A 3D part in Eternalism is equivalent to a 3D object at a time in Presentism. Both describe the mug on my desk at time t. — Luke

To anticipate a possible objection, it may be argued that, given the above equivalence, my argument against motion in Eternalism will allow for the same argument to be made against motion in Presentism, thus making motion also impossible in Presentism.

My response is that there is no difference between the Eternalist part at t and the Presentist object at t, or between the Eternalist part at t' and the Presentist object at t'. As I said, a 3D Presentist object at a time is equivalent to a 3D Eternalist part. The reason that motion is possible in Presentism, and what distinguishes this view from Eternalism, is that the Presentist object at t and the Presentist object at t' are considered to be the same object (by Presentists). However, the Eternalist part at t and the Eternalist part at t' cannot be considered to be the same part (by Eternalists). When talking about motion, it is presumed that the same 3D object/part moves through time (i.e. travels) from t to t'. This is a Presentist assumption which only makes sense in Presentism.

the Eternalist part at t and the Eternalist part at t' cannot be considered to be the same part (by Eternalists) — Luke

They are not the same part, any more than the top of a mountain is the same part of the mountain as the bottom. But they are nevertheless still parts of the same object.

But they are nevertheless still parts of the same object. — Pfhorrest

Parts of the same 4D object, certainly. Are you wanting to argue that the 4D object moves?

Edit: Or are you implying that these different parts (e.g. of the mountain) are all the same part?

Are you wanting to argue that the 4D object moves? — Luke

Moves with respect to what? Time is one of the four dimensions.

If you're looking at a 4D object, where one of the four dimensions is time, then you're standing outside of time, and there is no dimension that seems timelike to you in which for the 4D object to move.

An object moving in three dimensions with respect to the fourth will just look like a 4D object to you, though.

This is why I brought up the line thing. (And the tower, and Kenoshi brought up the mountain, and I brought up the pipe). This is the thing you're really not getting, and explicitly denied is what eternalism is about earlier.

Moves with respect to what? Time is one of the four dimensions. — Pfhorrest

I know. I was wondering whether you wanted to follow that problematic route.

An object moving in three dimensions with respect to the fourth will just look like a 4D object to you, though. — Pfhorrest

Sorry, but this has all been covered previously. I don't wish to rehash it again here. Is there something you think I failed to address earlier in the discussion?

Edit: Basically, I've been arguing that Eternalism logically precludes motion throughout the thread. If correct, this implies that an Eternalist universe is motionless (inside and out). I can't really condense that into a few sentences to try and convince you. Take a look at the last 2-3 pages.

I've been following. I told you earlier, your depiction of eternalism is a straw man. You're arguing against something that nobody is defending. Eternalists don't think that the universe is motionless. They think motion has to be with respect to something. 3D objects move with respect to a fourth dimension of time, tracing out a 4D shape as they do so. Those 4D objects have nothing defined to move in respect to, but they don't need to move in order for motion as we normally think of it to be possible, because that's the motion of 3D objects with respect to time, not the motion of 4D objects with respect to... what exactly?

You're arguing against something that nobody is defending. — Pfhorrest

I'm not arguing against anything. I'm trying to demonstrate the logical implications of the concept of Eternalism.

Eternalists don't think that the universe is motionless. — Pfhorrest

I think that some do, actually.

They think motion has to be with respect to something. 3D objects move with respect to a fourth dimension of time, tracing out a 4D shape as they do so. — Pfhorrest

I'm pretty sure Eternalist objects have 4D existence, rather than "tracing out a 4D shape".

not the motion of 4D objects with respect to... what exactly? — Pfhorrest

Again, I wasn't arguing for this. I was checking whether you wanted to.

This underlies my whole view of the matter (although somewhat vaguely): that Eternalism is all position and Presentism is all momentum. — Luke

Space is present in both, so therefore momentum is possible in both.

Motion implies that the same object moves from t to t'. This is a Presentist assumption which makes no sense in Eternalism. — Luke

As defined, yes. But you can define something else, xotion for instance, as moving one object in one place and time to another in another, if that process is continuous. This would look identical to what we call motion, obey the same equations, have the same causes and effects, but it would start with an x instead of an m, and have a different definition.

