Naturalism and perdurance

According to one version of naturalism, the only objects that have causal influence are objects posited by a completed science.

According to perdurantism, changing persisting objects have temporal parts which have the changing properties more fundamentally.

The changing properties of objects are causally efficacious. Thus, if perdurantism is true, the temporal parts have causal influence.

But the temporal parts of changing persisting objects are not among the objects posited by our current science. For instance, our current physics holds electrons and quarks to be fundamental, i.e., not made up of other objects studied by physics. The temporal parts of electrons and quarks are thus not studied by physics. Yet they have causal influence. If the completed physics is relevantly similar to our current physics in this regard, it won’t include temporal parts, either. And hence perdurantism posits causally efficacious entities that are unlikely to be posited by a complete science.

Thus perdurantism does not appear to fit with naturalism understood as above.

Perdurance, physicalism and relativity

Here is a very plausible thesis:

1. Exactly one object is a primary bearer of my present mental states.

This is a problem for the conjunction of standard perdurance, physicalism and special relativity. For according to standard perdurance on physicalism:

2. The primary bearers of my mental states are time slices.

Now consider all the time-slices of me that include my present mental states. There will be many of them, since there will be one corresponding to each reference frame. On relativistic grounds none of them is special. Thus:

3. Either all or none of them are the primary bearers of my present mental states.

If all of them are the primary bearers of my present mental states, we violate 1. If none of them are, then there is no primary bearer of my present mental states by 2, which also violates 1.

Perdurance

Here’s an interesting thing. Suppose perdurance is true. Then God cannot be in time. For if perdurantism is true and God is in time, then God is composed of infinitely many temporal parts. But:

1. This violates divine simplicity.

2. These parts are concrete and presumably not created by God, so there are concrete things other than God that God didn’t create.

3. God acts in virtue of the temporal parts acting, but then God’s actions are not the fundamental explainers.

4. The temporal parts are all-knowing, so God is not the only all-knowing entity.

This is utterly unacceptable. So, one cannot both accept perdurantism and that God is in time.

Perdurance and particles

A perdurantist who believes that particles are fundamental will typically think that the truly fundamental physical entities are instantaneous particle-slices.

But particles are not spatially localized, unless we interpret quantum mechanics in a Bohmian way. They are fuzzily spread over space. So particle-slices have the weird property that they are precisely temporally located—by definition of a slice—but spatially fuzzily spread out. Of course, it is not too surprising if fundamental reality is strange, but maybe the strangeness here should make one suspicious.

There is a second problem. According to special relativity, there are infinitely many spacelike hyperplanes through spacetime at a given point z of spacetime, corresponding to the infinitely many inertial frames of reference. If particles are spatially localized, this isn’t a problem: all of these hyperplanes slice a particle that is located at z into the same slice-at-z. But if the particles are spatially fuzzy, we have different slices corresponding to different hyperplanes. Any one family of slices seems sufficient to ground the properties of the full particle, but there are many families, so we have grounding overdetermination of a sort that seems to be evidence against the hypothesis that the slices are fundamental. (Compare Schaffer’s tiling requirement on the fundamental objects.)

A perdurantist who thinks the fundamental physical entities are fields has a similar problem.

A supersubstantialist perdurantist, who thinks that the fundamental entities are points of spacetime, doesn’t run into this problem. But that’s a really, really radical view.

An “Aristotelian” perdurantist who thinks that particles (or macroscopic entities) are ontologically prior to their slices also doesn’t have this problem.

Perdurance, Relativity and Quantum Mechanics

It is known that perdurantists, who hold that objects persisting in time are made of infinitely thin temporal slices, have to deny that fundamental particles are simple (i.e., do not have (integral) parts). For a fundamental particle is an object persisting in time, and hence will be made of particle-slices.

But what is perhaps not so well-known is that on perdurantism, the temporal slices a particle is made of will typically not be simple either, given some claims from standard interpretations of Quantum Mechanics and Special Relativity. The quick version of the argument is this: the spatial non-localizability of quantum particles requires typical temporal slices to be non-localized simples (e.g., extended simples), but this runs into relativistic problems.

Here is a detailed argument.

A perdurantist who takes Relativity seriously will say that for each inertial reference frame R and each persistent object, the object is made of R-temporal slices, where an R-temporal slice is a slice all of whose points are simultaneous according to R.

