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

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

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.

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

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

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.

It's not my definition, blame Galileo! — Kenosha Kid

Your wrong, it's not Galileo's definition of motion. It's yours.

An effect of the motion of the teacup is that it is now on the floor. — Kenosha Kid

Right, that's exactly what you claimed motion is:

my everyday experience of motion: the thing is not where it once was. — Kenosha Kid

See what I mean? You are taking an effect of motion, "the thing is not where it once was" (the teacup is now on the floor), and claiming that this is motion.

If that's your level of argumentation, we cannot trust that each other are trying their best to explain what seems true to them. Further discussion would be pointless. I'm not having a go; you've described exactly how I feel about everything you have said. I just would have persevered and tried to reconcile our different experiences of motion, or perhaps got a consensus on another thread. — Kenosha Kid

You obviously haven't a clue of what you are talking about. Good luck in your attempts at discussion!

Picture if you will a skyscraper in a timeless world; it is eternal and unchanging. Also, every floor of this skyscraper is strictly two-dimensional; it’s really a bunch of flat sheets stacked in a tower, but I’m going to talk about them like they’re floors of a building.

The top of the tower is a point, and the floors get wider toward the bottom. We don’t have to worry about where the bottom is for now, for our purposes the tower may as well be infinitely tall, and we’re looking at it from the top down.

Every lower floor is identical to the floor above it except for one tiny change to each thing on the floor. These changes have to follow certain rules, and over time interesting patterns in the things on the floors develop. Patterns that, under the influence of the rules, lead to more copies of themselves being around on the lower floors, tend to become more common the lower you look in the tower, for obvious reasons.

One such kind of pattern turns out to be having as a part of its pattern copies of other patterns from upper floors, arranged in order by floor, and also extrapolations of that series of patterns into ones likely to appear on lower floors. Lower-floor variations of those patterns continue to build on their series’ of images from upper floors, and update their projections of expected images of lower floors accordingly.

So within these 2D patterns of stuff are contained representations of 3D sections of this building, sections that span multiple floors, but are represented inside of things that exist on just a single floor. In a sense, an image of part of the 3D building is contained within one thing that only exists as such in 2D.

I hope I don’t need to spell out this analogy.

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.

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

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

No. 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? The extent to which that is a meaningless question is the extent to which "what changes temporal position?" is a meaningless argument. In 4D, space and time are exactly analogous. If you are satisfied that a mountain in 4D has spatial length, you are satisfied that it has temporal duration.

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.

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?

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. — Luke

I'm not asking about motion, I'm asking about length. It is relevant because duration in 4D is a length. 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. Nor does that gradient depend on me measuring it.

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.

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 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

Precisely, and yet it has spatially-dependent altitude (a gradient). So why can you not admit that in 4D a body has time-dependent positions (another gradient) and therefore motion?

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

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

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

None. You do not need to "change" spatial location to have a length, or properties depending on space, unless, as I've repeatedly asked, you're using "change" with some unobvious meaning:

Nor does that gradient depend on me measuring it. — Kenosha Kid

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.

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. — Luke

No, but I feel you are, whenever you sense impending progress, drawing back. If you agree that motion depends only on time-dependent spatial positions, the crux now seems to be: what needs to change temporal position such that spatial positions may change? The question is perfectly analogous to: what needs to change spatial position such that spatial position may change? If you can understand how the altitude of a mountain can change with position, without some other thing having to change in order for that position to change, then understanding how a 4D body can have movement is in principle trivial.

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. I am sure you do not think this, but the extent to which you think 3D mountains aren't flat but 4D motion is impossible is the extent to which you're switching definitions when you go from space to time. They are both gradients of geometric objects in some space. If you can account for this difference, we have progress.

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.

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. — Luke

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.

I don't think you really dispute this. But I don't think you're apt to follow that to its logical conclusion, which is that motion is therefore well-defined in 4D (a truism, given the kinematic definition of motion). I can't make you see where you refuse to look.

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.

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. — Luke

Yes. By the kinematic definition of motion, motion is possible in eternalism. As I said ages ago and multiple times, if you have a different definition of motion, different rules and outcomes will fall out.

Your definition is seemingly presentist-specific, though you deny it: the only reason "motion is impossible" in eternalism is because motion is defined in presentist terms. Therefore your argument is nothing more than: "motion is impossible in Eternalism by definition". In other words, you're just reiterating Zeno's paradox.

This was all covered several pages ago.

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

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

You agree that motion, as I have defined it, falls out eternalism by definition, or, in your own words:

Your argument is little more than motion is possible in Eternalism by definition. — Luke

And yet "motion is impossible" in eternalism according to whatever definition you use.

It follows logically that you must have a different definition, otherwise motion would also appear possible to you "by definition".

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?

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?

My argument is based on these definitions. — Luke

Then motion is possible by definition, since the time-dependence of an object's position is retained in the eternalist picture. Again, refer to the image for illustration.

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

I've attempted to explain it in multiple different ways with a great deal of patience, occasionally stretched. Your responses have amounted to circular arguments, contradicting yourself, and refusing to ever consider any point that would resolve the argument when offered. I am sure this is top-notch by your standard, but it is woeful by mine.

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.

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

Because if a 4D object's position depends on time, it has a gradient with respect to time (equivalent statements). By definition that is motion.

[EDIT: Assuming continuity, i.e. that the 4D object is a continuous body in 4D]

^ This is an example of taking the time to explain oneself. My approach has been thus from the start. Stating otherwise is just openly being an arse. If your counterargument depends on that, fine. It'll be dismissed on those grounds. If you have an actual counterargument that makes sense, don't cheapen it with personal invective.

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.