is that not only is there space between objects, but objects also occupy space. You might say that the only real objects are point particles, which occupy no space, but then you rob objects of their reality, only to hand it to space.

Well on the one hand we have the space that we do see, the unoccupied volume between tangible objects, that's where our very notion of space comes from. — leo

I think you have this wrong, not only do we not "see" space (it is conceptual), our notion of space comes from measuring objects, and this means it is derived from the "space" occupied by things, not the space between things. Consider the development of ancient geometry, the right angle was developed for the purpose of measuring land for example, and the principles of a "circle" are the principles of a thing.

But history has shown that when we apply these principles produced for the purpose of measuring things, to measuring the "space" between things, there is a problem. That problem is that things are moving in relation to each other. This adds another "dimension" to the problem of "space", because "space" is now not the static area occupied by a thing, it is the changing distance between things.

The issue, as I pointed out earlier is that the "space" occupied by a thing is fundamentally different from the "space" between things. The two concepts of "space" are incompatible because the space occupied by a thing is static and the space between things is changing. When we move to allow that the thing is changing, and therefore the space occupied is not static, we describe the changing thing, as parts moving relative to each other. But then we're not talking about the original "thing" anymore, as the parts are now things in themselves, the subjects of discussion.

So I'd reverse your order of space 1 and 2

So what I was doing, is that I used the notion of space1 to explain that when the shape of space1 changes, it's merely that the tangible objects (which define the very shape of space1) are moving, so we don't need to say that space1 is a substance that curves or expands and that is responsible for making the objects move. When we talk of space1 curving or expanding, we're not doing anything more than describing the motions of the tangible objects, there is no need to reify space1 as a substance. — leo

You can't do this with "space 1" though. In space 1, space is the thing measured, so if the distance between objects changes, then the measurement changes, therefore space, as the thing measured, changes.

Then usually the notions of space1 and space2 are conflated, that is usually we imagine that the tiny invisible particles that make up a tangible object are real things and not just theoretical entities, so in that context we can apply the same reasoning as in the paragraph above to say that the space between these particles refers merely to the unoccupied volume between them, that it is not a substance that has any causal influence on the motions of these particles. — leo

So this is false too. You are actually removing "substance" from the things, making them point particles, and making space, as the thing measured, into the substance. Since space is the thing measured, you cannot interpret this model as saying that space is not substance.

We're talking past each other here. Sure if you want let's say that there is space between objects and that objects occupy space. You agree that this space is conceptual, that it comes from measurements, either measurements between objects or measurements of objects themselves.

So what does it mean to say that space "bends", or "curves", or "expands"? It simply means our measurements are changing, that is the distance between objects changes, or the shape of the objects change. It decidedly does not mean that space is not merely a concept but a tangible substance that physically bends or curves or expands and is responsible for the changing distance between objects. An object is a tangible thing, a measuring device is a tangible thing, space is not, you said it yourself it's a concept, you can't take a spoon of space, you can't boil space or cut it in half, you can't throw space, you can't lick space, ...

So, when people say that planets revolve around the Sun because they follow straight lines in a curved space, that's wrong, the curved space is not the cause, it is a model, a representation, we don't detect a space substance that is physically curved, and we are not forced to invoke a curving space to model the motions we observe. To say that curved space is a cause of the motions we observe is to give an illusion of explanation and to reify space as a tangible thing.

We're talking past each other here. Sure if you want let's say that there is space between objects and that objects occupy space. You agree that this space is conceptual, that it comes from measurements, either measurements between objects or measurements of objects themselves. — leo

We're talking past each other because you are not listening to what I am saying. The point I was making, is that the space which is between objects (which is how you define "space"), is apprehended, or conceived of as being substantial. When you measure, there is necessarily something which is being measured. When you measure the distance between objects that something is space.

So what does it mean to say that space "bends", or "curves", or "expands"? It simply means our measurements are changing, that is the distance between objects changes, or the shape of the objects change. It decidedly does not mean that space is not merely a concept but a tangible substance that physically bends or curves or expands and is responsible for the changing distance between objects. An object is a tangible thing, a measuring device is a tangible thing, space is not, you said it yourself it's a concept, you can't take a spoon of space, you can't boil space or cut it in half, you can't throw space, you can't lick space, ... — leo

So this is wrong, when we say that space bends, curves, or expands, we are saying that space is substantial, and these are the properties that it has. Yes, "space" is a concept, but within that concept, as necessarily implied, or dictated by the concept, is that space is something real, substantial. This can be readily understood through what I said above. When we measure, there must be something which is measured or else the measurement is meaningless. It is invalid as an actual measurement if there is nothing substantial which is being measued. So when we measure the distance between objects, we presuppose the substantial existence of "space", as the thing being measured.

