Transsubstantiation and the conversion of bread into Christ's body

One of the philosophical challenges of Aquinas’ account of transsubstantiation is his insistence that the bread and wine are not merely annihilated and replaced by Christ’s body and blood, but that they are changed into Christ’s body and blood.

Now, it is easy to see how bread could be changed into a part of Christ’s body. That routinely happened when Christ ate bread in his earthly life. But Aquinas thinks that Christ is wholly present in the Eucharist, so that can’t be the account. But it is very puzzling what it would mean for an item B to be changed into an individual item C that already existed prior to the change. What would it mean, for instance, for the chair I am sitting on to change into the laptop I am typing this on? It is easy to imagine God moving the fundamental particles of the chair into positions such that they constitute a laptop. But that would be a case of the chair changing into a second laptop, not into the laptop that I am typing this on. Indeed, it seems like it’s impossible for something to change into something that already exists, simply because the thing already exists.

Aquinas is well aware of this objection, and has a fascinating response:

A form cannot be changed into another form, or one [designated] matter into another [designated] matter, by the power of a finite agent. However, such a conversion can be effected by the power of an infinite agent, which has an action on the whole entity. For the common nature of being belongs to each form and to each [designated] matter, and the author of being (auctor entis) is able to convert what there is of being in the one (id quod entitatis est una) into what there is of being in the other (id quod est entitatis in altera), by removing that by which it was distinguished from the latter.

Here is what I think is going on. Like many other philosophers before and after him, Aquinas thinks that individual objects need something whereby they are individuated—something that distinguishes them from other things. The project of figuring out what individuates things from other things is indeed a major part of Aristotelian metaphysics. Aquinas’ point seems to be this. God wields a very fine scalpel at the level of being, a scalpel so infinitely sharp that no finite being can wield it. That scalpel allows God to slice off an individual B that which distinguishes B from an individual C. When God slices that off, B literally loses its identity, and becomes C, as there is then nothing whereby B can be distinguished from C. (That God has such a fine scalpel is also indicated by the way that in the Eucharist he can slice a substance away from its accidents, and have the accidents remain without the substance.)

Let’s explore this account. First note that it seems to commit Aquinas to a different account of the individuation of material objects from his usual one. Aristotelians normally think that material objects are distinguished either by having different forms or, when the form is the same, by having different matter. Now, the bread on the altar and the body of Christ do have different forms: one is bread and the other is a human body. So on the usual Aristotelian account of what makes the bread different from the body of Christ, it is the bread’s bready form. But slicing away the bready form does not turn the bread into the body of Christ, or indeed into any human body. It just turns the bread into a formless lump of matter.

Perhaps we should suppose, however, that there is more than just literal removal going on. Maybe what happens is that God removes the bready form and replaces it with the form of the human body. But great as that miracle would be, that would just turn bread into a human, not into this human, Jesus Christ.

What if we suppose that God removes the bready form and replaces it with the form of Jesus Christ (namely, the soul of Jesus Christ)? But now the bread is simply becoming a new part of the body of Christ (in a miraculous verison of the way that the bread you may have for lunch may become new cells in you), and so only a part of Christ is present in the Eucharist.

But perhaps what I have described doesn’t slice away enough. Suppose the following happens. God slices the bready form away from the bread. That still leaves the bread’s matter. And the matter of the bread is distinct from the matter of Christ’s body. God continues removing the grounds of distinctness. He wields his infinitely sharp scalpel and carefully removes that in the matter of the bread which makes it be distinct from the matter of Christ’s body. The result is that that now the matter of the bread is not distinct from the matter of Christ’s body. Indeed, the matter of the bread literally converts into the matter of Christ’s body, not merely a new part of Christ’s body.

A major problem with this interpretation is that the form of bread is annihilated, whereas Thomas thinks the form of bread is also converted into the form of Christ’s body (admittedly with a qualification; see ST III.75.A6repl2 for details).

But perhaps we should make another move. Suppose that we have a non-Aristotelian account of individuation that works as follows: for any two created things, B and C, there is a relation that B has to C that individuates B from C and a relation that C has to B that individuates C from B. We can imagine each created thing having a vast number of labels. Somehow Alice has written into her being “I am not Bob” and “I am not Seabiscuit” and “I am not Oak Tree #18289”, and Bob has written into his being “I am not Alice” and “I am not Seabiscuit” and “I am not Oak Tree #18289”. This relational account of individuation does not require form or matter. It is not very Aristotelian. But it has a great theological merit: it makes the individuation of creatures be an image of the individuation of persons in the Trinity, which also proceeds (according to Western Christians) by opposed relations. Now imagine that God slices off of Alice the label “I am not Seabiscuit.” Instantly, Alice is converted into Seabiscuit. (Of course, it’s not right to say that Alice is Seabiscuit now. In this respect, it’s like when Bucephalus turned into a cadaver: Bucephalus and the horse-shaped cadaver are distinct entities.)

