Temporary intrinsics and internal time

The main problem the literature presents for eternalist theories is the problem of temporary intrinsics: how an object can have an intrinsic property at one time and lack it at another.

The most common solution is perdurantism: four-dimensional objects have ordinary properties derivatively from their instantaneous temporal parts or slices having them, and since the slices only exist at one time, the properties can be as intrinsic as one likes.

Another solution that has found some purchase is a view on which the properties that we previously thought were intrinsic, such as shape and charge, are in fact fundamentally relational, defined by a relation to a time. Thus, to be square is to be square at some time or other. This results in a more commonsense ontology than perdurantism, but it has the problem of just denying that there are temporary intrinsic properties.

This morning it’s occurred to me that if we say that substances carry with them an internal time sequence that is intrinsic to them, then relationalism can admit temporary intrinsic properties. A property of a substance, after all, can be intrinsic even if the property is relational, as long as the relations that the possession of the property is grounded in are intrinsic to the object, say by being relations between parts or other metaphysical components of that object. After all, shape is seen as the paradigmatic case of an intrinsic property, and yet it is often seen as grounded in the relations between the particles making up an object. But on a view on which substances carry an internal time sequence, the internal times can be taken to be intrinsic aspects of the substance, and then ordinary properties can be seen as relational to the these internal times. Thus, to be square is more fundamentally to be square at some internal time or other.

What kinds of intrinsic aspects of the substance are the internal times? Here, there are multiple options. They could be sui generis aspects of the substance. They could be tropes—for instance, if substances all have beginnings, one could identify a time with the trope of having survived for a temporal duration D.

Internal times could even be time slices of the substance. This last option may seem to take us back to perdurantism, but it does not. For it is one thing to say that I am in pain because my temporal part ARP_t is in pain—it sure seems implausible to say that I am in pain derivatively from something else being in pain—and another to say that my being in pain is constituted by a relation to ARP_t, which part is in no pain at all. (That pain is constituted by a relation between the aspects of a substance is not at all strange and unfamiliar as a view: a materialist may well say that pain is constituted by relations between neuronal activities.)

Note, too, a view on which intrinsics are relational to internal times also solves another problem with views on which ordinary properties are relational to times: if those times are external, then time travel to a time at which one “already” exists is ruled out.

My own preferred view is that a nested trope ontology. I have a trope of being human. That trope then has an infinite number of temporal existence tropes, corresponding to all the different internal times at which I exist. These temporal existence tropes—or maybe even temporal human existence tropes—are then the internal times. And I can even say what the relation that makes a temporary intrinsic obtain at a temporal existence tropes t is: that temporary intrinsic obtains at t provided that it is a trope of t.

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.

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 reversed adverbial account of temporary intrinsics

It seems that I am bent and straight. Minutes earlier, when I was standing up, I was straight. Right now, however, I am sitting and writing this post, bent at an ergonomic 135 degrees. But no one can be both bent and straight. The presentist has no problem here: I am bent, but I was straight. Eternalists, however, have to work harder to remove the appearance of contradiction. One of the stock solutions is adverbial:

• I am straight at t₁ and I am bent at t₂.

I am not fond of the adverbial solution. After all, just as it is a contradiction to be standing still and running, it is a contradiction to be standing still patiently and running calmly. It is not clear why adding adverbs to contradictory predicates should remove a contradiction, unless the adverbs are truth-canceling or alienans ("I am bent and straight" is contradiction, but if I qualify "bent" with the truth-canceling adverb "apparently", the contradiction disappears). And positing truth-canceling adverbs all over the place is unattractive.

But there is a reversed adverbial account. Rather than taking the temporal qualification as the adverb, one can turn it into a predicate and turn the apparent predicate into an adverb. Thus:

• I exist at t₁ straightly and I exist at t₂ bently.

All appearance of contradiction disappears. There is no more contradiction here than in thinking quickly and running slowly, or eating elegantly and writing sloppily.

An ontology that naturally corresponds to this resolution is a nested mode ontology. I have a mode of presence at t for every time t at which I exist. (This mode might be directly an accident of me, though I prefer the view that it is a mode of my human nature.) Each of my temporary intrinsics then corresponds to a mode of the mode of presence at t.

