Time without anything changing

Consider this valid argument:

1. Something that exists only for an instant cannot undergo real change.

2. Something timeless cannot undergo real change.

3. There can be no change without something undergoing real change.

4. There is a possible world where there is time but all entities are either timeless or momentary.

5. So it is possible to have time without change.

Premises 1 and 2 are obvious.

The thought behind premise 3 is that there are two kinds of change: real change and Cambridge change. Cambridge change is when something changes in virtue of something else changing—say, a parent gets less good at chess than a child simply because the child gets really good at it. But on pain of a clearly vicious regress, Cambridge change presupposes real change.

The world I have in mind for (4) is one where a timeless God creates a succession of temporal beings, each of which exists only for an instant.

(I initially wanted to formulate the argument in terms of intrinsic rather than real change. But that would need a premise that says that there can be no change without something undergoing intrinsic change. But imagine a world with no forces where the only temporal entities are two particles eternally moving away from each other at constant velocity. They change in their distance, but they do not change intrinsically. This is not Cambridge change, for Cambridge change requires something else to have real change, and there is no other candidate for change in this world. Thus it seems that one can have real change that is wholly relational—the particles in this story are really changing.)

All that said, I am not convinced by the argument, because when I think about the world of instantaneous beings, it seems obvious to me that it’s a world of change. But even though it’s a world of change, it’s not a world where any thing changes. (One might dispute this, saying that the universe exists and changes. I don’t think there is such a thing as the universe.) This suggests that what is wrong with the argument is that premise (3) is false. To have change in the world is not the same as for something to change. This is more support for my thesis that factual and objectual change are different, and one cannot reduce the former to the latter.

Natural kinds across categories

Most philosophical discussions of natural kinds concern entities in the category of substance: particles, chemical substances, organisms, etc. But I think we shouldn’t forget that there is good reason to posit natural kinds of entities in other categories.

For instance, you and I are each engaging in a token activity that falls under the natural kind (say) mammalian breathing. The natural kind specifies some essential properties of the kind, namely that it is a kind of filling and/or emptying of the lungs, as well as some teleological features, such as that the filling and emptying should be rhythmic. Instances of the kind may be better or worse: given that I am congested after a long drawn-out cold, likely your breathing is better than mine.

There are, plausibly, such things as natural activities, which fall under activity natural kinds. These may kinds may include gravitational attraction, mating, fish respiration, etc.

Dispositions, too, may fall under natural kinds, indeed a nested sequence of them. We might say that some dispositions are habits, and some habits are virtues. Thus, perhaps, you and I each have a certain disposition to rationally withstand danger, a disposition that is a token of courage, a kind of virtue. Your and my courages are different: for instance, perhaps, I am more willing to withstand social danger while you are more willing to withstand physical danger. Whether indeed virtues are natural kinds seems to me to be a central question for the metaphysics of virtue ethics.

There may be natural kinds of relations, too. Thus, I think marriage is a natural kind. On the other hand, I think presidency is not.

Immortality of the soul and the soul's proper operation

This is an attempt to make an argument for the natural immortality of the soul from the premise that the soul has a proper operation that is independent of the body. The argument is going to be rather odd, because it depends on my rather eccentric four-dimensionalist version of Aristotelian metaphysics.

Start with the thought of how substances typically grow in space. They do this by causing themselves to have accidents in new locations, and they come to exist where these new accidents are. Thus, if I eat and my stomach becomes distended, I now have an accident of stomachness in a location where previously I didn’t, and normally I come to be partly located where my accidents are.

It is plausible (at least to a four-dimensionalist) that spatiotemporal substances grow in time like they grow in space. Thus, they produce accidents in a new temporal location, a future one, and typically come to be located where the accidents are—maybe they come to be there by being active in and through the accidents. (There are exceptions: in transsubstantiation, the bread and wine don’t follow their accidents. But I am focusing on what naturally happens, not on miracles.)

Suppose now that the soul has a proper operation that is independent of the body. Given the fact that my intellectual function is temporal in nature, it is plausible that in this proper operation, my soul is producing a future accident of mine—say, a future accident of grasping some abstract fact—and does so regardless of how sorry and near-to-death a state my body has. But a substance normally stretches both spatially and temporally to become partly located where its accidents are. So by producing a future accident of mine the soul normally ensures that I will be there in that future to be active in and through that accident. Thus the soul, in exercising that future-directed proper activity, makes me exist in the future.

Now that I’ve written this down, I see a gap. The fact that the soul has a proper operation independent of the body does not imply that the soul always engages in that operation. If it does not always engage in that operation, then there is the danger that if my body should perish at a time when the operation is not engaged in, the soul would fail to extend my existence futureward, and I would perish entirely.

