Perdurance and slices

One of the main problems with perdurance is thought to be that it makes intrinsic properties be primarily properties of slices, and only derivatively of the four-dimensional whole.

The most worrisome case of this problem has to do with mental properties. For if our slices have the mental properties primarily, and we only have them derivatively, then that leads to a sceptical problem (how do I know I am a whole and not a slice?) and besides violates the intuition that we have our mental properties primarily.

But someone who accepts a perdurantist ontology and accepts the idea that we are four-dimensional wholes does not have to say that intrinsic properties are primarily had by slices. For a property that involves a relation to one’s parts can still be intrinsic (having one’s parts is surely intrinsic!). Now instead of saying that, say, Bob has temporary property P at time t in virtue of his slice B_t at t having P, we can say that Bob has P in relation to B_t. This is very similar to how relationalist endurantists say that we have our temporary properties in relation to times, except that times are normally thought of as extrinsic to the object, while the slices are parts of the objects.

In fact, this helps save some intuitions of intrinsicness. For instance, it seems to be an intrinsic property of me that my heart is beating. But if t is now and A_t is my slice now, then A_t does not seem to intrinsically have the property of heart-beat. It seems that heart-beat is a dynamical property dependent not just on the state of the object at one time but also at nearby times. Thus, if we want to attribute heart-beat to A_t primarily, then heart-beat will not be intrinsic, as it will depend on A_t as well as slices A_t′ for t′ near t. But if we see my present heart-beat as a property of the four-dimensional worm, a property the worm has in relation to A_t (as well as neighboring times), then heart-beat can be an intrinsic property—and it can be had primarily by me, not my slices.

It is plausible that mental properties are dynamical as well: that one cannot tell just from the intrinsic properties of a three-dimensional slice whether thought is happening. (This is pretty much certain given materialism, but I think is plausible even on dualism.) So, again, mental properties aren’t going to be intrinsic properties of slices. But they can be primarily the intrinsic properties of four-dimensional persons, had in relation to their slices.

On a twist on too-many-thinkers arguments

One of the ways to clinch a too-many-thinkers argument (say, Merricks’ argument against perdurantism, or Olson’s argument for animalism) is to say that the view results in an odd sceptical worry: one doesn’t know which of the many thinkers one is. For instance, if both the animal and the person think, how can you know that you are the animal and not the person: it seems you should have credence 1/2 in each.

I like too-many-thinkers arguments. But I’ve been worried about this response to the sceptical clinching: When the animal and the person think words like “I am a person”, the word “I” refers to the person, even when used by the animal, and hence both think the truth. In other words, “I” means something like: the person colocated with the the thinker/speaker.

But I think I have a good response to this response. It would be a weird limitation on our language if it did not allow speaker or thinker self-reference. Even if in fact “I” means the person colocated with the the thinker/speaker, we should be able to stipulate another pronoun, “I*”, one that refers just to the thinker/speaker. And it would be absurd to think that one not be able to justifiably assert “I* am a person.”

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.

Perdurance and consciousness

The standard perdurantist theory of consciousness is that the whole four-dimensional individual is derivatively conscious in virtue of the slices being non-derivatively conscious.

Here is a quick objection:

1. A human-type pain needs to last more than a nanosecond to be noticed.

2. A human-type pain needs to be noticed to exist.

3. So, a human-type pain needs to last more than a nanosecond to exist.

4. For an entity to host a pain that needs u units of time to exist, the entity needs to exist for u units of time.

5. A momentary slice exists for less than a nanosecond.

6. So, no momentary slice hosts a human-type pain.

(One can also try running a somewhat similar argument against presentism. There are interesting parallels between perdurantism and presentism.)

I think what the perdurantist needs to do is to deny 4, and hold that a momentary slice of the person is in pain because of what is going on with temporally neighboring slices. In other words, being in pain is not an intrinsic property of a momentary slice. Moreover, to avoid circularity or regress, our perdurantist has to say that the pain of a slice does not depend on the neighboring slices being in pain, but on some other state of the neighboring slices.

Thus, the view has to be that there have to be some more fundamental states of slices such that a slice is in pain in virtue of itself and its temporal neighbors being in those more fundamental states.

Corollary: A perdurantist must be a reductionist about qualia.