A problem for my view of change

I think that claims like "x is green at t" should receive a relational analysis, like: GreenlyOccupies(x, t).  I also think this can be independently motivated: we need the relation of greenly occupying for other reasons and cannot reduce it to a monadic greenness, so the Ockhamly thing to do is to reduce greenness to greenly occupying.

But here is a hitch.  If x is green at t and non-green at t*, then how has x changed?  It seems that both at t and at t*, x greenly occupies t and fails to greenly occupy t*.  Granted, we might say that x is green at t and non-green at t*.  But on the view in question, being green or being non-green are not real properties.  So there seems to be no real change.  If there is a real property in view, it's being green at t and being non-green at t*. But it is always the case that x has both of these properties.  For every time t**, x is green at t at t**, and x is non-green at t* at t**.

Should this bother me?  Perhaps not.  I have a reductive analysis of accidental change.  Accidental change between two times is just standing in a relation to one time and not standing in that relation to another time.

But that doesn't seem right.  For instance, let's say that I am interested in the year 1716 (why? because I'd like to figure out what was going on in Leibniz's mind in that year given his correspondence with Des Bosses and Masson).  Then I stand in a relation of being deeply interested in to 1716, but I do not stand in the relation of being deeply interested in to 1715.  So on the view just offered, I have accidentally changed between 1715 and 1716.  But I didn't exist then, so I didn't change then.

Maybe I can rule out this case as follows.  The relation of being deeply interested in is a Cambridge relation in respect of its second relatum--1716 is no different for my being interested in it.  So perhaps accidental change between two times requires standing in a relation to one time and not to another, where the relation is non-Cambridge in respect of either relatum (it's easy to see that it also shouldn't be a Cambridge relation in respect of the changer).

But that may not be right either.  Suppose that times are constituted by the events that happen at them.  (A kind of Aristotelian view.)  Suppose in 2004, and only in 2004, there is an intense flurry of excitement about Leibniz's correspondence with Masson.  Then Leibniz stands in the relation of having caused an intense flurry of excitement in to the year 2004, but not to the year 2005.  Causing is a non-Cambridge relation in respect of either relatum, and since years are constituted of the events that stand in the causing relation, it seems that this relation is non-Cambridge in respect of the year, too.  But while Leibniz may have changed between 2004 and 2005 (e.g., in heaven, he may have come to a greater love of God), his being the cause of an intense flurry of excitement in 2004 but not in 2005 is not sufficient for change.

At this point, the unsatisfying state of affairs is that some relations imply change and some don't.  Greenly occupying 2004 but not 2005 does imply change.  Causing an intense flurry of excitement in 2004 but not 2005 does not imply change.

Interestingly, the relation of having caused an intense flurry of excitement in is actually a ternary relation.  Thus, we might say that in 1716, Leibniz caused an intense flurry of excitement to happen in 2004 (viz., by writing the letter to Masson): it is a relation between a substance (Leibniz) and two times (1716 and 2004).  And a difference between times in respect of the first temporal relatum (the one filled by 1716) does imply change, while a difference between times in respect of the second temporal relatum (the one filled by 2004) does not: if in 1715 Leibniz did not cause an intense flurry of excitement to happen in 2004, but in 1716 he did, then he changed between 1715 and 1716.  This means that we can't simply distinguish between relations and say some give rise to change and some don't.  For there are relations R such that R(x,t,u)&~R(x,t*,u) implies change in x but R(x,t,u)&~R(x,t,u*) does not.  What we need is some way of saying in respect of which pair of relata the relation gives rise to change.

The presentist has a nice story here.  She can say that the property of presently causing an intense flurry of excitement in 2004 is a non-Cambridge property, albeit a non-intrinsic one, and that Leibniz has this property at one time and doesn't have it at another.  But the kind of B-theorist that I am interested in does not say that: she just has a ternary relation of ___ in ___ causing an intense flurry of excitement in ___.

Now, it is true that the presentist's story does make use of the notion of a non-Cambridge property, a difficult notion to explicate that probably has to be made primitive.  Vaguely speaking, a non-Cambridge property is one that a thing has in part because of how it presently is.  Maybe the B-theorist can also primitively talk about a relation that an entity stands in in part because of how the entity is at one of the temporal relata of that relation.

Maybe, though, instead of talking about what it is to change, we should just talk about what it is to change in respect of some relation.  And that the B-theorist may be able to do.