On this version of the proper function argument, we thus need a proper operation that the soul normally or naturally always engages in. We might worry, however, that the intellectual operations all cease when we are in dreamless sleep. However, we might suppose that the soul by its nature always carries forward in time some aspect of the understandings or abstractions that it has gained, and this carrying forward in time is indeed a proper operation that occurs even in dreamless sleep, since we do not lose our intellectual gains when we are asleep. (We should distinguish this carrying forward of an aspect of the intellectual gains from the aspects of memory that are mediated by the brain. The need to do this is a weakness of the argument.)

The above depends on my idiosyncratic picture of persistence over time: substances cause their future existence. Divine sustenance is divine cooperation with this causation. The argument has holes. But I feel I may be on to something.

The argument does not establish that we necessarily are immortal. We are only naturally immortal, in that normally we do not perish. It is possible, as far as the argument goes, that the proper operation should fail to succeed in extending us into the future, if only because God might choose to stop cooperating in the way that constitutes sustenance (but I trust he won’t).

Events and the unreality of time

When I think about McTaggart’s famous argument against the A-theory of time—the theory that it is an objective fact about the universe what time it is—I sometimes feel like it’s just a confusion but sometimes I feel like I am on the very edge of getting it, and that there is something to the argument. When I try to capture the latter feeling in an argument that actually has a chance of being sound, I find it slipping away from me.

So for the nth time in my life, let me try again to make something of McTaggart style arguments. Last night I gave a talk at University of North Texas. When I gave the talk, it was present, and afterwards it became past, and every second that talk is receding another second into the past, becoming more and more past, “older and older” we might say. There is something odd about this, however, since the talk doesn’t exist now. Something that no longer exists can’t change anymore. So how can the talk recede into the further past, how can it become older and older?

Well, we do have a tool for making sense of this. Things that no longer exist can’t really change, but they can have Cambridge change, change relative to something else. Suppose a racehorse is eventually forgotten after its death. The horse isn’t, of course, really changing, but there is real change elsewhere.

More generally, we learn from McTaggart that events can’t really change, but can only change relative to real change in something other than events. The reasoning above shows that events can’t really change in their A-determinations. And they can’t change in their intrinsic non-temporal features, as McTaggart rightly insists: it is eternally true that my talk was about God and mathematics; all the flaws in the talk eternally obtain; etc. So if events can’t really change, but only relatively to real change elsewhere, and yet all of reality is just events, then there is no change.

But reality isn’t just events, and in addition to events changing there is the possibility for enduring entities to change. Here’s perhaps the simplest way to make the story go. The universe is an enduring entity that continually gets older. My talk, then, recedes into the past in virtue of the universe ever becoming older than it was when I gave the talk. (If one is skeptical, as I am, that there is such an entity as the universe, one can give a more complex story about a succession of substances becoming older and older.)

Can one run any version of the McTaggart argument against a theory on which fundamental change consists in a substance’s changing rather than in the change of events? I am not sure, but at the moment I don’t see how. If a person changes from young to old, we have two events: their youth A and their old age B. But we can now say that neither A nor B changes fundamentally: A recedes into the past because of the person’s (or the universe’s) growing old.

If this line of thought is right, then we do learn something from McTaggart: an A-theorist should not locate fundamental change in events, but in enduring objects.

Some finitisms

I’m thinking about the kinds of finitisms there are. Here are some:

1. Ontic finitism: There can only be finitely many entities.

2. Concrete finitism: There can only be finitely many concrete entities.

3. Generic finitism: There are only finitely many possible kinds of substances.

4. Weak species finitism: No world contains infinitely many substances of a single species.

5. Strong species finitism: No species contains infinitely many possible individuals.

6. Strong human finitism: There are only finitely many possible human individuals.

7. Causal finitism: Nothing can have infinitely many items in its causal history.

8. Explanatory finitism: Nothing can have infinitely many items in its explanatory history.

I think (1) and (2) are false, because eternalism is true and it is possible to have an infinite future with a new chicken coming into existence every day.

I’ve defended (7) at length. I would love to be able to defend (8), but for reasons discussed in that book, I fear it can’t

I don’t know any reason to believe (3) other than as an implication of (1) together with realism about species. I don’t know any reason to believe (4) other than as an implication of (2) or (5).

I can imagine a combination of metaphysical views on which (6) is defensible. For instance, it might turn out that humans are made out of stuff all of whose qualities are discribable with discrete mathematics, and that there are limits on the discrete quantities (e.g., a minimum and a maximum mass of a human being) in such a way that for any finite segment of human life, there are only finitely many possibilities. If one adds to that the Principle of the Identity of Indiscernibles, in a transworld form, one will have an argument that there can only be finitely many humans. And I suppose some version of this view that applies to species more generally would give (5). That said, I doubt (6) is true.

Even more on pointy beginnings

In a recent post I argued that in Aristotelian substantial change, given special relativity, the resultant substance starts as basically a point—it is arbitrarily small.

I think the argument doesn’t actually require much in the way of Aristotelian assumptions, but works for any caused extended substance, or at least any ordinary one.