Now, suppose that p is a fundamental particle and that p is made up of a family F₁ of temporal slices defined by an inertial reference frame R₁. Now, particles are rarely if ever perfectly localized spatially on standard interpretations of Quantum Mechanics (Bohmianism is an exception): except perhaps right after a collapse, their position is fuzzy and wavelike. Thus, most particle-slices in F₁ will not be localized at a single point. Consider one of the typical unlocalized particle-slices, call it S. Since it’s not localized, S must cover (be at least partially located at) at least two distinct spacetime points a and b. These points are simultaneous according to R₁.

But for two distinct spacetime points that are simultaneous according to one frame, there will be another frame according to which they are not simultaneous. Let R₂, thus, be a frame according to which a and b are not simultaneous. Let F₂ be the family of temporal slices making up p according to R₂. Then S is not a part (proper or improper) of any slice in F₂, since S covers the points a and b of spacetime, but no member of F₂ covers these two points. But:

1. If a simple x is not a part of any member of a family F of objects, then x is not a part of any object made up of the members of that family.

Thus, if S is simple, then S is not a part of our particle p, which is absurd. Therefore, for any reference frame R and particle p, a typical R-temporal slice of p is not simple.

I think the perdurantist’s best bet is supersubstantialism, the view that particles are themselves made out of points of spacetime. But I do not think this is a satisfactory view. After all, two bosons could exist for all eternity in the same place.

Without Relativity, the problem is easily solved: particle-slices could be extended simples.

It is, I think, ironic that perdurantism would have trouble with Relativity. After all, a standard path to perdurantism is: Special Relativity → four-dimensionalism → perdurantism.

I myself accept four-dimensionalism but not perdurantism.

Perdurance, physicalism and mind

According to standard perdurantism, we are four-dimensional beings made out of three-dimensional slices, and properties such as mental ones are primarily had by the slices, and only derivatively by the four-dimensional whole.

Here are two problems with this when conjoined with widely held views.

First, mental states are intrinsic to the entity that has them primarily. But most perdurantists are physicalists. If mental states are intrinsic and had by three-dimensional slices, then it is possible to have a world with just one such three-dimensional slice with mental properties, isolated from other slices. But a single three-dimensional slice, isolated from other slices, does not have the functonal properties that the more plausible physicalist theories of mind require.

Second, it is clearly worse if someone has a constant headache for two hours than for one hour. But if time is continuous, as is widely held, then both the one-hour headache scenario and the two-hour headache scenario have the same infinite number of aching slices that are the primary bearers of the pain. But two scenarios which have the same number of primary painbearers are equally bad. Hence, a two-hour headache is no worse than a one-hour one. Which is absurd.

The perdurantist can escape this by saying that mental states are primarily had by the four-dimensional entity, and the three-dimensional slices, if they have mental states at all, have them derivatively. There are two ways of running this story. One way is that the slices have mental* states: states that aren’t mental states but that ground mental states in the four-dimensional whole. Thus, a four-dimensional entity hurts at time t just in case its slice at t hurts, but hurting isn’t a mental state, and doesn’t have the negative significance of hurting.

A second way is to say that the mental states of the four-dimensional entity reduce to ordinary physical states (positions, shapes, momenta, charges, etc.) of multiple three-dimensional slices.

4D, 3D and 2D

No three-dimensionalist has this ludicrous picture of the human being:

1. The human being is a three-dimensional whole whose functioning derives from the functioning of many two-dimensional slices that make her up.

But some four-dimensionlists have this picture of the human being:

2. The human being is a four-dimensional whole whose functioning derives from the functioning of many three-dimensional slices that make her up.

But it seems to me that (2) is not much better than (1). Just as we should be very dubious that there are any such things as two-dimensional slices of us—infinitely thin slices—we should be very dubious that there any such things as three-dimensional slices of us. And even if there are such slices, they are more like abstractions than components from which we derive our functioning.

So just as all three-dimensionalists deny 2D-slicism, all four-dimensionalists should deny 3D-slicism.

Now, let’s turn to three-dimensionalists. The following proposition is crazy:

1. The human being is two-dimensional.

But some think:

2. The human being is three-dimensional.

Why think (1) is false? The best reason is that the characteristic functioning of a human being requires more than just an infinitely thin section. Any thin section—whether infinitely thin or of non-zero thickness—through a human being is going to be quite unnatural, being intimately connected causally to other sections that are just as important to the characteristic functioning of a human being.

But the same reason applies against (2). Any temporally thin section—whether infinitely thin or of non-zero temporal thickness—through a human being is going to be quite unnatural, being intimately connected causally to other sections that are just as important to the characteristic functioning of a human being.

A secondary reason against (1) is that it is implausible that are privileged 2D slices. But likewise it is implausible (though maybe a bit less so) that there are privileged 3D slices.