I don't understand your use of the word "redundant" here. — Luke

If motion were impossible, then x(t) = x, which a constant. We could write a position as (x, y, z, m, n, t). But since (x, y, z, t) fully determine position, i.e. (m, n) don't do anything, this is merely describing a 4D something in a 6D space for no reason: it is still 4D. Likewise if nothing moved, (x, y, z) cannot change thus those coordinates define everything.

Motion implies that the same object moves from t to t'. This is a Presentist assumption which makes no sense in Eternalism.
— Luke

As defined, yes. — Kenosha Kid

Wait... Are you saying you are satisfied that Eternalism logically precludes motion (according to our agreed upon definition of motion)?

Wait... Are you saying you are satisfied that Eternalism logically precludes motion (according to our agreed upon definition of motion)? — Luke

No, for two reasons:

1) Eternalism does not say that the cup at time t is a different cup at time t', so the above is unnecessary
2) It still yields motion, just via an additional variable.

There is something that turns the cup at t into the cup at t'. Let us identify the temporal cup slices as c(t), such that c(t') = c(t) only if t'=t. Which 3D cup we speak of depends on when we speak of.

We can then define the positions of a history of cup transformations as x(c): where the cup is depends on which 3D cup it is.

Motion still falls out: dx/dt = (dx/dc) x (dc/dt)

So as long as x, c, and t are continuous, i.e. so long as objects don't disappear then later reappear, motion is still possible.

Eternalists don't think that the universe is motionless. — Pfhorrest

To support this thought, they define "motion" in very strange ways, as Kenosha has demonstrated. This makes the thing described as "motion" something completely different from what we commonly refer to as motion.

There is something that turns the cup at t into the cup at t'. — Kenosha Kid

Now your catching on. Motion is that thing in between, which is not represented.

Motion still falls out: dx/dt = (dx/dc) x (dc/dt) — Kenosha Kid

The problem is that this is not what motion is. It is not the difference between two states, it is the act of moving.

So as long as x, c, and t are continuous, i.e. so long as objects don't disappear then later reappear, motion is still possible. — Kenosha Kid

What separates me from Luke, is that I think motion is possible in an eternalist framework, if we provide the appropriate additional premises, such as those used in religion, or Luke's spot light theory. However, Luke insists that adding such additional premises makes it no longer eternalism.

Space is present in both, so therefore momentum is possible in both. — Kenosha Kid

Momentum requires only space?

If motion were impossible, then x(t) = x, which a constant. We could write a position as (x, y, z, m, n, t). But since (x, y, z, t) fully determine position, i.e. (m, n) don't do anything, this is merely describing a 4D something in a 6D space for no reason: it is still 4D. Likewise if nothing moved, (x, y, z) cannot change thus those coordinates define everything. — Kenosha Kid

Those co-ordinates might define everything for a 3D part. What about the rest of the 4D object?

1) Eternalism does not say that the cup at time t is a different cup at time t', so the above is unnecessary — Kenosha Kid

Eternalism logically entails that the cup at time t and the cup at time t' both co-exist as separate objects/parts. They exist as different 3D parts of the same 4D cup, but always as different parts. You can call them the same cup if you like, but you can also say that time passes if you like.

2) Is still yields motion, just via an additional variable.

There is something that turns the cup at t into the cup at t'. — Kenosha Kid

The additional variable is motion? That is, what is this "something"?

Momentum requires only space? — Luke

This is quantum mechanics now. We are far from Galileo. The momentum of a quantum mechanical body at a particular time is a feature of its wavefunction's geometry at that time. Precisely, it is, in a given direction, proportional to the number of wave peaks per metre in that direction. It is still related to time, but indirectly, via something called the dispersion relation, which is energetics not kinematics.