Suppose that a substance B is caused to exist by A (which might be a single entity or a plurality) and initially (at least) at distinct points in spacetime. There is a reference frame according to which one of these points is earlier than the other (this is true in all frames if the points are timelike-related and some frames if they are spacelike-related). Let F be a frame where this happens, and let z₁ be the F-earlier and z₂ the F-later point. From now on, work in F.

Let t_i be the time of z_i. Now B is at least partly present arbitrarily close to z₁, and hence arbitrarily close to t₁, and since t₁ < t₂, it follows that B already existed before t₂. Therefore, any causal influence of A sufficiently close to time t₂ is irrelevant to B’s existence. In fact, B wasn’t even partly caused by A to exist at times close to t₂, since it had already existed for a while before this. And this contradicts our assumption that A caused B at both z₁ and z₂.

A crucial assumption here is that nothing that happens later than a time t is relevant to whether a substance B exists at t.

What if there is backwards causation? If so, then this argument fails. But even if there is backwards causation, it is rare and extraordinary. It is still true that in ordinary cases, substances are caused to exist at a single point.

What if B is uncaused? Again, the argument fails. But even if there are uncaused extended substances, they are not the norm. So, again, the argument still works in ordinary cases.

Matter and distinctness of substance

According to Aristotelianism, the distinctness of two items of the same species is grounded in the distinctness of their matter. This had better be initial matter, since an item might change all of its matter as it grows.

But now imagine a seed A which grows into a tree. That tree in time produces a new seed B. The following seems possible: the chunk of matter making up A moves around in the tree, and all of it ends up forming B. Thus, A and B are made of the same matter, yet they are distinct. (If one wants them to be at the same time, one can then add a bout of time-travel.)

Probably the best response, short of giving up the distinctness-matter link (which I am happy to give up myself), is to insist that a chunk of matter cannot survive substantial change. Thus, a new seed being a new substance must have new matter. But I worry that we now have circularity. Seed B has different matter from seed A, because seed B is a new substance, which does not allow the matter to survive. But what makes it a new substance is supposed to be the difference in matter.

Substances and their existences

I used to think that:

1. x is a substance just in case  <x exists> is not grounded in any fact about any other entity other than x.

But it is plausible that a finite creature’s existing is its being created. And that Alice is created seems to be grounded in God creating Alice, which seems to be a fact about God.

There is a nice response to this worry. On standard medieval views, creation is a one-way relation. When God creates Alice, there is a relation of being-created-by-God in Alice but no relation of creating-Alice in God. We can say, then, that in an important sense the fact that God creates Alice is not a fact about God, but about Alice, where we say that a fact is about x provided the fact is in part a fact of x’s existing or there being some property or relation in x.

It’s interesting that the very plausible account (1) of substance combined with a theistically plausible view that the esse of a finite thing is its being-created yields the rather abstruse one-way relation thesis.

This line of thought does not, however, fit well with the claim that I made in The Principle of Sufficient Reason that for a caused entity, its esse is its being caused. For Alice is also caused by her parents. And while divine causation may be a one-way relation, it seems unlikely that creaturely causation is.

There are three ways out of this worry. (i) We could say that creaturely causation is also a one-way relation. (ii) We could say that I was slightly wrong, and for a caused entity, its esse is its being primarily caused, i.e., caused by God. (iii) We could modify (1) to:

2. x is a substance just in case  < x exists> has a grounding in a fact that is neither about any entity other than x nor grounded in a fact about any entity other than x.

For we can then say that while Alice’s being-caused is grounded in her parents’ activity, which is a fact about her parents, it is also grounded in God’s causing Alice, which is not a fact about God in the sense of being grounded in a relation or property of God’s.

I like both (ii) and (iii). What is especially attractive about (ii) is that if the esse of Alice is her being caused, then the esse of Alice is highly disjunctive, being multiply grounded—in God’s causing Alice, in her parents causing her, in her parents’ gametes causing her, maybe even in her grandparents’ causing her, etc. But it doesn’t seem right to say that Alice’s esse is highly disjunctive. So a focus on primary causation seems attractive. And I think—but without a careful examination—that the arguments in Principle of Sufficient Reason work with that modification still.

Transsubstantiation and magnets

On Thomistic accounts of transsubstantiation, the accidents of bread and wine continue to exist even when the substance no longer does (having been turned into the substance of Christ’s body and blood). This seems problematic.

Here is an analogy that occurred to me. Consider a magnet. It’s not crazy to think of the magnet’s magnetic field as an accident of the magnet. But the magnetic field extends spatially beyond the magnet. Thus, it exists in places where the magnet does not.

Now, according to four-dimensionalism, time is rather like space. If so, then an accident existing when its substance does not is rather like an accident existing where its substance does not. Hence to the four-dimensionalist, the magnet analogy should be quite helpful.