The exegetical problem with this interpretation is that it forces one to reject the standard Aristotelian story about individuation across species being by form and within a species being by matter. Instead, individuation is always by “individuating relations”. I am happy with this, because I never liked the standard Aristotelian story. But it makes it unlikely that the story is what Thomas has in mind.

But suppose one wants this to be more Aristotelian. Here is a way to do this. Take the orthodox Aristotelian account that across species individuation is by form and within species by matter. This account leaves unanswered the question of what makes a human form and a horse form different, as well as the question of what makes Peter’s matter different from Paul’s matter. Suppose we answer these questions by the relational account, thereby combining the Aristotelian account with the relational. Thus, a human form has (perhaps primitive) distinctness relations to all other kinds of forms, and Peter’s matter has a (perhaps primitive) distinctness relation to all other chunks of matter.

We can now imagine the following happening. There is bread on the altar. At the moment of consecration, God (a) removes from the bready form that which distinguishes it from a human form and (b) removes from the bread’s matter that which distinguishes it from Christ’s matter. Step (a) ensures that now the bread has human form, while step (b) ensures that the human form is that of Christ, since within a species the numerical distinction of forms is due to matter.

This last account is quite Aristotelian, and only requires that we go one step further than Aristotle by supposing an answer to the question of what makes different kinds of forms different and distinct chunks of matter distinct. It’s too Aristotelian for my taste—I don’t want matter to play that much of a metaphysical role. But it is a cool account, I think. And it could be Aquinas’.

Aristotle on sexual reproduction

Infamously, Aristotle thought that in animal reproduction (including the human case) the male contributed form and the female the matter.

I think it would have made for a neater metaphysics if he thought it was the other way around. For his story involves the complication that there are three ways that a form of an animal exists:

1. as informing a piece of matter and making it an animal of the relevant type

2. as being transmitted by semen, without turning the semen into an animal of the relevant type

3. as being found abstracted in an intellect thinking about the animal.

But if he supposed instead that the form was contributed by the female, he could have said that the semen contributes a small packet of initial matter for the organism and the female’s form works upon that packet in utero. At no point in this process is there a form that is separated out from an organism with that form (such a case will still have to happen when an intellect abstracts that form from matter), and so case (b) disappears, along with all the consequent metaphysical complications to the system.

It’s not clear to me how exactly Aristotle handled this. In Generation of Animals, he talks of the “power of the male residing in the semen”. This sounds like a kind of virtual presence of the form of the animal, a presence of the form as implicit in a causal power. It would be nice to be able to skip this complication. (Granted, Aristotle would still have a similar problem with regard to his view of delayed ensoulment, on which the offspring of a human is first a kind of plant, then gains an animal form, and then gains a rational form, for then the plant has a power to make an animal and the animal a human.)

I guess one might try to find Aristotle a way of reducing (b) to (a) while making the male still be the contributor of form as follows. One might think the semen is a living part of the male’s body, metaphysically like other parts, but separated spatially from the rest of the body (given what we know about how we are made of molecules, it is clear that spatial separation cannot be a bar to bodily unity). Thus, the semen would still be informed by the father’s form, in exactly the same way that the father’s ear or heart is. But this would have a downside. Suppose the father apparently died while the semen continued living, as does happen. Then it seems that the father would not have actually died—instead, his body would be reduced to a packet of semen, and he will have literally gone to seed. This seems absurd.

Why did Aristotle not go for the female as source of form solution, which is so neat metaphysically? Maybe for two reasons. First, the semen obviously could only contribute very little matter. (But then why not suppose that the initial organism is very small?) Second, sexism.

Change and matter

Aristotle’s positing matter is driven by trying to respond to the Parmenidean idea that things can’t come from nothing, and hence we must posit something that persists in change, and that is matter.

But there two senses of “x comes from nothing”:

1. x is uncaused

2. x is not made out of pre-existing materials.

If “x comes from nothing” in the argument means (1), the argument for matter fails. All we need is a pre-existing efficient cause, which need not be the matter of x.

Thus, for the argument to work, “x comes from nothing” must mean (2). But now here is a curious thing. From the middle ages to our time, many Aristotelians are theists, and yet still seem to be pulled by Aristotle’s argument for matter. But if “x comes from nothing” means (2), then theism implies that it is quite possible for something to come from nothing: God can create it ex nihilo.