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.

Two problems of temporary intrinsics

I've been thinking about the problem of temporary intrinsics and don't see much of a problem.  There are two kinds of ways of formulating the problem, and I think they are basically different problems, and neither is particularly compelling.


Formulation 1:

1. Socrates at t0 is bent.
2. Socrates at t1 is straight.
3. Socrates at t0 = Socrates at t1
4. So, Socrates at t0 is bent and is straight.  (Which is absurd.)

I think this is a linguistic paradox rather than a metaphysical problem, and hence deserving of being linguistically defused.  "Socrates at t0 is bent" is awkward English.  The normal word order is "Socrates is bent at t0."  But if we rephrase (1) this way (and (2) analogously), the argument becomes invalid.  Nothing untoward follows from Socrates being bent at t0 and Socrates being straight at t1.  All that follows is that he is bent at t0 and straight at t1.

For the argument to be valid, we need to parse (1) as: "Socrates-at-t0 is bent", and (2)-(4) analogously.  But what is this Socrates-at-t1?  Suppose we say that it's just Socrates under another name.  Then we should deny (1), since Socrates isn't bent--he's dead (unless by "is bent" we mean "is bent at some time or other", in which case (4) tells us that "Socrates-at-t0 is bent at some time or other and is straight at some time or other", which is unproblematic).  Of course, if "Socrates-at-t0" is just another name for Socrates, we can say "Socrates-at-t0 is bent at t0".  But no untoward consequences follow from the claims that Socrates-at-t0 is bent at t0 and that Socrates-at-t1 is straight at t1.  We end up saying that Socrates-at-t0 is straight at t1, which sounds weird, but that weirdness only comes from this weird "Socrates-at-t0" name we've used.  It's like the weirdness of saying: "Ivan the Terrible was actually a pretty nice kid" (which for all I know is true).

I think what is going on here is this.  We sometimes speak in the historical present with a contextually implicit time.  We say things like: "September 1, 1939.  Germany invades Poland.  The Polish defenses crumble."  The two sentences following the contextual introduction of September 1, 1939 are to be understood as saying that Germany invades Poland and the Polish defenses crumble on that date.  We do the same thing spatially.  For instance, we can be describing the course of the (imaginary) Borogove River which comes from Oklahoma to Texas.  We've just described it in Oklahoma.  We now say: "Texas.  The Borogove is very silty."  We mean that it is silty in Texas.  In the case of "Socrates-at-t0", the "-at-t0" determines the context of evaluation for the historical present "is bent."  So all we are saying is that Socrates-at-t0 is bent at t0.  And no paradox ensues.

Now, there is another reading.  We sometimes adopt a metaphor of a individual being split into multiple individuals, either by means of time or role.  Thus we say things like:

5. Late Plato disagrees with Middle Plato on whether all the serious problems of philosophy are solved by positing the Forms.
6. Smith the Rhetorician loves this argument, but Smith the Philosopher hates it.

When we adopt this fiction, we do not allow intersubstitution--that would be inappropriate mixing of metaphor with reality, like when someone says that the lights came on for her after she read so-and-so's paper and we ask if they were incandescent or fluorescent.  In other words, on this metaphorical reading of (1) and (2), we will reject (3).

Granted, the perdurantist can take "Socrates-at-t0" and "Socrates-at-t1" to literally refer to two entities, and then reject (3).  But that kind of metaphysics is not at all required by the argument.

So, in the first formulation, the argument can be defused purely on linguistic grounds.  This point applies also to my favorite formulation of the problem:

7. The young Socrates is ignorant.
8. The old Socrates is wise.
9. The young Socrates is the old Socrates.
10. So the young Socrates is wise and the old Socrates is ignorant.

Formulation 2:

11. Presentism is true or the application of a temporarily applicable predicate to x is never correctly explained in terms of x's instantiation of a non-relational monadic property whose choice is dependent only the predicate (and not on the time of application).
12. The predication of shape (say) predicates is correctly explained in terms of the object's instantiation of corresponding shape properties.

Notice that while the first formulation could grip a non-philosopher, (11) is simply a constraint on philosophical theories of predicate application.  There seems to be very little cost in denying (12) and its parallels, since (12) and its parallels simply do not state any sort of ordinary intuition--they are a substantive claim about how to explain predication.