Actually, if we throw relativity into the mix, then we can get an even closer analogy, assuming still that a magnet’s field is an accident of the magnet. Imagine that the magnet is annihilated. The magnetic field disappears, but gradually, starting near the magnet, because all effects propagate at most at the speed of light. Thus, even when the magnet is destroyed, for a short period its magnetic field still exists.

That said, I don’t know if the magnet’s field is an accident of it. (Rob Koons in conversation suggested it might be.) But it’s comprehensible to think of it as such, and hence the analogy makes Thomistic transsubtantiaton comprehensible, I think.

The incoherence of Spinoza's mode ontology

According to Spinoza, I am a mode and God is the only substance. But I am not directly a mode of God. I am a mode of a mode of a mode of … a mode of God, with infinitely many “a mode of” links in between.

This is incoherent. It is an infinite chain with two ends, one being me and the other being God. But any infinite chain made of direct links has at most one end: it would have to be of the form 1:2:3:4:…, with one endpoint, namely zero. We can stick on another chain running in the other direction, like …:iv:iii:ii:i, and get the two ended sequence 1:2:3:4:…:iv:iii:ii:i. But this two-ended sequence is not a chain, because there is no connection between any of the arabic numbered nodes and any of the roman numbered nodes.

The composition of a substance

Start with this plausible observation:

1. Any part of me either is an accident of me or has an accident.

For consider this: my corporeal parts all have accidents of size, shape, color, etc. And my non-corporeal parts are my soul or form, as well as my accidents. My soul has accidents: such as the accident of thinking about this or that. And my accidents are my accidents.

Now, add this plausible thesis:

2. Any accident of a part of me is identical with an accident of me.

Thus, my arm’s being tanned is identical with my being tanned-in-the-arm. Further:

3. An accident of a thing is a part of that thing.

Given 1-3, we conclude the following:

4. Any part of me has at least one accident of me as a part.

For suppose that x is a part of me. Then by (1), x is an accident of me or has an accident. If x is an accident of me, then x has an accident of me, namely x itself, as an improper part. If x has an accident y, then y is a part of x by (3) and identical with an accident of me by (2), so once again x has an accident of me as a part.

Now the standard definition of composition is:

5. The xs compose y if and only if every part z of y has a part in common with at least one of the xs.

It follows from (4) and (5) that:

6. I am composed of my accidents.

For every part of me has one of my accidents as a part by (4), and that accident is of course an improper part of one of my accidents.

But (6) seems really wrong!

Thomas Aquinas has a nice way out of (6). One of my parts is my esse, my act of being, and my esse has no proper parts, and no parts in common with any of my accidents. If Aquinas is right, then it seems (4) needs to be modified to:

7. Any part of me is either my esse or has at least one accident of me as a part.

Replacing (4) with (7) in the argument, we get:

8. I am composed of my esse and my accidents.

But that seems wrong, too. For the omission of form is really glaring.

One could get out of (8) if one supposed that my form has its own esse as a part of it. But that doesn’t seem right.

My own view is that (8) may actually be correct if we stipulate “compose” to be defined by (5). But what that points to is the idea that “compose” is not rightly defined by (5).

Counting good and bad things

People sometimes wonder, perhaps in connection with the problem of evil, whether there is in total more good than evil in the world. The connection with the problem of evil is somewhat tenuous, of course. Even if it were agreed there is more good than evil, it could still be argued that there is gratuitous evil, inconsistent with the existence of God. And even if there is a God, there could presently be more evil than good, if, say, the evil is justified in connection with future good.

All that said, here is a question related to the question whether there is more good than evil:

• Are there more good things than bad things in the world?

I will argue that on two different takes on “things”, there are vastly more good things than bad—or even bad or neutral—things in the world as we know it. Even if we can generalize from the world as we know it, this still does not show that there is more good than evil: perhaps there are more goods, but the bad things are so very bad that the total evil is greater than the total good. Nonetheless, I think the answer has evidential bearing on the existence of God, because it would intuitively be at least a little bit more likely for there to be vastly more good things than bad or neutral things in the observed part of the world if God existed than if God didn’t exist.

On to the argument. On a first take, “things” are substances. Now, I think the best story about substance is a neo-Aristotelian one on which in the part of the world we collectively know, the substances are the organisms and the fundamental physical entities.

Now, our three best theories as to what the fundamental physical entities are is that they are:

1. particles,

2. global entities like fields and the wavefunction of the universe, or

3. particles and global entities.

Suppose that the correct answer is (a) or (c). Then in the known universe, the vast majority of substances are particles. There may be a lot of organisms in the world, but there are way more particles. And the number of global entities, like fields and the wavefunction, on our best theories is in the single digits. But every particle is good: it perfectly fulfills its nature, which is to dance its dance according to the beautiful mathematical laws of the universe. So, on (a) and (c), the vast majority of substances are good. (Maybe good in a very minor way.)

Suppose that the correct answer is (b). Then the substances of the known universe consist of organisms and probably a handful of global entities like fields or the wavefunction. The organisms outnumber the global entities so much that we can neglect the global entities and, besides, the global entities are good, for the same reason the particles are. Among the known organisms there are some that are bad. The clearest cases are a sizeable proportion of humans.

