Fine fine fine. Not a trick at all. We only need consider an atom. This is also kinematic motion: different spatial positions at different times, i.e. time-dependent positions. — Kenosha Kid

Hold on. You said the atom was "part of a 4D object", not a 4D object. It depends on Presentism or Eternalism whether this remains the same object at different times.

[EDIT: I see now that I should have clarified this earlier. Sorry, it's 3am here.]

I didn't claim that it wasn't the same mountain — Luke

Don't read anything into this comment. I'm just trying to figure out how @Pfhorrest's response relates to what he quoted.

The gradient of the mountainside is not a change in the spatial position of the mountain, as you implied earlier. The mountain hasn't moved.
— Luke

It may help to imagine a pipe going down the mountainside. The answer to where the pipe is on the 2D surface of the Earth depends on which altitude you’re asking about: the pipe changes 2D location with altitude. If the pipe is on the east aide of the mountain, for instance, it gets further east the lower down the mountain it goes. It’s not moving over time, but the relevant segment of it at a given altitude is further east the lower the altitude. Yet at every altitude, it is still the same pipe. — Pfhorrest

Sorry, I don't understand what you're getting at. I didn't claim that it wasn't the same mountain.

Do you agree that even a part of a 4D object, such as an atom in the window of a car, has different spatial positions at different times? — Kenosha Kid

I get the sense this could be a trick question, but yes, I think so.

A body at a spatial coordinate (x,y,z) at time t may have a different spatial coordinate (x',y',z') at time t' (a path). This does not mean that the body at coordinate (x,y,z,t) moves. That is not shown, nor is it sensible. — Kenosha Kid

A body at (x,y,z) at t or at (x', y', z') at t' is not a 4D object; it is part of a 4D object. I was countering this statement:

you are presumably happy that a 4D object's position changes with with respect to time — Kenosha Kid

If you are happy that a 4D object exists at more than one time — Kenosha Kid

Just as I am not happy that a 3D object exists at more than one space (the object fills the space), I am equally not happy that a 4D object exists at more than one time (the object fills the time). And just as I agree that different parts of a 3D object exist at more than one space, I agree that different parts of a 4D object exist at more than one time.

And if you're happy with time intervals in 4D, and you are happy that the spatial position at one end of the interval may be different to that over the othet end, you are presumably happy that a 4D object's position changes with with respect to time, i.e. it's position at one time (x, y, z, t) maybe different at another. — Kenosha Kid

I have no qualms with saying that different parts of the 4D object have different spatial positions at different times. I disagree that the 4D object as a whole has different spatial positions at different times.

There is the kinematic definition of motion — Kenosha Kid

Following your reasoning above, this would imply that the 4D object as a whole moves.

This is leading us back around to my argument.

...the spatial part of the spatiotemporal position depends on the temporal part, that is: for each time, the object has a position. Assuming continuity. — Kenosha Kid

Is this different for Presentism?

What is it that changes position at all? Forget eternalism. Just a mountain at a given moment in time, an aerial photograph if you will. The summit is in one place. The foot is far away from it. It exists in more than one position. By your argument, radius is impossible because what changes spatial position? — Kenosha Kid

I've answered this, but perhaps it depends on what you mean by "exist in more than one position". The position of the mountain as a whole object doesn't "exist in more than one position". The 3D mountain exists in the spatial position of the 3D mountain. It would need to be displaced from that position in order to change position. However, if what you mean by "exist in more than one position" is to have a part of the mountain existing at one spatial position and another part of the mountain existing at another spatial position, then I agree that different parts of the mountain "exist in more than one position". I don't follow how this implies that "radius is impossible". Perhaps you mean something else by "exist in more than one position"?

What does "depends on time" mean?
— Luke

It means:

Motion is change in spatial position over change in temporal position.
— Luke

i.e. that where something is depends on when. — Kenosha Kid

What comes before and after the "i.e" is not equivalent. Motion is not defined as merely having a spatiotemporal position.

I have answered every question you have asked. You have not done the same. — Kenosha Kid

Did you have questions? I thought you were just telling me what's what.

a 4D object's position depends on time — Kenosha Kid

What does "depends on time" mean?