Many perdurantists are materialists and will be happy to embrace this corollary. But let’s think some more. If the conscious state of a momentary slice depends on the states of the slices and its neighbors, then the conscious states of momentary slices are not temporally (or otherwise) intrinsic. But now there are two problems. First, intuitively, conscious states are intrinsic. Indeed, they seem paradigms of intrinsic states. Second, the whole point of primarily attributing states to slices rather than to the four-dimensional whole was to solve the problem of temporal intrinsics. So once we see the conscious states as non-intrinsic, the motivation for attributing them to slices should disappear.

Thus, at this point it is very natural, I think, for the perdurantist to opt for a different theory of consciousness. Consciousness (and presumably the same thing goes for other mental properties) is a property of the four-dimensional whole, and it is had in virtue of the properties of slices—but non-conscious properties of slices. Whether this is plausible depends on how plausible it is to think consciousness is reducible to non-conscious states.

A theological argument for four-dimensionalism

One of the main philosophical objections to dualist survivalism, the view that after death and prior to the resurrection we continue existing as disembodied souls is the argument that I am now distinct from my soul and cannot come to be identical with my soul, as that would violate the transitivity of identity: my present self (namely, I) would be identical to my future self, the future self would be identical to my future soul, my future soul would still be identical to my present soul, and so my present self would be identical with my present soul.

(This, of course, won’t bother dualists who think they are presently identical with souls, but is a problem for dualists who think that souls are proper parts of them. And the latter is the better view, since I can see myself in the mirror but I cannot see my soul in the mirror.)

It’s worth noting that this provides some evidence for four-dimensionalism, because (a) we have philosophical and theological evidence for dualist survivalism, while (b) the four-dimensionalist has an easy way out of the above argument. For the four-dimensionalist can deny that my future self is ever identical with my future soul, even given dualist survivalism. My future self, like my present self, is a four-dimensional temporally extended entity. Indeed, the future self and the present self are the same four-dimensional entity, namely I. My future soul, like my present soul, is a temporally extended entity (four-dimensional if souls have spatial extension; otherwise, one-dimensional), which is a proper part of me. And, again, my future soul and my present soul are the same temporally extended entity. At no future time is my future self identical with my future soul even given dualist survivalism. At most, it will be the case that some future temporal slices of me are identical with some future temporal slices of my soul.

Self-causation, persistence and presentism

Fido exists now because of various things Fido did a couple of minutes ago, such as breathe, pump blood with his heart, etc. So, it seems, Fido's existence is caused by Fido. But self-causation is absurd. So what's going on? Well, that depends on the theory of persistence.

Perdurantists and exdurantists have no problem at all. One temporal part causes another. There isn't even a whiff of absurd self-causation, either. Four-dimensionalist worm-theorists who don't believe in temporal parts can say that Fido doesn't cause his existence, but only aspects of his spatiotemporal dimensions. So on four-dimensional theories, we don't have absurdity.

But what about three-dimensionalist theories? Suppose Fido wholly exists at this time. Then it seems that all of Fido (now) is caused by Fido (five minutes ago), and that would be absurd. But that's not quite right. The eternalist or growing block three-dimensionalist can distinguish. Fido doesn't cause Fido's existing simpliciter. Fido only causes Fido's existing now. If we want more precision, we can say that Fido in virtue of existing five minutes ago causes himself to exist now. No problem, again.

That leaves the other three-dimensionalist option: presentism. And now we have a problem. According to presentism, to exist is to exist presently. Fido's present existence is (was? -- the tenses are hard to get right) caused by Fido. But that just means that Fido's existence is caused by Fido. And that's self-causation.

But perhaps we should take account of the sorts of things presentists say about the problem of transtemporal causation. Maybe it's not quite correct to say that Fido's existence is caused by Fido, but rather that Fido's existing is caused by Fido's having existed five minutes ago. Plus, talking like this makes causation a relation between states of affairs, and some will prefer that. But we still have a problem. For Fido's having existed five minutes ago is a state of affairs involving Fido. But it's absurd for Fido's existing to be caused by any state of affairs involving him, since Fido's existing is explanatorily prior to any state of affairs involving Fido.