Objects move and change, because time is passing. In our attempts to understand and conceptualize these changes we've come to the conclusion that space curves, bends, and expands. This is what happens to space, as time passes, and this new, more comprehensive way of understanding space has left the ancient concept, of a static space, as inadequate for the progression, and evolution of knowledge. But it is implied within this new concept of space, that space is real, substantial, as the thing with these properties.

So, when people say that planets revolve around the Sun because they follow straight lines in a curved space, that's wrong, the curved space is not the cause, it is a model, a representation, we don't detect a space substance that is physically curved, and we are not forced to invoke a curving space to model the motions we observe. To say that curved space is a cause of the motions we observe is to give an illusion of explanation and to reify space as a tangible thing. — leo

Everything that we say about things is a model, or representation, that's just a fact of how we speak. But that doesn't mean that we are not speaking about, referring to, what we believe are real, substantial things. One might say "the sky is blue", and that's a model or representation, but 'the sky" is referred to as a real thing. You might say, that "the sky" is not a real thing, by your ontological principles, but in that model, the sky is a real thing, the thing referred to as being blue. It would require that you produce another model, one which doesn't hold 'the sky" as the real thing being referred to, in order to support your ontological principles. But it's inconsistent, and contradictory to use the model, and also claim that the sky is not a real thing.

Likewise, you use a model which represents "space" as a real, substantial thing, the thing that exists between objects, which is measured when we measure distances, but you claim to hold as an ontological principle that space is not real or substantial. Well, to support your ontology, you need a model of "space" which does not represent space as something real, substantial. What is it that exists between objects, that is being measured when we measure distance, an aether o something? In other words, you might insist that we ought not reify space, but this is irrelevant to the fact that the model you use actually does reify space.

This question doesn't make sense to me.

If space can bend, what is the space that it is bending in? If there is no space outside of it, then there is no framework for bending to occur in.

Gaussian curvature
Curved Space

We're talking past each other because you are not listening to what I am saying. — Metaphysician Undercover

I hear what you’re saying, but I disagree, which is another instance of us talking past each other, and you’ll probably disagree with me disagreeing, which will be yet another instance, and so on.

When you measure the distance between objects that something is space.

So when we measure the distance between objects, we presuppose the substantial existence of "space", as the thing being measured. — Metaphysician Undercover

I disagree, when you put a ruler between two objects you’re not measuring space, you could simply say “this object that I call a ruler visually fits between these two objects”, no need to invoke a separate substance that is supposedly measured.

Objects move and change, because time is passing. — Metaphysician Undercover

Now you’re refying time. It’s the other way around, we observe change, and then we come up with the concept of time. There is no entity called “time” that we have identified that is responsible for the change we observe. We simply relate change to some reference change that we call a clock. We don’t observe “time passing”, we observe objects that we call clocks change.

In our attempts to understand and conceptualize these changes we've come to the conclusion that space curves, bends, and expands. — Metaphysician Undercover

That’s wrong, considering there is no need to talk of space curving or bending or expanding to describe precisely how planets and galaxies and light move. The same observations can be modeled as precisely in a space that curves and in a Euclidean space that doesn’t. Observations don’t lead us to the conclusion that space curves.

Your point of view implies among other things that if two objects get closer to each other it’s because space is shrinking between them. I disagree.

One might say "the sky is blue", and that's a model or representation, but 'the sky" is referred to as a real thing. You might say, that "the sky" is not a real thing, by your ontological principles, but in that model, the sky is a real thing, the thing referred to as being blue. — Metaphysician Undercover

You can define the sky as the area above the Earth as seen from the Earth. You do see blue when you look up. In what instances do you see space curving or bending or expanding?

I hear what you’re saying, but I disagree, which is another instance of us talking past each other, and you’ll probably disagree with me disagreeing, which will be yet another instance, and so on. — leo

I've provided arguments for my position, based on the definition of "space" which you gave, evidence that I'm not "talking past" you. If anyone is talking past the other, it is you, asserting that "space" as it is commonly understood, is not something substantial, in complete ignorance of what the models, and your definition of "space" indicate.

I disagree, when you put a ruler between two objects you’re not measuring space, you could simply say “this object that I call a ruler visually fits between these two objects”, no need to invoke a separate substance that is supposedly measured. — leo

Placing object Y between object X and Z, is not a case of making a measurement. This is a diversion, a ruse, or distraction created by you, in an effort to avoid the point of my argument. For me to construe this as a measurement, you'd need to produce a scale by which the degree of "fits" is being judged.