Eternalism logically entails that the cup at time t and the cup at time t' both co-exist as separate objects/parts. They exist as different 3D parts of the same 4D cup, but always as different parts. You can call them the same cup if you like, but you can also say that time passes if you like. — Luke

If it is irrelevant in eternalism whether consider the cup at time t' to be the same cup as the cup at time t, then it cannot form part of your argument one way or the other. (So here we agree.)

The additional variable is motion? That is, what is this "something"? — Luke

No, just whatever it is that connects the cup at t' to the cup at t. It's not something I postulate. I know the cup at t' is the same as the cup at t, that they are different cross sections of the same 4D object. But if you want to postulate they are not, then there needs to be some explanation for why, if I stare at a cup for a given interval of time, the cup at the end not only appears indistinguishable from the cup at the start, but appears continuously. Whatever causes that, whatever replaces continuity of identity, is c(t), and motion rears its ugly head once more via the chain rule: d/dt = (d/dc)*(dc/dt).

In other words, you can't escape motion by claiming that the 3D object at t' is different to the one at t. In 4D, it is still a continuous geometric object, and that geometry is motion.

The momentum of a quantum mechanical body at a particular time is a feature of its wavefunction's geometry at that time. Precisely, it is, in a given direction, proportional to the number of wave peaks per metre in that direction. It is still related to time, but indirectly, via something called the dispersion relation, which is energetics not kinematics. — Kenosha Kid

I'll have to take your word for it.

If it is irrelevant in eternalism whether consider the cup at time t' to be the same cup as the cup at time t, then it cannot form part of your argument one way or the other. (So here we agree.) — Kenosha Kid

I never meant to imply that it was irrelevant. They are different parts. If you want to refer to them as the same part, then you are ignoring the Eternalist reality and may as well be a Presentist. Hence, "you can also say that time passes if you want".

No, just whatever it is that connects the cup at t' to the cup at t. It's not something I postulate. — Kenosha Kid

In Presentism, what connects the cup at t' to the cup at t is temporal passage. An Eternalist can just reject that and attribute it to something else with an identical effect?

I know the cup at t' is the same as the cup at t, that they are different cross sections of the same 4D object. But if you want to postulate they are not, then there needs to be some explanation for why, if I stare at a cup for a given interval of time, the cup at the end not only appears indistinguishable from the cup at the start, but appears continuously. — Kenosha Kid

As an Eternalist, you know they are different 3D cross sections of the same 4D cup, but for a Presentist there is just one 3D cross section of the same 3D cup moving through time. What you need to account for as an Eternalist, which you have simply assumed here, is how you, or your consciousness, moves from one temporal cross section to another. As I said earlier: "Motion implies that the same object moves from t to t'. This is a Presentist assumption which makes no sense in Eternalism." So how is it that the same object moves from t to t'?

If you want to refer to them as the same part, then you are ignoring the Eternalist reality and may as well be a Presentist — Luke

Not remotely. There's nothing inconsistent with eternalism in saying that the apex of the mountain at time t is the same apex of the same mountain at time t'. That is not a problem for eternalism to resolve.

An Eternalist can just reject that and attribute it to something else with an identical effect? — Luke

No they can't. If the entire history of an object is laid out, i.e. if the past and future are real, then events in that history are connected. Again, it is yourself bringing non-eternalist ideas into the eternalism picture.

What you need to account for as an Eternalist, which you have simply assumed here, is how you, or your consciousness, moves from one temporal cross section to another. — Luke

No you don't, that is precisely what the eternalist viewpoint doesn't need. You don't need to account for how you get from an event at time t to one at time t', because it's all just laid out there and real. The continuity of 4D objects purely as geometric objects is sufficient, and that geometry is sufficient for motion. There's no "you" to get from one point to the other (presentism).

Unless you main one must account for the subjective human experience of presentism in an eternalist universe. But understand that is not needed for motion: motion is geometric in 4D just as shape is in 4D.

There's no "you" to get from one point to the other (presentism). — Kenosha Kid

So it's the same cup from t to t', but not the same you?

I'll come back to the rest later.