This is an example of taking the time to explain oneself. — Kenosha Kid

I've taken great pains to explain myself and present my argument, which you continue to ignore.

Then motion is possible by definition, since the time-dependence of an object's position is retained in the eternalist picture. — Kenosha Kid

What does "the time-dependence of an object's position" have to do with either of the definitions that we previously agreed to?

Your responses have amounted to circular arguments, contradicting yourself, and refusing to ever consider any point that would resolve the argument when offered — Kenosha Kid

The feeling is mutual.

Therefore your argument is nothing more than: "motion is impossible in Eternalism by definition". — Kenosha Kid

I've actually presented an argument. Where's yours?

Motion is change in spatial position over change in temporal position.

"Change in temporal position" means "is defined for more than one time". — Luke

My argument is based on these definitions. Are you using something different?

Show me where I've used a different definition of motion.

This seems to be par for the course: every opportunity I've suggested to consider how motion is possible in eternalism, you have given some excuse to look away. It all comes down to dx/dt being well-defined in eternalism as d(altitude)/d(radius) is defined for a mountain at any given time, and that the geometry of a 4D object is not dependent on how we calculate it, just as the geometry of a mountain is not dependent on how we calculate it. — Kenosha Kid

Oh my god. Your argument is little more than motion is possible in Eternalism by definition. The least you could do is address my argument if I'm so obviously wrong.

In short, your counter-argument is equivalent to saying that, at a given moment, a mountain must be flat because there is nothing "changing" position to allow its altitude to vary with position. — Kenosha Kid

I'm not sure why you're using scare quotes on "change", or asserting that I'm "using "change" with some unobvious meaning". I'm using our agreed upon definition of change in temporal location in my argument.

I'm not going to argue with you by analogy. There is no long-standing debate about whether altitude of a mountain can change with position. This is about time and motion.

You do not need to "change" spatial location — Kenosha Kid

Are you trying to "change" the subject? I thought the subject of our disagreement was whether there is motion in Eternalism. I've given my argument for why there isn't. You may need to clarify how this response addresses that argument.

Precisely, and yet it has spatially-dependent altitude (a gradient). — Kenosha Kid

What object has changed its spatial location? Please tell me.

I can calculate the gradient of the mountain at any point by measuring the "change" in altitude with "change" in radius. These are not changes over time, these are merely lengths. Not does that gradient depend on me measuring it. — Kenosha Kid

The gradient of the mountainside is not a change in the spatial position of the mountain, as you implied earlier. The mountain hasn't moved.

The same goes in 4D, where I can measure motion as "change" in spatial position with "change" in temporal position: these are lengths. And the motion is there whether I measure it or not. — Kenosha Kid

You're just repeating your assumptions instead of addressing my argument. I've used our agreed upon definitions of motion and of change in temporal location. Where's the error in my argument?

The summit is in one place. The foot is far away from it. It exists in more than one position. By your argument, radius is impossible because what changes spatial position? — Kenosha Kid

By your argument, a 3D object changes spatial position by being a 3D object. How is that a change of the object's position?

Forget eternalism. Just a mountain at a given moment in time, an aerial photograph of you will. The summit is in one place. The foot is far away from it. It exists in more than one position. — Kenosha Kid

Irrelevant. For which object are you measuring the motion? The mountain. So you need to measure the change in its temporal position. This will require that the same mountain (edit: object) is "defined for more than one time". And then see my argument.

What is it then that changes spatial position? — Kenosha Kid

In Eternalism? Nothing. That's what I'm arguing. Nothing moves; nothing changes.

What's required is continuity: the geometry of the mountain. — Kenosha Kid

This appears to be little more than an assumption. I've provided an argument that there is an inconsistency or implication for Eternalist motion with your claim that "change temporal position" means "is defined for more than one time".

Same goes for 4D objects. The Moon at some future event is the same as the Moon at some past event: both events are points on the Moon. What makes it the same Moon is continuity. — Kenosha Kid

I don't dispute that it's the same 4D object (or 4D moon). What I dispute is that any of its subdivided 3D parts are the same object/part. After all, it is the temporal and spatial positions of a particular 3D object/part that one would use to calculate the motion of that 3D object/part. In order for a 3D object/part to change temporal position from t1 to t2, it has to be the same 3D object/part at both times (i.e. the same object/part has to be "defined for more than one time"). Presentism will say it is the same object. I'm arguing that it cannot be for Eternalism.