To measure is to determine the quantity, extent, or size of something. To measure the distance between two objects, which is a common practise, requires that the quantity, extent, or size of something is being determined. That something is space. To place a ruler between objects X and Z, and say that the ruler fits between objects X and Z, is not a case of measurement unless the quantity, extent, or size of something is being determined. If the ruler placed between X and Z is being used to measure, it is being used to determine the quantity, extent, or size of something. If it is not determining the extent of the space between the two, then what is it determining the size of?

Now you’re refying time. It’s the other way around, we observe change, and then we come up with the concept of time. There is no entity called “time” that we have identified that is responsible for the change we observe. We simply relate change to some reference change that we call a clock. We don’t observe “time passing”, we observe objects that we call clocks change. — leo

Of course time is reified. Time is understood as a dimension of space, and space is necessarily reified according to the concepts we use to measure it, as explained above. Therefore time is necessarily reified as well. But it's not me who is reifying these, they are already reified by the concepts we use to understand time and space. I am just explaining this fact to you. This is a fact which you are having a hard time apprehending because you seem to hold as an ontological principle, that space and time are not substantial. And, despite me demonstrating that this ontological principle is not supported by the concepts of "space" and "time" in common usage, you have provided no support for your personal ontological principle.

Your point of view implies among other things that if two objects get closer to each other it’s because space is shrinking between them. I disagree. — leo

OK, that's fine, you disagree. I already know that, because that's what you keep asserting. Now support your principles, justify your disagreement. Suppose we measure the distance between X and Z at one time, and we measure the distance between X and Z at a later time, and find that the distance is less. If this is not a case of the space between them shrinking, what is it? Don't say that it is a case of the objects moving relative to each other, because that is exactly what movement is, a change in the space between objects. I want you to justify your belief by explaining how objects could move without there being a real substantial space which changes when objects move.

I've provided arguments for my position, based on the definition of "space" which you gave, evidence that I'm not "talking past" you. If anyone is talking past the other, it is you, asserting that "space" as it is commonly understood, is not something substantial, in complete ignorance of what the models, and your definition of "space" indicate. — Metaphysician Undercover

Space can be defined in various ways, let's go with your definition (state it precisely so we can be on the same page).

Strictly speaking I wouldn't say there is space between objects and that objects occupy space, when I do that it's a figure of speech, just like I would say there is love between two people, I don't literally mean that somewhere between these people there is some entity or substance called love that I have observed.

We're also talking past each other because we don't seem to give the same meaning to the word "substance", by substance I mean some sort of liquid or solid or gas, something detectable in some way, space is none of that, to me space isn't a substance just like an idea isn't a substance. You seem to consider that anything that can be thought is substantial, that's not how I'm using the word substance here.

Placing object Y between object X and Z, is not a case of making a measurement. — Metaphysician Undercover

Plenty of measurements precisely involve placing an object between or along other objects.

This is a diversion, a ruse, or distraction created by you, in an effort to avoid the point of my argument. — Metaphysician Undercover

No, that's you believing I'm creating a diversion/ruse/distraction and attempting to avoid the point of your argument, whereas I disagree with your argument and I'm trying to make you see why while you don't see. Misinterpreting and misrepresenting my intentions and thoughts leads to talking past each other.

To place a ruler between objects X and Z, and say that the ruler fits between objects X and Z, is not a case of measurement unless the quantity, extent, or size of something is being determined. — Metaphysician Undercover

Measurements boil down to comparisons. At some point you're judging whether something fits, you're making a comparison when you make a measurement, you can't escape that.

When you place a ruler along two objects, you're judging how the objects fit next to the ruler, you aren't forced to invoke an underlying space that you are supposedly measuring.

Of course time is reified. Time is understood as a dimension of space, — Metaphysician Undercover

No, you and some other people reify time, and you and some other people "understand" time as a dimension of space. Time doesn't have to be reified, and time doesn't have to be treated as a dimension of space. You can do that if you like (as long as you understand it's a model, otherwise you're committing a logical fallacy), but stop pretending it's a necessity.

and space is necessarily reified according to the concepts we use to measure it, as explained above. Therefore time is necessarily reified as well. But it's not me who is reifying these, they are already reified by the concepts we use to understand time and space. — Metaphysician Undercover

And I explained why I disagree.

you seem to hold as an ontological principle, that space and time are not substantial. And, despite me demonstrating that this ontological principle is not supported by the concepts of "space" and "time" in common usage — Metaphysician Undercover

Are you saying that space and time are substantial because in common usage they are treated as substantial? So if something in common usage is treated as substantial then it becomes substantial? If in common usage pink elephants on the moon are treated as substantial then there are pink elephants on the moon? Either you're committing the very fallacy of reification, or you're playing with semantics.