So it's the same cup from t to t', but not the same you? — Luke

No, it's the same you, but the "you" in "you, or your consciousness, moves from one temporal cross section to another". "you" are laid out in 4D like everything else.

The impression of presentism when you are laid out in 4D is a different question that does not bear on whether or not motion is possible.

No you don't, that is precisely what the eternalist viewpoint doesn't need. You don't need to account for how you get from an event at time t to one at time t', because it's all just laid out there and real. The continuity of 4D objects purely as geometric objects is sufficient, and that geometry is sufficient for motion. — Kenosha Kid

Are you denying that we "get from an event at time t to one at time t'"? Or are you saying that "history is laid out there and real" somehow provides this motion? If so, how?

Unless you main one must account for the subjective human experience of presentism in an eternalist universe. But understand that is not needed for motion: motion is geometric in 4D just as shape is in 4D. — Kenosha Kid

You introduced this aspect into the discussion:

"there needs to be some explanation for why, if I stare at a cup for a given interval of time, the cup at the end not only appears indistinguishable from the cup at the start, but appears continuously" — Kenosha Kid

The impression of presentism when you are laid out in 4D is a different question that does not bear on whether or not motion is possible. — Kenosha Kid

If you're just going to assume that motion is possible because it's "in the model", then I suppose there's nothing to discuss. I guess your model contains no assumptions.

The continuity of 4D objects purely as geometric objects is sufficient, and that geometry is sufficient for motion. — Kenosha Kid

Why is it sufficient?

Or are you saying that "history is laid out there and real" somehow provides this motion? If so, how? — Luke

This. As I've said before, motion is the geometry of the 4D object. Any point on that object will have a coordinate (x, y, z, t). If two points (x, y, z, t) and (x', y', z', t') on the same 4D object have different time coordinates (t' != t) but the same spatial coordinates (x'=x, y'=y, z'=z), the object is not in motion. Otherwise it must be by definition, since its position is different at different times.

If you're just going to assume that motion is possible because it's "in the model", then I suppose there's nothing to discuss. I guess your model contains no assumptions. — Luke

It contains the 4D geometry of eternalism and the kinetic model of motion, but nothing else.

Why is it sufficient? — Luke

Because any continuous geometry has well-defined gradients in any dimension with the respect to any of the others at all coordinates. The geometry of the object will dictate, for instance, dx/dz for all times (x,y,z,t), or dy/dx, or dx/dt, dy/dt and dz/dt. The first two are spatial slopes, like the gradient of a mountain side. Those last three are its velocity. It's all the same kind of thing in 4D.

Motion in 3D + time = geometry in 4D.

As I've said before, motion is the geometry of the 4D object. Any point on that object will have a coordinate (x, y, z, t). If two points (x, y, z, t) and (x', y', z', t') on the same 4D object have different time coordinates (t' != t) but the same spatial coordinates (x'=x, y'=y, z'=z), the object is not in motion. Otherwise it must be by definition, since its position is different at different times — Kenosha Kid

I'm attempting to argue that motion is a Presentist notion. I don't doubt that you can calculate a value for motion for a given section of a 4D object (i.e. in Eternalism), but doesn't the very concept of motion assume that a 3D object moves from t to t' in some fashion akin to temporal passage? You can say that there's motion in Eternalist geometry, but the concept of motion is based on Presentist assumptions, I would argue.

Motion in 3D + time = geometry in 4D. — Kenosha Kid

What is motion in 3D? How does that work without time?

doesn't the very concept of motion assume that a 3D object moves from t to t' in some fashion akin to temporal passage? — Luke

No, it just depends on position being a continuous function of time. What you're talking about is a kind of propagator. That can be made consistent with kinematics, but not derived from it.

the concept of motion is based on Presentist assumptions, I would argue. — Luke

Which, again, means that the concept of motion is not that of normal kinematics, which contains no knowledge of a 'now'. Past motion, future motion, present motion, all are describable. If anything, kinematics' natural home is eternalism. It derives from the sorts of graphs you did at school, where you have the height of the ball (or whatever) on the vertical axis and time on the horizontal. This is just a simplified spacetime, the sorts of geometry I and Phforrest have been talking about.