Whether there are any bad non-human organisms on earth (essentialy the only place we know of with organisms) depends on whether we count instrumental value. For if we limit ourselves to intrinsic badness, plausibly all organisms that aren’t persons are good (and there are many good persons), and non-personal organisms vastly outnumber personal ones. If badness (and goodness), however, includes instrumental assessment, then there are bad organisms. But how many? There may be some species most of whose members are bad: perhaps some mosquito species are like that. But it seems very plausible that such species form a very small portion of the whole, and that the vast majority of species are such that the vast majority of their members are good. (Quick thought experiment: Suppose by pressing a button you could wipe out a randomly chosen non-human species? Surely it would be a very, very bad idea to press the button.) So, it seems quite plausible that the vast majority of organisms are good.

On a second take, “things” include events in addition to substances. Well, now, the vast majority of events in the known universe seem to be purely physical events that are neither good nor bad for living things, and they do no harm to non-living things either. But they are an intrinsically good part of the dance of nature according to beautiful mathematical laws. So, it seems, the vast majority of events is good.

The evanescent world of becoming

An old idea in philosophy, going back to Plato, is that things that are becoming are less beings than things that are timeless. This is a mysterious view, but I have just found that my own preferred four-dimensionalism implies a clear and unmysterious version of this view.

On my preferred four-dimensionalism, material substances are four-dimensional entities. Since they are substances, they are explanatorily prior to any parts or accidents they may have. This four-dimensionalism, thus, cannot hold that four-dimensional entities are constructed out of three-dimensional time slices, or even that the slices are somehow ontologically on par with the four-dimensional substances.

Nonetheless, it makes sense to talk of a three-dimensional time slices as a kind of derivative entity.

It may, for instance, turn out to be like the Thomist’s “virtual entities”. The Thomist does not think that the electrons that help make up my body are substances, but thinks that our scientific language can be saved: the electrons “virtually exist” in virtue of my pattern of (accidental) causal powers.

Or it might even be that three-dimensional time slices just are accidents: that the four-dimensional entity that I am has an accident corresponding to every time at which it exists, an accident which itself is the bearer of further accidents. Thus, the fact that I have a certain three-dimensional shape s at a time t could be analyzed in terms of me having an existence-at-t accident E_t, and E_t in turn having an s-shape accident.

Virtual entities and accidents are unmysteriously less beings than substances: for them to be is to qualify a substance.

So, now, here is a reconstruction of the Platonic insight. A lot of our ordinary talk about material substances is most straightforwardly construed as about time slices rather than four-dimensional substances. When we talk of the shape of a flower, we mean its three-dimensional shape with respect to a particular slice, and so on. Now, we identify something like the Platonic world of becoming as the world of three-dimensional time slices. These are completely evanescent entities—they exist literally only for a moment each—and their being is derivative from the being of substances.

Presentists have long complained that four-dimensional entities are not really becoming. We can embrace an aspect of that insight. There is a way in which the four-dimensional entities form a world where time is less important. Granted, they indeed are spatio temporal entities: they do exist in time as well as in space. But there is little reason to think that their very being is somehow ontologically tied to time in the way that the presenists think the world of becoming is. On the other hand, the time slices are very much time slices: their very being is tied to their temporality.

Of course, this reconstruction of the Platonic insight into a world of becoming is in the end quite unfaithful to Plato: for we, who are four-dimensional substances, end up not being in the world of becoming, though we ground it. We are almost like Kantian noumena, grounding a world of becoming phenomena.

I don't know that the standard presentist can reconstruct the Platonist insight. For the standard presentist, to be is to be at present. The only difference between eternal things and things in the world of becoming is that eternal things were and will be in the same state, while things in the world of becoming were and/or will be in a different state. This is not a difference with respect to a way of being.

Aquinas and Descartes on substance dualism

Roughly, Aquinas thinks of a substance as something that:

1. is existentially independent of other things, and

2. is complete in its nature.

There is a fair amount of work needed to spell out the details of 1 and 2, and that goes beyond my exegetical capacities. But my interest is in structural points. Things that satisfy (1), Aquinas calls “subsistent beings”. Thus, all substances are subsistent beings, but the converse is not true, because Aquinas thinks the rational soul is a subsistent being and not a substance.

Descartes, on the other hand, understands substance solely in terms of (1).

Now, historically, it seems to be Descartes and not Thomas who set the agenda for discussions of the view called “substance dualism”. Thus, it seems more accurate to think of substance dualists as holding to a duality of substance in Descartes’ sense of substance than in Aquinas’.

But if we translate this to Thomistic vocabulary, then it seems we get:

3. A “substance dualist” in the modern sense of the term is someone who thinks there are two subsistent beings in the human being.