Whereas you know why I don't treat space and time as substantial? Because I don't see space nor time, I see objects, rulers, clocks. The concepts of space and time stem from observations of these substantial things, not the other way around, and that you don't seem to get despite me explaining it to you again and again.

Suppose we measure the distance between X and Z at one time, and we measure the distance between X and Z at a later time, and find that the distance is less. If this is not a case of the space between them shrinking, what is it? Don't say that it is a case of the objects moving relative to each other, because that is exactly what movement is, a change in the space between objects. — Metaphysician Undercover

If I'm looking at two objects moving towards each other that's what I see, two objects moving towards each other, I can imagine putting a ruler next to them and reading a decreasing measurement, but I don't see any substance between the objects that shrinks.

Would you say that they move towards each other because space is shrinking between them? That would be again the fallacy of reification.

If I wasn't looking at them moving and I only saw them at rest and I made two measurements and the second one was less, I would say that the objects have got closer to one another, I wouldn't say that some space substance has physically shrunk between them.

If you like you can say that the distance between them has decreased, or you can even say that the space between them has decreased, as long as you understand space to be a concept, an idea, a tool of thought, and not a physical thing like the objects, not a substance. Just like a distance isn't a substance, it's a concept, a tool of thought.


Also, realize that if you consider that when objects move relative to each other it's because space is shrinking or expanding between them, then in your view objects never move relative to space, they are always at rest in space, and that's surely not the concept of "space" in common usage, it's your idiosyncratic one.

Space can be defined in various ways, let's go with your definition (state it precisely so we can be on the same page). — leo

There is no single acceptable definition of "space". We discussed this already, there are two distinct conceptions of space. One is derived from our measurements of objects, and this produces the "space" which is occupied by an object, and the other is derived from the measurements of distance between objects, and this produces the "space" between objects. As I explained, these two conceptions of "space" are incompatible, because the former sees space as static, and the latter sees space as active.

We're also talking past each other because we don't seem to give the same meaning to the word "substance", by substance I mean some sort of liquid or solid or gas, something detectable in some way, space is none of that, to me space isn't a substance just like an idea isn't a substance. You seem to consider that anything that can be thought is substantial, that's not how I'm using the word substance here. — leo

You misunderstand the meaning of "substance" if you believe that substance must be sensible. What is sensible is the form of a thing, it's shape, colour, etc. We do not sense a thing's material substratum, what makes it a real thing, its substance. "Substance" is a concept introduced by Aristotle to validate our assumptions that the material world must be real. So it is not something whose existence we detect, we conclude through logic, that there must be "substance", or else the sensible world would be an illusion. So things which we assume to have real material existence, we say have substance.

Plenty of measurements precisely involve placing an object between or along other objects. — leo

Yes, that's true many measurements involve placing one object beside another, but there is more to a measurement than just that. And that's not relevant, what is at question here, is the fact that if a measurement is made, there is necessarily something which is measured. Why do you resist the idea that when we measure the distance between two objects, what is being measured is the space between them? This is not speaking metaphorically, because the thing being measured (space in this case) must have substantial existence or else the measurement is invalid, it's just an illusion. Therefore "space" must have real substantial existence to validate measurements of distance.

When you place a ruler along two objects, you're judging how the objects fit next to the ruler, you aren't forced to invoke an underlying space that you are supposedly measuring. — leo

What are you talking about here, measuring objects, or measuring the distance between objects? If you are measuring the objects, there is no need to assume an underlying space, the substance measured is the object itself. But if you are measuring the distance between them, you are not measuring the objects, and therefore you must assume "space" as the thing which you are measuring. Otherwise you are not measuring anything, and your measurement is not a valid measurement because there is nothing which has been measured.

No, you and some other people reify time, and you and some other people "understand" time as a dimension of space. Time doesn't have to be reified, and time doesn't have to be treated as a dimension of space. You can do that if you like (as long as you understand it's a model, otherwise you're committing a logical fallacy), but stop pretending it's a necessity. — leo

You don't seem to understand, a model must model something, or else it's not a model, just like a measurement must measure something or else it's not a measurement. Therefore it really is a necessity that the thing modelled must be real, substantial, or else the model is invalid, meaningless nonsense, because you have a model which doesn't model anything real.

Are you saying that space and time are substantial because in common usage they are treated as substantial? So if something in common usage is treated as substantial then it becomes substantial? If in common usage pink elephants on the moon are treated as substantial then there are pink elephants on the moon? Either you're committing the very fallacy of reification, or you're playing with semantics. — leo

But pink elephants on the moon are not treated as substantial, so you have no point here. Again, you don't seem to understand. The things which are treated as substantial are the things which are believed to be substantial. What other possibility is there? If time and space are treated by us as having substantial existence, then they are believed by us to have substantial existence. What more is there that I am missing? What you are missing is that it is contradictory to treat space and time as having substantial existence (as you do), yet claim to believe that they do not have substantial existence (as you do).