What is motion in 3D? How does that work without time? — Luke

Allow me to fix the ambiguity:

Motion in (3D + time) = geometry in 4D. — Kenosha Kid

To support this thought, they define "motion" in very strange ways, as Kenosha has demonstrated. This makes the thing described as "motion" something completely different from what we commonly refer to as motion. — Metaphysician Undercover

We ordinarily talk quite readily of motion or change with respect to a dimension other than time as we usually experience it. Hence the mountain that gets smaller with altitude even though it stays the same size with time; the pipe along its side that gains altitude as it moves westward, even though it’s not moving with respect to time; the abstract line that moves in a y-ward direction over the x-ward direction, even though it too doesn’t move with respect to time.

Eternalism just says that motion and change over time is no different than such “motion” or “change” in one spatial dimension over another, except that we experience the dimension of time differently.

doesn't the very concept of motion assume that a 3D object moves from t to t' in some fashion akin to temporal passage?
— Luke

No, it just depends on position being a continuous function of time. What you're talking about is a kind of propagator. That can be made consistent with kinematics, but not derived from it. — Kenosha Kid

How is continuity sufficient? What does change/motion mean without temporal passage? Isn't such a "propagator" being implicitly assumed when you talk about deriving motion from the geometry? Surely any concept of motion assumes that something gets from t to t'. Otherwise, what else could motion be? Change has no meaning in a static world.

Isn't such a "propagator" being implicitly assumed when you talk about deriving motion from the geometry? — Luke

No, not at all, as per the mountain example. You don't need a hiker to have a gradient. You don't need a temporal hiker to have a gradient either.

No, not at all, as per the mountain example. You don't need a hiker to have a gradient. You don't need a temporal hiker to have a gradient either. — Kenosha Kid

What does a gradient have to do with motion? It's just an assumption that there is motion in the gradient. A universe without change or motion is equally conceivable, so why do you get to assume your gradient has motion rather than doesn't? Again, what does motion mean without a change from t to t'?

We ordinarily talk quite readily of motion or change with respect to a dimension other than time as we usually experience it. Hence the mountain that gets smaller with altitude even though it stays the same size with time; the pipe along its side that gains altitude as it moves westward, even though it’s not moving with respect to time; the abstract line that moves in a y-ward direction over the x-ward direction, even though it too doesn’t move with respect to time. — Pfhorrest

Sorry to have to inform you of this, but this talk makes no sense to me. And I've never heard anyone talk like this prior to seeing it on this thread. So I think you guys are just making it up. The mountain gets smaller with altitude? What could that even mean? It's the same mountain. If you're at a lower spot on the mountain than someone else, this does not make the mountain any smaller. Nor does walking down the mountain from top to bottom make it any smaller. That's nonsense to say that the mountain is smaller or larger according to one's altitudinal position.

Would you not say that a cone is smaller at the point than at the open end? A mountain is cone-shaped, roughly, with the pointy end up. So it’s smaller at the top than at the bottom. Its size is different at different altitude. Not the 3D size of the entire mountain, but the part of the mountain that’s at a given altitude. Is that really such a weird way to speak to you?

Would you not say that a cone is smaller at the point than at the open end? — Pfhorrest

No, a cone is the whole thing, not just one end or the other. One cone is smaller than another cone, but it makes no sense to say that a cone is smaller than itself at one end or the other. Are you lacking in English skills? It might make sense to say that the circumference of the cone is smaller at one end than the other, but it makes no sense to say that the cone itself is smaller, because "cone" refers to the entirety of the shape.

Is that really such a weird way to speak to you? — Pfhorrest

Yes, it's a very primitive and misleading way to speak, to say that because the circumference of the cone is smaller at one end than the other, then the cone is smaller than itself at one end or the other. If you really think that this is an acceptable way to speak, then ask yourself, if "the cone is smaller", then what is it smaller than. You will see that there is nothing else referred to but itself, and you are saying that the cone is smaller than itself. Truly a very weird way to speak.