As I pointed out earlier, according to our agreed upon definitions:

Motion is change in spatial position over change in temporal position.

"Change in temporal position" means "is defined for more than one time".

However, if a 3D part cannot be defined for more than one time (per Eternalism), then change in temporal position cannot be calculated and neither can motion.

The mountain at the summit is the same mountain as the one at the foot. What is it then that changes spatial position? — Kenosha Kid

Perhaps you don't understand what I mean by 3D object/part. It is the whole mountain at a time. The 3D object (the mountain) irrespective of the temporal (4th) dimension. At any given time, the 3D object (or the 3D part of a 4D object) has a spatial location.

Whether the object/part can change temporal location depends on whether it can be "defined for more than one time". This, in turn, depends on whether it is the same object/part at those (multiple) times. Given that a 4D (Eternalist) object consists of the existence of different 3D parts, then no two parts can be the same. Therefore, there is no object/part which changes its temporal location in Eternalism.

Yes, iirc I did ask for clarity on "3D part", I wasn't sure if you meant the body or its spatial coordinates. Continuity is what makes it the same object. Although, the ship Theseus and all that. — Kenosha Kid

You may wish to argue that it is the same object in Eternalism: the 4D object. But this would imply that it is the 4D object which moves or changes temporal location, and that makes little sense. — Luke

Yes, iirc I did ask for clarity on "3D part", I wasn't sure if you meant the body or its spatial coordinates. Continuity is what makes it the same object. Although, the ship Theseus and all that. — Kenosha Kid

Apologies. I thought you might have seen my earlier post (from which I am quoting all these comments):

To compare Presentism and Eternalism we need to talk about 3D objects, which is what motion typically deals with anyway. Eternalism doesn't have 3D objects so we need to use 3D parts of a 4D object instead. — Luke

It is quite clear that, in Eternalism, the 3D part existing at t1 is not the same as the 3D part existing at t2. You wouldn't say that the 3D part at t1 moves to t2; clearly not: a different part exists at t2. — Luke

Edit:

You may wish to argue that it is the same object in Eternalism: the 4D object. But this would imply that it is the 4D object which moves or changes temporal location, and that makes little sense. — Luke

Yes but it is not the same object, even in presentism. — ChatteringMonkey

A presentist would disagree.

As I've repeatedly asked: what is it that changes temporal location?
— Luke

I think you need to reword the question then. I can't make sense of something "changing temporal location" beyond "existing at multiple times". They means the same thing to me. Can you differentiate them for us? — Kenosha Kid

Why would I? I agree to your definition.

As I've repeatedly asked: what is it that changes temporal location? It has to be considered the same object to meet the definition "is defined for more than one time". You can't determine the change of temporal location of an object if it's not the same object that changes temporal location. — Luke

To repeat @Kenosha Kid's definition, to change temporal location means "is defined for more than one time". As I've repeatedly asked: what is it that changes temporal location? It has to be considered the same object to meet the definition "is defined for more than one time". You can't determine the change of temporal location of an object if it's not the same object that changes temporal location. To compare Presentism and Eternalism we need to talk about 3D objects, which is what motion typically deals with anyway. Eternalism doesn't have 3D objects so we need to use 3D parts of a 4D object instead. It is quite clear that, in Eternalism, the 3D part existing at t1 is not the same as the 3D part existing at t2. You wouldn't say that the 3D part at t1 moves to t2; clearly not: a different part exists at t2. However, in Presentism it is considered to be the same object that changes temporal location from t1 to t2.

You may wish to argue that it is the same object in Eternalism: the 4D object. But this would imply that it is the 4D object which moves or changes temporal location, and that makes little sense.

To borrow @Kenosha Kid's definition, to change temporal location means "is defined for more than one time". This makes sense in Presentism where the same 3D object moves through time from t1 to t2. It does not make sense in Eternalism where different 3D parts exist at t1 and t2.

...so cannot change temporal position.

Edit: It's not the same 3D part or "object" at both t1 and t2, so it is not defined for more than one time and so it cannot change temporal position. To consider it the same object is a Presentist notion.