Perhaps, though, the presentist can bring in Fido's haecceity H. Fido's existing is caused by H's having been instantiated five minutes ago. That is, I suspect, the presentist's best bet here. But there is a problem for that. For it sure seems like the state of affairs that caused Fido's present existence isn't a state of affairs of his haecceity having had something happen to it (say, being co-instantiated with respiration), but but it is the state of affairs of Fido having done certain things five minutes ago, like breathing. If it is states of affairs about haecceities that are causally relevant, then it looks like the things that are fundamentally involved in causation aren't particulars like Fido but are are abstracta like haecceities. And that's not right.

There is a direct argument here against presentism, too.

1. Fido's presently existing is caused by Fido's having existed five minutes ago.
2. If presentism is correct, Fido's presently existing is Fido's existing.
3. Fido's having existed five minutes ago is a state of affairs of which Fido is a constituent.
4. No state of affairs of which Fido is a constituent causes Fido's existing.
5. So, if presentism is correct, Fido's existing is caused by Fido's having existed five minutes ago. (1, 2).
6. So, if presentism is correct, Fido's existing is caused by a state of affairs of which Fido is a constituent. (3, 5).
7. So, presentism is not correct. (4, 6)

Thinking derivatively

In a lovely recent paper, Andrew Bailey has argued for the priority principle, that we think our thoughts not derivatively from another entity's thinking them--for instance, we don't think our thoughts derivatively from a brain's thinking them, or from a soul's thinking them, or a temporal part's thinking them, etc. I think this is all correct, but it seems to me that arguments of this sort don't go as far as they at first sight seem (this isn't a disagreement with anything Bailey writes).

For it has long appeared to me that the philosopher who is inclined to say that our thinking is derivative from the activity of a proper part of us should deny that the relevant activity of the proper part is thinking. Instead, there is some activity of the proper part which we might call "thinking*", and our thinking is derivative from the part's thinking*. For instance, a materialist might say that our brains think* (and analogously believe*, choose*, etc.), and that to think is to be a maximal organic whole that has a part that thinks*. This seems exactly right. For even if materialism is true, our brains don't think, but we think with our brains. And what our brains do when we think with them isn't thinking, and the materialist shouldn't say it is. (Likewise, when I nail something with a hammer, it is I who nail and not the hammer that nails. Nonetheless, the hammer does something which we can call nailing*, and I nail with a hammer if and only if I stand in the right kind of complex relationship to a hammer's nailing*.)

Once we see things this way, it unfortunately undercuts various arguments that otherwise I would be quite fond of. For instance, Trenton Merricks has a wonderfully clever argument against temporal parts on the grounds that if I have many temporal parts, then I don't know my age, since most of my present temporal parts are younger than me, and yet they think the same thoughts about age as I do. But wonderful as this argument is, and correct as its conclusion is (I don't have any proper temporal parts), the temporal part theorist should (though generally doesn't) say that my proper temporal parts have no opinions as to age, but only opinions*.

Could one strengthen Bailey's priority principle and say that my mental properties are fundamental? That's too strong. Plausibly some mental properties are not fundamental but are grounded in others. Maybe, though, we can say that some mental property is fundamental? That sounds right to me, but it's hard to argue for.

A perdurantism without temporal parts

Standard perdurantism holds that we are four-dimensional worms made up of three-dimensional temporal parts. Many of the changing properties that we think of ourselves as having directly, we actually have derivatively from the temporal parts. Thus, I am typing a post in virtue of having a temporal part typing it up, and I am conscious of the screen in front of me in virtue of a temporal part of me being conscious of it.

Standard perdurantism has many problems, for instance:

1. Perdurantism commits one to proper parts, and implausibly thin and hyperplanar ones.
2. Surely I am that entity which is non-derivatively consciously rather than that entity which is derivatively conscious.
3. Perdurantism normally comes along not just with slices, but thicker temporal parts. But then Merricks argues that we cannot know how old we are. For all I know, I might be the temporal part from five minutes ago until now (in which case I am five minutes old), or from ten minutes ago until now (in which case I am ten minutes ld), and so on. Only a handful of temporal parts containing my present stage have the age I think myself to have, so probably I don't have the age I think myself to have.

There is, however, a perdurantism without any of these problems, if one accepts the right kind of trope theory. Suppose I exist at t. Then my existing at t is a trope of me, call it e_t. At least unless t is the first moment of my existence, e_t is an accidental trope: if I perished before t, then I wouldn't have had e_t. (If essentiality of origins holds, then it is an essential property of me that I exist at the first moment of my existence.) Note that I am not committing myself to the controversial thesis that existence is a property. Even if existence isn't a property, it is plausible that existence in a location—i.e., spatial locatedness at x—is a property. And if so, then why shouldn't temporal locatedness at t be a property?