Whereas you know why I don't treat space and time as substantial? Because I don't see space nor time, I see objects, rulers, clocks. The concepts of space and time stem from observations of these substantial things, not the other way around, and that you don't seem to get despite me explaining it to you again and again. — leo

But you do treat space as substantial, you defined it as "the unoccupied volume between tangible objects", and spoke about measuring that volume. It just appears now, that you have a misunderstanding of what "substance" means, such that you believed that substance was necessarily something you could see. I hope you now realize that this is incorrect, we see colours, and different shapes, but we don't see substance.

Would you say that they move towards each other because space is shrinking between them? That would be again the fallacy of reification. — leo

This is false. As I explained, under your conception of "space", space is necessarily something real, substantial, so there is no fallacy of reification here. The space between the two object is shrinking, or else your measurements are invalid because they are not measuring anything.

If I wasn't looking at them moving and I only saw them at rest and I made two measurements and the second one was less, I would say that the objects have got closer to one another, I wouldn't say that some space substance has physically shrunk between them.

If you like you can say that the distance between them has decreased, or you can even say that the space between them has decreased, as long as you understand space to be a concept, an idea, a tool of thought, and not a physical thing like the objects, not a substance. Just like a distance isn't a substance, it's a concept, a tool of thought. — leo

It's fine and acceptable to talk about them being closer to each other, but then you do not mention "space". As soon as you mention "the space between them", you have referred to a real substantial thing which lies between them. What sense does it make to talk about "the space between them" unless you are actually referring to the space between them?

Also, realize that if you consider that when objects move relative to each other it's because space is shrinking or expanding between them, then in your view objects never move relative to space, they are always at rest in space, and that's surely not the concept of "space" in common usage, it's your idiosyncratic one. — leo

I don't think that anyone conceives of motions as objects moving relative to space, so I think it's you who has a rather idiosyncratic concept of "space".

there are two distinct conceptions of space. One is derived from our measurements of objects, and this produces the "space" which is occupied by an object, and the other is derived from the measurements of distance between objects, and this produces the "space" between objects. As I explained, these two conceptions of "space" are incompatible, because the former sees space as static, and the latter sees space as active. — Metaphysician Undercover

I don't know why you make a distinction there. In both cases measurements are involved, in both cases the measurements can change (the shape of an object can change, so can the distance between objects).

There are other conceptions of space. The one customarily used in physics is something like:

a boundless three-dimensional extent in which objects and events occur and have relative position and direction (Merriam-Webster dictionary)
the dimensions of height, depth, and width within which all things exist and move (Oxford dictionary)

Notice how these definitions do not refer specifically to measurements of objects or measurements between objects, they refer to a thing within which objects exist and move.

I don't think that anyone conceives of motions as objects moving relative to space — Metaphysician Undercover

As above, in physics the very customary thing to do is to conceive of motions as objects moving in space. In classical physics you have objects moving within Euclidean space. In general relativity you have objects moving within curved space.

For instance in classical physics, when two objects move towards each other they move in space, space doesn't shrink between them. Sure the distance between them decreases, the unoccupied volume between them shrinks, but the reference background relative to which objects are tracked, space, doesn't shrink.

Now of course that reference background is not something we observe or detect, it is a reference frame that is defined from things we do observe, which is why I say that this background is not something tangible, is not a material substance, it's a concept, a tool of thought, and to treat it as tangible like an object is the fallacy of reification.

You misunderstand the meaning of "substance" if you believe that substance must be sensible. What is sensible is the form of a thing, it's shape, colour, etc. We do not sense a thing's material substratum, what makes it a real thing, its substance. "Substance" is a concept introduced by Aristotle to validate our assumptions that the material world must be real. So it is not something whose existence we detect, we conclude through logic, that there must be "substance", or else the sensible world would be an illusion. So things which we assume to have real material existence, we say have substance. — Metaphysician Undercover

I do not misunderstand the meaning of "substance", rather I use a definition of "substance" different from yours, your definition is not the only one that exists, and it isn't the most widespread either.

The definition I use would be something like a material with particular physical characteristics (Cambridge dictionary), whereas your definition seems to be something like the essential nature underlying phenomena (Oxford dictionary). So obviously if we're not using the same definition we talk past each other when we talk about substance.