Where does all this leave us? We should be at least four-dimensionalists (there might turn out to be more dimensions), and we should not think of ourselves as derivative from 3D or thinner slices. We should, indeed, be sceptical of the existence of such slices.

Aristotelian perdurance

The perdurantist thinks that we are four-dimensional beings made up of three-dimensional slices, temporal parts, from which we inherit our changing properties such as thinking. One good reason to deny perdurance is that implies that our thinking is derivative from another entity's thinking, namely from the part's thinking, pace Andrew Bailey's very plausible thesis that our thinking does not derive from another entity's thinking. Another issue is that perdurance has at most a 50% chance of being true for me: since the slice thinks the same thoughts as the four-dimensional being, I have at least a 50% chance of turning out to be the slice--contrary to perdurance.

But there is an interesting Aristotelian version of perdurance. I am a four-dimensional being, but I have a sequence of special accidents D_t corresponding to the times t at which I exist. Then all my changing features are grounded in features of these accidents. For instance, I am thinking at t provided that D_t is thinking*, where thinking* is whatever feature of an accident D_t that makes the possessor of D_t be thinking. For categorial reasons, thinking* isn't thinking: only substances think, but non-divine substances think in virtue of having an accident that in turn is thinking*.

What are the D_t accidents? One option is that they are the accident of existing at t. But perhaps there is a more Thomistic option: perhaps in the case of material substances they can be identified with something like Thomas's accidents of dimensive quantity. Thomas thought that material substances had a special accident, a dimensive quantity, and all their other accidents were in turn accidents of its dimensive quantity. This is a very similar role to that played by D_t. Or, perhaps, we could take D_t to be an accident of occupying such-and-such a three-dimensional region of four-dimensional space. There is room for further research here (and if anybody wants to work more out and co-author, they are very welcome).

There is a major difference in outlook between this and typical perdurance pictures. On typical perdurance views, the slices are prior to the four-dimensional whole. On this Aristotelian perdurantism, the D_t accidents are, like all accidents, posterior to the substance, which is four-dimensional. Apart from this, the view might not be that distant from standard perdurantism. I have proposed in another post that an Aristotelian could identify parts with certain kinds of accidents. On that identification, the D_t accidents could turn out to be parts. But the difference in outlook remains: the parts really are just accidents of the whole. And the parts don't have the same features as the whole does. They have features for which we have no names, features we can only identify as that feature of the accident that grounds the substance as being F.

This post is really just a combination of this and this.

A problem with Special Relativity Theory for perdurantists

There seems to be a problem for the conjunction of Special Relativity and perdurantism.  Maybe this is a standard problem that has a standard solution? Let's say that being bent is an intrinsic property. Perdurantists of the sort I am interested in think that Socrates is bent at a time in virtue of an instantaneous temporal part of him being bent (I think the argument can be made to work with thin but not instantaneous parts, but it's a little more complicated). Therefore:

1. x is bent at t only if the temporal part of x at t is bent simpliciter.

The following also seems like something perdurantists should say:

2. x is bent simpliciter only if every temporal part of x is bent simpliciter.

Now, we need to add some premises about the interaction of Special Relativity and time.

3. There is a one-to-one correspondence between times and maximal spacelike hypersurfaces such that one exists at a time if and only if one at least partly occupies the corresponding hypersurface.

Given a time t, let H(t) be the corresponding maximal spacelike hypersurface. And if h is a maximal spacelike hypersurface, then let T(h) be the corresponding time. Write P(x,t) for the temporal part of x at t. Then:

4. P(x,t) is wholly contained within H(t) and if z is a spacetime point in H(t) and within x, then z is within P(x,t)

and, plausibly:

5. If a point within x is within a maximal spacelike hypersurface h, then P(x,T(h)) exists.

Now suppose we have Special Relativity, so we're in a Minkowski spacetime. Then:

6. For any point z in spacetime, there are three maximal spacelike hypersurfaces h₁, h₂ and h₃ whose intersection contains no points other than z.

Add this obvious premise:

7. No object wholly contained within a single spacetime point is bent simpliciter.

Finally, for a reductio, suppose:

8. x is an object that is bent at t.

Choose a point z within P(x,t) and choose three spacelike hypersurfaces h₁, h₂ and h₃ whose intersection contains z and only z (by 6). Now define the following sequence of objects, which exist by 4 and 5:

• x₁=P(x,t)
• x₂=P(x₁,T(h₁))
• x₃=P(x₂,T(h₂))
• x₄=P(x₃,T(h₃))

Observe that x₄ is wholly contained in the intersection of the three hypersurfaces h₁, h₂ and h₃, and hence:

9. x₄ is wholly at z.
10. It is not the case that x₄ is bent simpliciter.