There are at least two possible responses from a theistic Aristotelian who likes the argument for matter. The first response is that only God can make things come from nothing in sense (2), and hence things caused to exist by finite causes (even if with God’s cooperation) cannot come from nothing in sense (2). But there plainly are such things all around us. So there is matter.

Now, at least one theistic Aristotelian, Aquinas, does explicitly argue that only God can create ex nihilo. But the argument is pretty controversial and depends on heavy-duty metaphysics, about finite and infinite causes. It is not just the assertion of a seemingly obvious Parmenidean “nothing comes from nothing” principle. Thus at least on this response, the argument for matter becomes a lot more controversial. (And, to be honest, I am not convinced by it.)

The second and simpler response is to say that it’s just an empirical fact that there are things in the world that don’t come from nothing in sense (2): oak trees, for example. Thus there in fact is matter. This response is pretty plausible, but can be questioned: one might say that we have continuity of causal powers rather than any matter that survives the generation.

Finally, it’s worth noting that I suspect Aristotle misunderstands the Parmenidean argument, which is actually a very simple reductio ad absurdum:

3. x came into existence.
4. If x came into existence, then x did not exist.
5. So, x did not exist.
6. But non-existence is absurd.

The crucial step here is (6): the Parmenidean thinks the very concept of something not existing is absurd (presumably because of the Parmenidean’s acceptance of a strong truthmaker principle). The argument is very simple: becoming presupposes the truth of some past-tensed non-existence statements, while non-existence statements are always false. Aristotle’s positing matter does nothing to refute this Parmenidean argument. Even if we grant that x’s matter pre-existed, it’s still true that x did not exist, and that’s all Parmenides needs. Likewise, Aristotle’s famous actuality/potentiality distinction doesn’t solve the problem. Even if x was pre-existed by a potentiality for existence, it’s still true that x wasn’t pre-existed by x—that would be a contradiction.

To solve Parmenides’ problem, however, we do not need to posit matter or potentiality or anything like that. We just need to reject the idea that negative existential statements are nonsensical. And Aristotle expressly does reject this idea: he says that a statement is true provided it says of what is that it is or of what is not that it is not. Having done that, Aristotle should take himself as done with Parmenides’ problem of change.

Relativistic Aristotelian beginnings

From purely geometrical facts, it follows that every spatially extended entity is arbitrarily small at its beginning and at its end in almost every reference frame.

A stronger result is possible in the special case of the beginnings of substances in simple Aristotelian substantial change. In simple Aristotelian substantial change, substance A wholly changes into a new substance B by having all of the terminal matter of A be the proximate matter of B without any temporal gap. I claim that then substance B comes into existence at a single point in every reference frame (i.e., the temporal bottom of B fits into a light cone).

For suppose that in some frame F, substance B comes into existence at two F-simultaneous and distinct spacetime points z₁ and z₂ (these could be points at which there is still A but arbitrarily close to points of B or these could be points at which there is B but that are arbitrarily close to points of A). Then there is another frame F′ at which z₁ is earlier than z₂. Let t′_i be the time of z_i in F′. Because of how the terminal matter of A is the proximate matter of B, there is matter of A arbitrarily close to z₂. Hence, arbitrarily close to time t′₂, we will have A still existing. However, arbitrarily close to time t′₁ we will have B already existing. Since t′₁ < t′₂, it follows that according to F, we will have A still existing after B has already come to exist. So the cause is partly later than the effect, which is absurd.

Maybe there is a way around this in more complex cases where multiple substances result in one new substance. I am not sure.

But here is another way to see the pointiness of the beginnings of substances if one accepts the Aristotelian idea that substances are individuated by their initial matter and we take matter to be infinitely subdivisible. Suppose in frame F, substance B begins at distinct and simultaneous points z₁ and z₂. Let F′ as before be a frame where z₁ is earlier than z₂. Then according to frame F, substance B already exists before its matter close to z₂ exists (I am assuming matter is infinitely subdivisible, and in this case a relevant division happened). So its matter close to z₂ cannot be essential to its individuation. And there is a third frame, F″, where z₁ is later than z₂, and so the matter close to z₁ cannot be essential to B’s individuation. It follows that none of the matter can be essential to the individuation of the substance if the substance starts at two or more places at once. Thus, a substance must start at a single point.

What happens in substantial change then? It seems that if we are to preserve relativity, we have to say that the new substance comes into existence at a single point z out of one or more preceding substances. If matter individuates (which I am dubious of), then the matter immediately around z is what does the individuating. The substance’s form then spreads out from z, perhaps incorporating more and more of the stuff around z, at the speed of light or less.