Now that you know in what sense I use the words "space" and "substance", and so as to not get too carried away, the whole point of the discussion is what does it mean to say that space curves? Plenty of people say that gravity is the curvature of space, that planets orbit the Sun because space is curved around the Sun and because they follow straight lines in curved space, people are made to believe that we have found the cause of gravity, that this cause is that space is curved, as if space was a tangible thing, a tangible material, a tangible substance that we have detected to curve, and as I keep saying this is false, we have detected no such thing, the curvature of space is an abstraction, a concept, a tool of thought, not something that is physically detected in any way, and to treat that abstraction as a material thing is the fallacy of reification.

People are made to believe that we can't model gravity precisely without invoking a curved space, as a supposed proof that space really is a tangible material that really does curve even though we don't directly observe it, this is false, we can model observations as precisely without invoking a curved space.


And when I say that space is not a tangible material that curves or expands like a sheet curves or a balloon expands, I'm not saying that we don't perceive objects that are visually separated. And when I say that time is not a tangible material that passes or flows like a train passes or water flows, I'm not saying that we don't perceive change.

I don't know why you make a distinction there. In both cases measurements are involved, in both cases the measurements can change (the shape of an object can change, so can the distance between objects). — leo

Do you not see a difference between measuring an object, and measuring the distance between two objects? In the first case, you would be dealing with the properties of one individual object, and in the second case you would be dealing with a relation between two objects.

There are other conceptions of space. The one customarily used in physics is something like:

a boundless three-dimensional extent in which objects and events occur and have relative position and direction (Merriam-Webster dictionary)
the dimensions of height, depth, and width within which all things exist and move (Oxford dictionary)

Notice how these definitions do not refer specifically to measurements of objects or measurements between objects, they refer to a thing within which objects exist and move. — leo

If space is "a thing within which objects exist and move", how can it not be a substance? You are saying that it is a thing, like a medium, within which objects exist, like they exist in water, or air. How could there be a thing, with objects existing within it, and this thing does not have substantial existence?

For instance in classical physics, when two objects move towards each other they move in space, space doesn't shrink between them. Sure the distance between them decreases, the unoccupied volume between them shrinks, but the reference background relative to which objects are tracked, space, doesn't shrink. — leo

OK, so there is a thing, with objects moving within it, just like objects move in water or air, but this thing is called "space". How can the objects move within this "space" without changing this thing? If an object moved, wouldn't some of the space be displaced, and therefore itself be moved? If the objects moved closer to each other, than the amount of space between them would necessarily shrink, as some would have to move aside, or else it might compress.

Now of course that reference background is not something we observe or detect, it is a reference frame that is defined from things we do observe, which is why I say that this background is not something tangible, is not a material substance, it's a concept, a tool of thought, and to treat it as tangible like an object is the fallacy of reification. — leo

Now you are contradicting what you said above. You said that space is a thing within which objects exist. How could this thing (space) be just a concept, or tool of thought? Either there is a thing (space), within which objects exist, or space is just a concept, a tool of thought. But it doesn't make sense to say that the thing within which objects exist, and move around, is a concept. Which do you believe? Is space a medium which has objects within it, as you say is the customary definition in physics, or is space just a concept or tool of thought, as it is in you ontology?

This is the problem I told you about already. Our definitions, concepts and models, treat space as a real, substantial thing, a medium within which objects exist,. Also, you use and refer to those concepts in your argumentation. Yet you assert an ontological principle which contradicts this, that space is only conceptual. Do you not realize that the definitions you cite do not support, and are actually opposed to the principle you assert?

The definition I use would be something like a material with particular physical characteristics (Cambridge dictionary), whereas your definition seems to be something like the essential nature underlying phenomena (Oxford dictionary). So obviously if we're not using the same definition we talk past each other when we talk about substance. — leo

OK, since we have different ideas of what substance means, lets leave that word. Let's just focus on your definition of "space" as a thing within which objects exist, and we'll forget about whether this thing is properly called a substance or not. Clearly you must see that this thing is not merely conceptual. How could objects exist within it if it were only conceptual?

Now that you know in what sense I use the words "space" and "substance", and so as to not get too carried away, the whole point of the discussion is what does it mean to say that space curves? Plenty of people say that gravity is the curvature of space, that planets orbit the Sun because space is curved around the Sun and because they follow straight lines in curved space, people are made to believe that we have found the cause of gravity, that this cause is that space is curved, as if space was a tangible thing, a tangible material, a tangible substance that we have detected to curve, and as I keep saying this is false, we have detected no such thing, the curvature of space is an abstraction, a concept, a tool of thought, not something that is physically detected in any way, and to treat that abstraction as a material thing is the fallacy of reification. — leo

OK, now according to your definition, space is a thing, like a medium, within which objects exist and move. Would you agree that there is a property of this medium (space) which causes things to move in a curved trajectory when we would otherwise think that these things ought to travel in a straight line, and that this is why some people talk about a curved space? If it is not a property of this thing, called space, then what could it possibly be that causes this? It cannot be that the concept of space, or that the tool of thought causes this curved motion, because the concept is simply supposed to represent, model, or demonstrate an understanding of this curvature.