I now suppose that I am a four-dimensional entity that has (where the "has" is not tensed) all of the e_t tropes (where t is a time during my existence): it is true to say that I exist at all these times. But many of the temporally qualifiable predicates, like "is conscious" and "is bent", that apply to me apply in virtue of e_t itself having certain tropes. Thus, I am now bent or conscious in virtue of e_now having a certain bendedness or consciousness trope.

Strictly speaking, it's not e_now that is bent or conscious, but it has the kind of trope which makes that substance that has the e_now trope be bent or conscious. Compare this: If I am gorging myself, then that happens in virtue of an eating trope itself having a gorging trope. But the eating trope isn't gorging itself. It is I who am gorging myself. So the gorging trope is a trope of eating such that any substance that has the eating trope with the gorging trope gorges itself. The gorging trope, thus, makes me—the substance—be a gorger and makes my eating trope be not a gorger, but gorgingly. This is linguistically tricky.[note 1]

On standard perdurantism, I persist over time in virtue of having temporal parts that exist at various times. On this trope perdurantism, I persist over time in virtue of having temporal locatedness tropes.

On this theory, the temporal locatedness tropes e_t play the role of the temporal parts of standard perdurance. But they aren't parts. So we aren't committed to parts, much less implausibly thin and hyperplanar ones.

We also do not have the problems in (2) and (3). For while I am conscious at t in virtue of e_t having a certain consciousness trope c_t, that consciousness trope doesn't make e_t be conscious. So while I am conscious in virtue of something other than me—namely, e_t—being a certain way, I am not conscious in virtue of something other than me being conscious. Thus, I do not derive my consciousness from the consciousness of anything else, and so I am non-derivatively conscious. I do derive my consciousness from something else being a certain way, but when that something else is a trope of me, that's quite innocent. Thus, (2) is not an issue here.

Nor is (3), for the obvious reason that a fusion of e_t-type tropes, even if there is such a fusion (which I very much doubt), doesn't think. It's substances that think, and they think in virtue of having certain tropes. The tropes don't think, and neither do their fusions.

I don't think this is the whole story. If I were seriously defending this story, I wouldn't say that I have the trope e_t directly. I might say that I have the trope e_t as a trope of my humanity, where my humanity may well be the only trope I have directly (see the paper of mine here).

I don't know if the above story is true. I am a bit sceptical of the thinness and hyperplanarity, as it were, of the e_t tropes—they don't seem to me to be very natural. And I am not 100% sure I want to commit to tropes. But this version of perdurantism might be true.

Note, also, a neat thing. Normally the perdurantist needs to argue why perdurance is preferable to exdurance. But I do not think there is any plausible trope exdurantism paralleling this trope perdurantism.

Objection: The trope e_t is a part of me, so this devolves to a more standard perdurantism.

Response: Maybe in some sense my tropes are parts of me. But they are different sorts of parts from the kinds of parts that standard perdurantism invokes. For tropes depend, at least for their identity, on that which they are tropes of. But the whole is constructed out of the temporal parts on standard perdurantism. So trope perdurantism reverses the order of grounding.

The importance of the future

It would be bad for me to permanently cease to exist in five minutes. But why? Suppose first a metaphysics of time on which there is no future, namely Growing Block or Presentism. On such a metaphysics there is no such thing as my future life, so how could it be bad for there to be a cessation of it?

Since the only tenable alternative to Growing Block and Presentism is Eternalism, the view that the past and future are real (oddly, there are no Futurists who think the future is real but deny the reality of the past), Eternalism is true.

Now, given Eternalism, we have a choice for three visions of our persistence through time. On one vision, Exdurantism, we are instantaneous stages that do not persist through time at all—at most we have temporal counterparts at other times. This does not fit with the intuition of my radical incompleteness should I cease to exist in five minutes. The second vision is Endurantism: I am wholly present at each time at which I exist. But then if the present moment is real, and eternally will be real, and I wholly exist at this present moment, then the intuition about the deep incompleteness I would have were my existence to permanently end in five minutes is undercut. So that can't be right either.