And now it looks like Aquinas himself is a substance dualist in this sense. For Aquinas thinks that there are two subsistent beings in Socrates: one of them is Socrates (who is a substance in the Thomistic sense of the word) and the other is Socrates’ soul (which is a merely subsistent being). To make it sound even more like substance dualism, note that Thomas thinks that Socrates is an animal and animals are bodies (as I have learned from Christopher Tomaszewski, there are two senses of body: one is for the material substance as a whole and the other is for the matter; it is body in the sense of the material substance that Socrates is, not body in the sense of matter). Thus, one of these subsistent beings or substances-in-the-Cartesian-sense is a body and the other is a soul, just as on standard Cartesian substance dualism.

But of course there are glaring difference between Aquinas’ dualism and typical modern substance dualisms. First, and most glaringly, one of the two subsistent beings or Cartesian substances on Aquinas’s view is a part of the other: the soul is a part of the human substance. On all the modern substance dualisms I know of, neither substance is a part of the other. Second, of the two subsistent beings or Cartesian substances, it is the body (i.e., the material substance) that Aquinas identifies Socrates with. Aquinas is explicit that we are not souls. Third, for Aquinas the body depends for its existence on the soul—when the soul departs from the body, the body (as body, though perhaps not as matter) perishes (while on the other hand, the soul depends on the matter for its identity).

Now, let’s move to Descartes. Descartes’ substance dualism is widely criticized by Thomists. But when Thomists criticize Descartes for holding to a duality of substances, there is a danger that they are understanding substance in the Thomistic sense. For, as we saw, if we understand substance in the Cartesian sense, then Aquinas himself believes in a duality of substances (but with important structural differences). Does Descartes think there is a duality of substances in the Thomistic sense? That is not clear to me, and may depend on fine details of exactly how the completeness in nature (condition (2) above) is understood. It seems at least in principle open to Descartes to think that the soul is incomplete in its nature without the body or that the body is incomplete in its nature without the soul (the pineal gland absent the soul sure sounds incomplete) or that each is incomplete without the other.

So, here is where we are at this point: When discussing Aquinas, Descartes and substance dualism we need to be very careful whether we understand substance in the Thomistic or the Cartesian sense. If we take the Cartesian sense, both thinkers are substance dualists. If we take the Thomistic sense, Aquinas clearly is not, but it is also not clear that Descartes is. There are really important and obvious structural differences between Thomas and Descartes here, but they should not be seen as differences in the number of substances.

And here is a final exegetical remark about Aquinas. Aquinas’ account of the human soul seems carefully engineered to make the soul be the sort of thing—namely, a subsistent being—that can non-miraculously survive in the absence of the substance—the human being—that it is normally a part of. This makes it exegetically probable that Aquinas believed that the soul does in fact survive in the absence of the human being after death. And thus we have some indirect evidence that, in contemporary terminology, Aquinas is a corruptionist: that he thinks we do not survive death though our souls do (but we come back into existence at the resurrection). For if he weren’t a corruptionist, his ontology of the soul would be needlessly complex, since the soul would not need to survive without a human being if the human being survived death.

And indeed, I think Aquinas’s ontology is needlessly complex. It is simpler to have the soul not be a subsistent being. This makes the soul incapable of surviving death in the absence of the human being. And that makes for a better view of the afterlife—the human being survives the loss of the matter, and the soul survives but only as part of the human being.

Two attempts at deriving internal time from the causal order of modes

It would be nice to define the internal time of a substance in terms of the causal order of its accidents.

For each mode (i.e., accident or substantial form) α that a finite substance x has, there is the event c_α of α’s being caused. Causal priority provides a strict partial ordering on the events c_α.

Perhaps the simplest theory of the internal time of the substance x is that the moments of internal time just are the events c_α and their order just is the causal priority order.

This has the consequence that internal time need not be totally ordered, since one can have cases where α ≠ β but there is no priority relation between c_α and c_β. This consequence is welcome and unwelcome. It is welcome, as it allows one to give a nice account of bilocation involving the bifurcation of internal time. It is unwelcome, as intuitively time is linear. Let’s see if we can do something to reduce the unwelcome consequence.

Let’s suppose—as per causal finitism—that causal interactions are discrete. Then we can define a fundamental distance between the moments of internal time: d(c_α, c_β) is the length of the longest unidirectional causal priority chain between c_α and c_β. One might reasonably hypothesize that d(c_α, c_β) is something of the order of magnitude of the temporal distance between c_α and c_β in the rest frame of the substance in units of the order of Planck time. (Note that d is not a metric because of the unidirectionality constraint on the chains.)

This lets us have a second way of defining the internal time of a substance x. Let f be x’s substantial form. Then we can define “the start time” of a mode α as d(f, α): the length of the longest internal causal priority chain from c_f to c_α. Now likely some modes will have a simultaneous internal start time—they will have the same distance to c_f.

For this to define an intuitively plausible time sequence, we need the substance to have lots of interconnections between its accidents. Ordinary substances do seem to have that.