People are made to believe that we can't model gravity precisely without invoking a curved space, as a supposed proof that space really is a tangible material that really does curve even though we don't directly observe it, this is false, we can model observations as precisely without invoking a curved space. — leo

OK, let's suppose that this is true, space can be modeled with or without the curvature, and each model is as accurate, and reliable as the other. What does this indicate other than the fact that we really don't know what space is?

I've thought about the subject for a long time, I believe there are things you could learn from me on that subject, I might learn some things from you too, but then I'm more interested in a discussion where the other side is also willing to learn rather than a debate where you're only trying to prove me wrong. I'm not saying I never make mistakes, but up to now all my supposed contradictions that you have highlighted stem from you misunderstanding the context in which I said these things and from misinterpreting the words I use, so it's a bit tiresome to keep having to justify myself against someone who doesn't really seem interested in what I have to say.

Do you not see a difference between measuring an object, and measuring the distance between two objects? — Metaphysician Undercover

I meant why the distinction between static space and active space, since the shape of an object is not necessarily static.

You are saying that it is a thing, like a medium, within which objects exist, like they exist in water, or air. — Metaphysician Undercover

No I'm not saying that, I said that the definitions refer to it like a thing, some sort of container in which objects move. In physics space used to be thought as a medium (the luminiferous aether), then failures to detect it experimentally led to abandon the idea of it as a medium (as Einstein did with special relativity in which there is no more reference to an absolute space but instead to relative reference frames), and then Einstein reintroduced it as some sort of a medium in general relativity since in it space has properties such as curvature. But even though in his theory space has properties, Einstein was well aware that space is a "tool of thought" (that's his own words), in no way did he pretend that his theory somehow proved that space is an actual medium that really does curve, only people who misinterpret him and misinterpret the function of scientific theories say that.

It could be that there really is a medium that permeates everything, or it could be that there is pure void between things, both ideas are compatible with what we observe. If there is pure void between things then space isn't a medium, it isn't an actual thing.

But it doesn't make sense to say that the thing within which objects exist, and move around, is a concept. — Metaphysician Undercover

It does make sense if it is said conceptually and not literally. We can imagine that planets follow curved trajectories in a flat space, or straight trajectories in a curved space, or some other trajectories in some other space, the conceptualization itself doesn't imply that space is an actual thing that is flat or curved, otherwise that leads to senseless conclusions, space would be at the same time flat and curved when one person conceptualizes it as flat and some other person as curved.

Yourself you have even come up with a concept of space in which objects don't move even when we perceive them to move. Do you conclude from that that space is an actual thing that shrinks and expands whereas objects remain at rest, or that it's a concept you have invented?

If simultaneously one person can imagine space as flat, some other person as curved, some other person as shrinking and expanding, some other person as being displaced by objects, do you not see that space is a concept, and that people conceptualize it by analogy with what they do observe? People observe flat surfaces, people observe curved surface, people observe balloons shrinking or expanding, people observe water displaced by objects moving within it, then they conceptualize space by analogy with what they have observed, but they can conceptualize it however they want, all their conceptions are compatible with observations, the very same observation can be translated in one conceptualization as an object having a straight trajectory, in another conceptualization as the object having a curved trajectory, in yet another as being at rest, all are valid depending on the concept you use.

So if space can be anything we want it to be, what is it? It's a creation of the imagination, a tool of thought, a concept. Yes we perceive objects, yes we perceive change, but I think if you trained your mind you could come to see all objects at rest while imagining (or seeing) space shrinking or expanding between them. Maybe then you would come to see space as a real tangible thing, and motions of objects as an illusion. Sometimes the line between reality and imagination can be blurry, who knows if we aren't the ones who impose that delimitation ourselves.

So I won't claim it's impossible to see space as a real tangible thing, after all I'm not in your mind. But I'll keep saying that it's possible to imagine it as flat, or curved, or as nothing at all, and as such that it is false to claim that planets revolve around the Sun because they follow straight lines in curved space as if we had detected space to be something that curves, conceptually we can see planets as following straight lines in curved space, but conceptually we can also see them as having curved trajectories in flat space or as some other thing.

What does this indicate other than the fact that we really don't know what space is? — Metaphysician Undercover

I think really your question boils down to why is there something rather than nothing. Because as soon as you identify several things within what you see you can come up with a concept of distance, and then a concept of space. Only if your experience was uniform (say you didn't experience anything except the color white, no sound no smell no taste no touch, no screen around the white just white) then you wouldn't come up with the concept of space. The concept is used to relate things that are identified as distinct.