It does not follow that the position of an object at a point in the future must equal the position of the object at a point in the past. — Kenosha Kid

It's not the spatial position which is at issue but the object itself. The same temporal part of a 4d object cannot be "defined for more than one time", so cannot change temporal position.

Right, I think I see what you're saying. If the path of the 4D object could be written as something like P(x,y,z,t), i.e. whether the object is present at a given spatial+temporal 4D position, you're saying that essentially P(x,y,z,t)=P(x,y,z), i.e. time is irrelevant in 4D. This would be like the Earth in Huw Price's picture. If every object were like this, this would be a 3D universe with a pointless fourth dimension added with no purpose. It would not correspond to motion as we perceive it or mean it in a Galilean sense. — Kenosha Kid

That's not quite right. I like it, but it's not really what I'm getting at. This is what I mean:

We define motion as change in spatial position over change in temporal position.

Furthermore, change in temporal position means "is defined for more than one time".

If a 3D part cannot be defined for more than one time (per Eternalism), then change in temporal position cannot be calculated and neither can motion.

No, because motion is differences of spatial positions over corresponding differences in temporal positions, and both spatial and temporal positions are present in 4D. — Kenosha Kid

Rght, but aren't you talking about the motion of some thing; an object? You've established that "change in temporal position" means "is defined for more than one time". I've argued that no 3D part is defined for more than one time. You've replied that what is defined for more than one time is the 4D whole.

This implies that the 4D whole is what changes temporal position. You can't measure just a part of that whole to derive a value for motion, because the part is neither defined for more than one time nor what changes temporal position. That was our agreed definition of motion. So either the 4D whole moves or nothing does.

What "is defined for more than one time" in a 4D universe? ... Instead, you have one part of 4D Earth existing at one temporal position and another part of 4D Earth existing at another temporal position.
— Luke

You have answered your own question: the geometry of the Earth. There is still time in 4D, it is just a dimension, the other 3 of those 4 dimensions being spatial. The spatial coordinates of an object are defined for a continuum of temporal coordinates, i.e. the geometry of a 4D object is a path through 4D space. — Kenosha Kid

Does this imply that the 4D Earth moves? But that would reintroduce the problem that a second temporal dimension is required.

Does it also imply that you can only measure the motion of the entire 4D object and not any of its parts? That's not what we've been discussing.

Edit: ...that is, if "change temporal position" means "is defined for more than one time" and if this can only refer to the 4D object, not to any 3D part.

I am satisfied that, in Einsteinian motion, a body moves from one time to another. I am satisfied that, in Gallilean motion, this is not held. — Kenosha Kid

In Gallilean motion, a body does not move from one time to another?

But you must have a consistent definition, and not say on the one hand that motion is e.g. Gallilean and on the other than, in the eternalist universe where by definition Gallilean motion is nonzero, that motion is not possible by definition. — Kenosha Kid

I can't say that motion is impossible by definition, but you can say that motion is possible by definition? That's hardly sporting.

If "change temporal position" means, as it should, "is defined for more than one time", there is no inconsistency: that holds true in an eternalist universe. — Kenosha Kid

What "is defined for more than one time" in a 4D universe? Once again, in Eternalism you don't have a 3D Earth that changes from one temporal position to another - that's Presentism. Instead, you have one part of 4D Earth existing at one temporal position and another part of 4D Earth existing at another temporal position. No two parts are the same, i.e., no part is "defined for more than one time". Therefore, no part changes temporal position.

Okay, I was agreeing with the emboldened part. — Kenosha Kid

To be clear, you disagree that "3D Earth doesn't move from t1 to t2"? That is, you believe that 3D Earth does move from t1 to t2?

The first part does not enter an everyday, Gallilean idea of motion, — Kenosha Kid

If you recall, I was saying that if you really want to take Eternalism seriously, then you should view objects as 4D rather than talking about them as though they are 3D objects which change temporal position. Of course this isn't a Gallilean or Presentist idea of motion; it's an Eternalist description.

Light, for instance, moves through space — Kenosha Kid

Light moves through space unlike everything else which simply exists in space? I'm happy to restrict the discussion to objects moving at less than c.