And perhaps some accidents won’t have an internal start time—if God turns me blue right now, my blueness won’t have an internal start time. But nonetheless that blueness can be “attached” to my internal temporal sequence by noting that it will be close according to d to some of my near-future accidents. For that miraculous blueness will interact with some of my other accidents to produce new accidents that are properly in my middle age. For instance, it will interact with my memories of observations of things not turning blue to generate the accident of surprise.

Substances are not parts of substances

Here is a quick and simple argument for the Aristotelian axiom that substances are not parts of substances.

1. The parts of substances are at least partly grounded in the substances.

2. Substances are not even partly grounded in other things.

3. Therefore, substances are not proper parts of other substances.

I suppose (1) is probably just as controversial as (3).

Aristotelian metaphysics and global physics

Too much of the contemporary ontological imagination is guided by the idea that the fundamental physical stuff in the world is discrete particles. Yet this is clearly dubious, since quantum mechanics (on non-Bohmian interpretations) suggests that the world is full of superpositions of states with different numbers of particles, while if discrete particles really exist, there had better be a well-defined number of them. Quantum mechanics instead suggests an ontology of the physical world where there is exactly one entity, “the Global Wavefunction”, whose physical state can be aptly represented as a vector in an infinite-dimensional vector space. And even if we didn’t have quantum mechanics’ vector-based approach on the table, we still wouldn’t be in an epistemic position to know that the right physics is based on particles rather than fields.

An ontology of material objects that composes these objects out of particles is held hostage to a particle-based physics that may well not be true. It would be best if one could work on the ontology of material objects without presupposing an answer to the question whether fundamental physical reality is field-like, vector-like or particle-like. I do not know if this is tenable. If it’s not, then the ontology of material objects needs to be done conditionally: If fundamental physical reality is of this sort, then material objects are like this.

Interestingly, some metaphysical problems may become easier given a non-particulate physical substratum. For instance, one of the hardest problems for a contemporary Aristotelian metaphysics has been the problem of what happens to particles that get incorporated into a substance, in light of the axiom that a substance cannot be composed of substances. But if we do not see fundamental physical reality as made of apparently substantial particles, the problem dissolves.

Today I want to sketch two Aristotelian approaches that take globalized vector- and field-approaches seriously. On the vector- and field-approaches, fundamental physical reality consists of a mere handful of entities: a single vector-like entity or several (hopefully no more than a dozen, and ideally only one) field-like entities. But being Aristotelian, we will think there are at least billions of substances: every organism is a substance. If these substances are to be related to fundamental physical entities, billions of them will have to be related to the same fundamental physical entities.

The ordinary substances on my stories will be organisms. There are billions of them. In addition to the ordinary substances, there are extraordinary substances: one for each of the handful of fundamental physical entities (fields or a vector).

My stories now diverge. On the first story, the billions of ordinary substances each encode and ground local features of the global fundamental physical entities. On a field version of the story, you encode and ground the features that the global fields have where you are located and your dog encodes and grounds the features that the global fields have where your dog is located (I am less clear on how to describe the vector version). This is not enough. For there aren’t enough organisms in the universe to ground all of the richness of the global fundamental physical entities: too much of the universe is lifeless. Thus, I propose that there are additional substances located where the organisms are not, and the features of these substances ground the rest of the features of the global fundamental physical entities. One way to run this story is to say that there is one of these additional substances per global fundamental physical entity, and each grounds the features of its corresponding global fundamental phsyical entity away from organisms. These additional substances are like swiss cheese, with the holes being filled with organisms like people and dogs.

On this version of the Aristotelian story—which can be varied in a number of ways—the global fundamental physical entities are not metaphysically fundamental. They are grounded in the many substances of the world.

On the second story, the global fundamental physical entities are substances. They are global substances. These global substances interact with the ordinary substances (there are many ways to spell out this interaction). We can now identify the matter of an ordinary substance x either with x’s powers and liabilities for interaction with the global substances or with the plurality of these global substances qua interacting with x.

There are many options here. Much detail to be worked out. Some options may be inferior to others, but I doubt in the end we will come to a single clearly best option.

Gunk, etc.

If we think parts are explanatorily prior to wholes, then gunky objects—objects which have parts but no smallest parts—involve a vicious explanatory regress. But if one takes the Aristotelian view that wholes are prior to parts, then the regress involved in gunky objects doesn’t look vicious at all: the whole is prior to some parts, these parts are prior to others, and so on ad infinitum. It’s just like a forward causal regress: today’s state causes tomorrow, tomorrow’s causes the next day’s, and so on ad infinitum.

On the other hand, on the view that parts are explanatorily prior to wholes, upward compositional regresses are unproblematic: the head is a part of the cow, the cow is a part of the earth, the earth is a part of the solar system, the solar system is a part of the Orion arm, the Orion arm is a part of the Milky Way, the Milky Way is a part of the Local Group, and this could go on forever. The Aristotelian, on the other hand, has to halt upward regresses at substances, say, cows.