So I would say our thoughts create the concept of space. And then I wonder to what extent our thoughts create what we see, to what extent they decide what's reality and what's imagination, to what extent they have created what they classify as reality...

I meant why the distinction between static space and active space, since the shape of an object is not necessarily static. — leo

Well I went through this already. An object must really be a static thing, because if it changes it is no longer the same object. Sure we say that it is the same object, only changed, but logically if it has changed, it can no longer be the very same thing. Aristotle tried to deal with this problem by employing the concept of matter, which allowed that the object would remain the same object, despite changing its form, so long as its matter stayed the same.

So Aristotle distinguished change of shape or form, from locomotion, as two distinct types of activity. In modern times, we have come to understand change of shape as the locomotion of a thing's parts. So we no longer have these two distinct types of activity, all is understood under the terms of locomotion. Change of the shape of an object, is supposed to be the movement of parts relative to each other. But then the parts are themselves objects, moving relative to each other, and there is no justification for the claim that a multitude of objects is really one object, the original "object". Either the circumstances being observed is a multitude of objects, or it is one object, but it can't be both at the same time because this is contradictory.

That is the problem with the part/whole ontology. Saying that an entity, an object which exists as a single, individual unity, is composed of other objects which are parts, is really contradictory. This is because we then consider the same thing to be both one object, and a multiplicity of objects, at the same time, and this is contradictory, like saying 1 is at the same time, 2. If we divide the one unity into parts, then it is no longer one unity. It cannot be divided and whole at the same time. So the one object, as a unity is divisible into parts, but it cannot actually be composed of parts, if the parts are considered to be objects themselves.

If the object, as a unity is not composed of parts, then it cannot be changing. If it is composed of parts, and changing, then the parts cannot be considered to be objects, and their activities cannot be understood as objects moving relative to each other.

No I'm not saying that, I said that the definitions refer to it like a thing, some sort of container in which objects move. In physics space used to be thought as a medium (the luminiferous aether), then failures to detect it experimentally led to abandon the idea of it as a medium (as Einstein did with special relativity in which there is no more reference to an absolute space but instead to relative reference frames), and then Einstein reintroduced it as some sort of a medium in general relativity since in it space has properties such as curvature. But even though in his theory space has properties, Einstein was well aware that space is a "tool of thought" (that's his own words), in no way did he pretend that his theory somehow proved that space is an actual medium that really does curve, only people who misinterpret him and misinterpret the function of scientific theories say that. — leo

I accept this description, but it does not explain how objects exist within space, yet space is just a tool of thought. The inconsistency, or contradiction, remains. If the conceptions of "space" model space as a medium within which objects exist, then it is absolutely incorrect to say that space is a "tool of thought". Space is something which is modelled as a medium within which objects exist. It is not modeled as a tool of thought, so it is incorrect to say that space is a tool of thought, because it is represented by the models as a medium within which objects exist. If we model water as something we can swim in, then it is incorrect to say that water is a tool of thought, that is not how it is modelled.

It could be that there really is a medium that permeates everything, or it could be that there is pure void between things, both ideas are compatible with what we observe. If there is pure void between things then space isn't a medium, it isn't an actual thing. — leo

It doesn't matter if you call this medium "pure void", it's still a medium. So your claim of two possibilities, medium, and pure void, is inaccurate because "pure void" is really just a special type of medium, and so there is really only one choice, medium. Many people speak of "pure void" as if it were something other than medium. But when we come to realize that "pure void" just refers to a special type of medium, an absolute medium which consists of absolutely nothing but itself, then we realize that it doesn't make sense even to speak of "pure void".

It does make sense if it is said conceptually and not literally. — leo

I don't understand this distinction. Do you recognize that a model must model something? If one were to make a model, and it didn't model anything, it would just be random nonsense, and not a model at a all.

So if you model planets as moving through space, it makes no sense to say that this is just what the model shows, and the planets are not really moving through space, we've just modelled them that way. If you model planets as moving through space, and insist that the planets aren't really moving through space, it's just that the model shows them as moving through space, then all you are doing is asserting that the model is wrong.

If simultaneously one person can imagine space as flat, some other person as curved, some other person as shrinking and expanding, some other person as being displaced by objects, do you not see that space is a concept, and that people conceptualize it by analogy with what they do observe? — leo

Not at all. What I would conclude from this is that space is a real thing, because many people are talking about it, but they just don't understand it, and this is evident because their concepts of it vary. It's very similar to when a few people try to recount an incident from many years ago. Some will remember it in one way, others in another way. This doesn't mean that the incident isn't a real thing which really happened, it just means that the people haven't conceptualized it well.