Now:

11. x₁ is bent simpliciter. (By 1 and 8)
12. x₂ is bent simpliciter. (By 2 and 11)
13. x₃ is bent simpliciter. (By 2 and 12)
14. x₄ is bent simpliciter. (By 2 and 13)

Since 14 contradicts 10, we have a problem.  It seems the perdurantist cannot have any objects that are bent at any time in a Minkowski spacetime. This is a problem for the perdurantist. If I were a perdurantist, I'd deny 2, and maintain that an object can be bent simpliciter despite having temporal parts that are bent and temporal parts that are not bent. But I would not be comfortable with maintaining this. I would take this to increase the cost of perdurantism. What is ironic here is that it is often thought that endurantism is what has trouble with Relativity.

Identity theory of mind

Here is a quick, and no doubt well-known, argument that mental states are not token-token identical with brain states. The argument makes assumptions I reject, but they are assumptions that, I think, will be plausible to a materialist. The idea is this. It is possible to transfer my mind into a computer, while preserving at least some of my memories, and with my brain being totally destroyed in the process (I reject this myself, but I think the materialist should accept Strong AI, and her best bet for a theory of personal identity is some version of the memory theory, which should allow this). Were such a transfer to be made, then I would have some of the numerically same token mental states (e.g., a memory of a particular embarassing episode) as I do now. But if these mental state tokens are now identical with brain state tokens, then it follows that it is possible that some of my brain states can survive the destruction of my brain, without any miracle, just by means of technological manipulation. But no brain state token of the sort that is correlated with memories[note 1], can survive the destruction of the brain, perhaps barring a miracle.[note 2] Hence, the mental states are not identical with brain states.

Of course, one might try a four-dimensionalist solution, supposing some temporally extended entity that coincides with the brain state prior to the destruction of the brain and with the electronic state after the destruction of the brain. But that won't save identity theory—it will only yield the claim that the mental state is spatiotemporally coincident with a brain state, or constituted by the brain state, vel caetera.

Maybe, though, what the identity theorist needs to do is to disambiguate the notion of a "brain state". In one sense, a brain state is the state of the brain's being a certain way. Call that an "intrinsic brain state" (note: it may be somewhat relational—I am not worried about that issue). If identity theory is understood in this way, the above argument against the identity theory works (assuming materialism, etc.) But a different sense of "brain state" is: a state of the world which, right now, as a matter of fact obtains in virtue of how a brain is.

Thus, consider the following state S: Alex's brain being gray, or there being a war in France. State S now obtains in virtue of how my brain is. But state S obtained in 1940 in the absence of my brain, since I did not exist then; instead, it obtained in virtue of there being a war in France. The state S is now a brain state, though earlier it wasn't. Call such a thing a "jumpy brain state": it can jump in and out of heads.

The identity theorist who accepts the possibility of mind transfer had better not claim that mental state tokens are identical with intrinsic brain state tokens but rather must hold that they are identical with jumpy brain state tokens. Put that way, the identity theory is much tamer than one might have thought. In fact, it is not clear that it says anything beyond the claim that the present truthmakers for mental state attributions are brain states.

Also, consider this. Presumably, for any jumpy brain state S, there is an intrinsic brain state S*, which right now coincides with S, and which is such that S obtains in virtue of S*. Thus, corresponding to the jumpy state Alex's brain being gray, or there being a war in France, there is the intrinsic brain state Alex's brain being gray. There is now a sense in which our identity theory is not faithful to its founding intuition that mental states are the states that neuroscience studies. For neuroscience certainly does not study jumpy brain states (neuroscience as such is not about wars in France, or information on hard drives). Rather, neuroscience studies intrinsic brain states. The identity theorist's mental state is identical with some jumpy brain state S, but it is S* that neuroscience studies.

And so there is a sense in which the identity theory is a cheat, unless it is supplemented with a non-psychological theory of personal identity that bans mind transfer between brains and computers. But the latter supplementation will, I think, also ban AI, since if computers can be intelligent, minds can be transfered between computers (think of a networked computation—the data can move around the network freely), and it would be weird if they could be transfered between computers but not from a brain to an appropriately programmed computer. Moreover, once one bans AI, one has made a claim that intelligence requires a particular kind of physical substrate. And then it becomes difficult to justify the intuition that aliens with completely different biochemical constitution (even an electronic one—cf. the aliens in Retief's War) could have minds.