What I've been asking you to do is stick to one definition of motion and not change the definition as one moves from a presentist picture to an eternalist picture, or from an eternalist picture with a spotlight to one without, etc. — Kenosha Kid

Where have I been inconsistent on this?

You said you meant by 'motion' the typical, everyday, kinematic idea of different positions at different times: dx/dt, dy/dt, dz/dt for instance. Is this present in eternalism? Yes, because things exist at different positions at different times. — Kenosha Kid

But when I ask you to explain what the motion in your model represents, you can only do so in "pseudo-presentist" terms. If there is really motion in the Eternalist universe, then explain it in Eternalist terms. Otherwise, it's clear that motion only makes sense in Presentist terms. It's not like the (3D) Earth actually moves from one place to another over time, right?

Yes, because again a continuous worldline through x, y, z, and t is defined, and so is the proper time T of the body under consideration. dx/dT, dy/dT, dz/dT and dt/dT are all there, and motion according to this definition is evident. — Kenosha Kid

I think where we disagree is that you think the ability to calculate motion in your model therefore implies that motion is possible in an Eternalist universe, or implies that motion is consistent with actual 4D existence. You might be able to calculate motion, but how does that make it Eternalist rather than Presentist motion? Isn't it the same calculation? It appears to me that you are finding a value for a Presentist concept within an Eternalist universe.

Another way of moving through time might be, as SophistiCat suggested, to posit a second temporal dimension, call it ? — Kenosha Kid

Again, I've never suggested anything about a second temporal dimension. I'm okay with the fact that 4D objects don't move, whether that makes sense or not.

The 3D Earth doesn't move from t1 to t2; two different parts of the 4D Earth each exist at those times. — Luke

Exactly as I described. — Kenosha Kid

I never claimed that you said it; I said I thought that you agreed to it.

I'm perfectly happy with the description of the Earth moving through time. I am happy with that in an everyday, subjective, pseudo-presentist, practical sense. — Kenosha Kid

I'm happy with it too. I don't know what other sort of motion there could be.

The Earth does move, though, in the same way we mean in our everyday, subjective, presentist definition of movement: the Earth has different spatial coordinates at different times. — Kenosha Kid

I thought you agreed that "The 3D Earth doesn't move from t1 to t2"? Now you're saying that it does?

Or are you saying that it doesn't really move in the block universe? If it doesn't move in the Presentist sense, then in what sense does it move? That is, I still don't understand what the motion in your model represents.

As I said, if you're abandoning kinematics (e.g. v = dx/dt), fine. If you're making claims about kinematics though ("no kinematic motion can exist in a 4D that has x and t"), they can be rejected on kinematic grounds. — Kenosha Kid

Okay, let's say I agree to the definition of kinematic motion, and I agree that motion can be calculated in your physical model.

Earlier you appeared to agree when I stated:

The 3D Earth doesn't move from t1 to t2; two different parts of the 4D Earth each exist at those times.
— Luke

Exactly as I described. — Kenosha Kid

So there is motion, even though the Earth doesn't move? Then what does the motion in your model represent?

If all objects are 4D, then they don't change over time. I'm not here to convert things to your physics model. I'm here to discuss metaphysics.

At the end of the day, unless you can demonstrate that dx/dt is everywhere zero or meaningless in the eternalist picture, velocity, and therefore motion, will assert itself. Asserting to the contrary is your prerogative, but it is not an argument. — Kenosha Kid

Yes, the maths can still be done in the model; you can continue to subtract the value at t1 from that at t2. But dx/dt is inconsistent with the static 4D nature of the universe as described by Eternalism, as there is no actual change in position over time.

If you really want to take Eternalism seriously "with both feet and think about things like motion and change in eternalistic terms", then you should seriously view any object, such as the Earth or the Moon, as a four-dimensional object. You keep talking about them as though they are 3D objects which change their spatiotemporal positions or which have a "path" over time. However, they are not whole 3D objects that change their spatial and temporal positions (i.e. that move). Instead, they are whole 4D objects which consist of different stationary 3D parts existing at different times. The 3D Earth doesn't move from t1 to t2; two different parts of the 4D Earth each exist at those times.

It doesn't seem like taking it seriously to maintain that there is motion in Eternalism. You can call it that if you want, I suppose, but it seems like more of a Presentist (3D+1) notion.