This suggests that nobody should accept an ontologically serious version of the Leibniz story on which composition goes infinitely far both downward and upward, and that it is fortunate that Leibniz doesn’t accept an ontologically serious version of that story, because only the monads and their inner states are to be taken ontologically seriously. But that's not quite right. For there is a third view, namely that parthood does not involve either direction of dependence: neither do parts depend on wholes nor do wholes depend on parts. I haven't met this view in practice, though.

Aristotelians shouldn't be presentists

A foundational commitment of Aristotelian philosophy is that all facts are grounded in what substances and features intrinsic to substances, namely forms and accidents, exist. But it is possible for the past to have been different without there being any difference in what substances and features intrinsic to substances presently exist. Therefore, the Aristotelian cannot equate present existence with existence.

In other words, Aristotelians cannot escape the standard grounding arguments against presentism.

Objection 1: A theistic Aristotelian can ground facts about the past in features of God (say, God’s memories).

Response: Only if God is mutable. And there are good reasons to believe that if God exists, he is immutable.

Objection 2: Past events affect present substances in various ways.

Response: There is a possible world with laws of nature similar to ours that starts at time 0 with nothing but two material causally isolated substances A and B (and God, if theism is true) that wiggle around in indeterministic ways. A month later, substance A ceases to exist (maybe God stops sustaining its existence), and no new substances come into existence. Now, in month 2, there is only one substance B. Since the two substances were causally isolated, substance B is not affected in its intrinsic features by anything that substance A did. Thus, the facts about how substance A used to wiggle about are not grounded in the intrinsic features of material substances in month 2. (If one says that we regain grounding when we take God’s intrinsic features into account, that will take us back to Objection 1.)

One might respond that complete causal isolation is impossible. But that’s not right. For imagine that, like in our world, causal influences cannot propagate faster than at the speed of light, and A and B start off one light-year apart, and while A perishes after a month, B perishes after six months. Then B is not going to be affected by A’s wiggles.

Objection 3: But maybe there has to be some kind of a metaphysical influence whereby all present substances are affected by all past substances.

Response: This is not plausible in light of the response to Objection 2. But let’s grant it. Then I transpose my argument to the future. Obviously, future contingent events don’t normally (apart from supernatural cases, like prophecy) affect how substances presently are. Hence even if we grant the mysterious metaphysical influence of past substances on present ones, we still have a problem about the future. That problem could be solved if we embraced an open future, as Aristotle did, but we shouldn’t follow Aristotle in that.

Can our cells be substances?

A standard Aristotelian principle says:

1. No substance is a part of another substance.

I was just struck by how (1) says less than it seems to. One interesting philosophy of biology question is whether our symbiont bacteria are part of us. But:

2. All bacteria are substances.

3. We are substances.

4. We are not bacteria.

5. So no bacteria are parts of us. (By 1-5)

This argument is fine as far as it goes. But there is a metaphysical possibility that its conclusion leaves open which it is easy to forget.

Let’s grant that our symbiont bacteria are not a part of us. But perhaps their matter is a part of us. In other words, maybe the bacteria are matter-form composites just as we are, but their matter is a part of our matter, whereas their form is not a part of us at all, and hence they as wholes are not parts of us. They merely overlap us in matter.

And the point can be generalized. Before I noticed this point today, I used to think that the Aristotelian commitment to (1) requires us to deny that our cells are substances. But (1) leaves open the possibility that our cells are substances whose matter is a part of us, while the cells as wholes are not parts of us.

I don’t really want to say this. I would like to supplement (1) with this principle which has generally been a large part of my reason for affirming (1):

6. The matter of one substance is never a part of another substance.

My reason for accepting (6) has been that the identify of the matter is grounded in its substance, and if the matter had its identity doubly grounded, it wouldn’t be one thing, but two, and so it wouldn’t be the same matter in each substance.

In fact, (6) is a special case of a stronger claim:

7. No two substances have any matter in common.

Here is an argument that establishes (7) directly. Start with this plausible thesis:

8. No two material substances have all of their matter in common.

But now if (7) is false, then it should be possible to have two plants that have some matter in common. We could further imagine that the non-common matter perishes, but both plants survive. If so, then we would have a violation of (8). So, it’s plausible that if (7) is false, so is (8).

Here is a different line of thought in favor of (7):

9. Matter is grounded in the accidents of a substance.

10. Two substances cannot have any accident in common.

11. If x is entity grounded in a and y is an entity grounded in b and a ≠ b, then x ≠ y.

12. So, two substances cannot have any matter in common.

So, all in all, while (1) leaves open the possibility of our cells and bacteria being substances and yet having their matter be a part of us, we have good reason to deny this possibility on other grounds.

It would be very neat if one could derive (1) from (7). From (7) we do directly get:

13. No substance with matter is a part of another substance.

But it would take more argument to drop the “with matter” qualifier.