What remains is a family of views on which we are strung out four-dimensionally. The most common member of the family is Perdurantism: I am four-dimensional but have three-dimensional stages localized at times. A less common view is that I am four-dimensional, but not divided up into stages. Both of these views do justice to the idea that my existence is deeply incomplete, in something like the way it would be if I were missing an arm, should I cease to exist in five minutes.

As far back as I thought much about time (probably going back to age 10) I was an Eternalist. Until a couple of years ago, I was an Endurantist. Then I started being unsure whether Endurantism or a stageless four-dimensional view is right. The above argument strongly pushes me towards a four-dimensional view, and since I don't believe in stages, a stageless one.

Moreover, the above may help with a puzzle I used to have, which was how a B-Theorist should think about the badness of impending evils (especially death). How can a B-Theorist make sense of the badness of being closer and closer to something bad? But that may primarily be a problem for the Endurantist, since the Endurantist thinks we are three-dimensional beings wholly located in the here and now (as well as in the there and later, of course).

Instantaneous stages

Perdurantism holds that we either are four-dimensional entities, stretching like worms through spacetime, or temporal stages of these. Most worm-theorists also believe in temporal stages—they just do not identify us with the stages, but with the whole. (I myself am attracted to stageless worm theory.)

Now here is something that strikes me as a bit interesting. The founding intuition of four-dimensionalist theories is that there is a very close analogy between space and time, and four-dimensionalists pay a lot of attention to science. But, then, positing stages goes against the spirit of four-dimensionalism. For if we pay heed to the space-time analogy intuition, we would have to posit something analogous to temporal stages, stretched out through time the way temporal stages are stretched out through space. While temporal stages are three-dimensional (maybe with a bit of thickening), spatial stages would be one-dimensional (maybe with a bit of thickening), stretched out through time—basically cores cut from the worm along timelike curves. And just as the four-dimensional worm is made out of temporal stages, we would have to think of it as made out of the spatial stages.

But that would be mistaken. The only plausible way in which we could be composed of spatial stages would be if we were made of particles, and we could trace the trajectory of each particle through spacetime. But even if there are particles, the uncertainty principle makes the possibility of such tracing dubious. And quite possibly, physics will dispense with localized particles altogether.

Endurantism and perdurantism

For a long time, I was a B-theoretical endurantist. As a B-theorist, I did not believe there was an objective difference between past, present and future--only a difference relative to the speech act or mental act. I still hold to this. As an endurantist, I believed that I was wholly present at every given time at which I existed. Not a part of me, a slice of me, but the whole of me.

But now I see that I don't really have a very good objection to a perdurantism that says I am a four-dimensional entity, transcending particular times. Most perdurantists believe that there are temporal parts, slices of the four-dimensional entities that we are. But there is no need to believe that. Certainly, I don't believe that we have horizontal or vertical parts. If I have parts at all, they are parts like heart, leg, brain hemisphere, not neat slices along planes such as "my left half" or "my bottom third". I have no idea what the persistence conditions for "my left half" or "my bottom third" would be. Likewise, if I have temporal parts, they're going to be cut along natural cutting hyperplanes. But in fact, I doubt there are any natural cutting hyperplanes for temporal parts, except perhaps death where the soul separates from the body.

So if I opted for perdurantism, I would not believe in temporal parts or slices. I would think of myself as a single organic entity, stretched out in time.

There is something attractive about this view. It makes us be in time but also transcend particular times, since we're not contained in any time slice.

Moreover, this view escapes the following objection against endurantism: If we're wholly present at every time at which we exist, there is not much to that "whole". It's very "thin"--it's merely three-dimensional. But insofar as we're merely three-dimensional, we don't do very much--the lesson of Zeno's paradox of the arrow is that on a (three-dimensional) time-slice the arrow doesn't move, and there perhaps isn't much to us except insofar as we're moving. I think a presentist endurantist can overcome this worry, but an eternalist endurantist will have some trouble with it. But maybe I am confusing motion with activity here--contemplation is an activity which does not involve motion. So perhaps a three-dimensional entity can have activity without having motion, and then there will be a lot to it (there still won't be a lot to the arrow, but that's OK).

On the other hand, the perdurantist view may have some trouble with transsubstantiation. (That's just a hunch.) If the trouble can't be overcome, I'll stick to endurantism.