Of course, all these problems disappear if we allow for faster-than-light causation in substantial change. But that should be a last resort.

An Aristotelian argument for presentism

Here is a valid argument:

1. Matter survives substantial change.

2. It is not possible that there exist two substances of the same species with the very same matter.

3. If matter survives substantial change, it is possible to have two substances of the same species existing at different times with the very same matter.

4. So, it is possible to have two substances of the same species existing at different times with the very same matter. (1,3)

5. If presentism is not true, and it is possible to have two substances at different times existing with the very same matter, it is possible to have two substances of the same species existing with the very same matter.

6. So, if presentism is not true, it is possible to have two substances of the same species existing with the very same matter.

7. So, presentism is true. (2, 5)

Let’s think about the premises. I think Aristotle is committed to (1)—it’s essential to his solution to the alleged problem of change. Claim (2) is a famous Aristotelian commitment. Claim (3) is very, very plausible—surely matter moves around in the world, and it is possible to set things up so that I have the same atoms that Henry VIII had at some point in his life. Claim (5) follows when we note that the only two plausible alternatives to presentism are eternalism and growing block, and on both views if two substances of the same species exist at different times with the very same matter, then at the later time it is true that they both exist simpliciter.

However, given that there is excellent Aristotelian reason to deny presentism, the above argument gives some reason for Aristotelians to deny (1) or (2). Or to be more radical, and just deny that there is any such thing as the “matter” of traditional Aristotelianism.

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.

A Thomistic argument for the possibility of an afterlife for animals

1. Accidents are more intimately dependent on substance than substantial forms on matter.

2. If (1) is true and God can make accidents survive without the substance, then God can make forms survive without matter.

3. If God can make forms survive without matter, then God can ensure life after death for animals by making their forms survive and restoring their matter.

4. God can make accidents survive without the substance.

5. So, God can ensure life after death for animals.

The most controversial claim here is (4), but that follows from the Thomistic account of the transsubstantiation.

Of course, there is a great gap between the possibility of an afterlife for an animal and its actuality. And the above argument works just as well for plants and fungi.

What is a material thing?

Here's a theory: a material thing is something that has or is a causal power that is not a mental causal power. Variant: that is not a rational causal power.

Ill-suited matter, form, and immortality

A question I haven’t seen explored much by contemporary neo-Aristotelian metaphysics is that of matter ill-suited to the form. Is it metaphysically possible for a bunch of molecules arranged like a normal oak tree to have the form of a pig? It would be, of course, a very unfortunate pig. Or is some minimal amount of match between the actual arrangement of the molecules and the form needed?

On light-weight neo-Aristotelianism, on which forms are simply structural properties, the answer has got to be negative.

But on heavy-weight neo-Aristotelianism, on which forms are irreducible entities, it seems like there should be no such restrictions. Why couldn’t God unite the form of a pig with a body as of an oak tree, or the form of an oak tree with a body as of a human?

However, supposing that we take such a liberal view on which there is no such thing as matter metaphysically incompatible with a form (presumably pace historical Aristotelians), we then have a puzzle. If it would be metaphysically possible for a pig form to be united to a bunch of organic gases, why is it that when pigs are vaporized, they (we assume) invariably die? Here is my story. Assume for simplicity time is discrete. At each time t, a pig—in virtue of its form—has a causal power to continue existing at the next time. But causal powers have activation conditions. The activation condition for the causal power to continue existing at the next time is an appropriate arrangement of the pig’s body. When the pig’s body becomes so distorted that this activation condition is no longer satisfies, the pig loses the power to go on living. And so it dies. However, of course, God could make it keep on living by a miracle: a miracle can supply what the causal powers of a thing are incapable of.

This account has one somewhat implausible prediction. Suppose that some powerful being instantaneously scatters the molecules of an ordinary pig across the galaxy, so that at t₁ we have an ordinary pig and at the next time, t₂, the pig molecules are scattered. Because at t₁ the pig has a causal power of continuing to exist conditionally on its molecules being appropriately arranged at t₁, and this condition is indeed satisfies at t₁, the pig will live one moment in scattered condition at t₂—and then perish at the next moment, t₃.

On this account, external causes do not directly destroy an object. Rather, they destroy the activation condition for the object’s power to continue existing. When that activation condition is destroyed, the object (barring a miracle) ceases to exist. But it has that one last existential hurrah before it falls into nonbeing.

Does it follow that on a heavy-weight Aristotelianism with my story about death, a pig metaphysically could survive the annihilation of its body? I am not sure, but I am inclined to think so. Indeed, I am inclined to think that if we had a normal pig at t₁, and then at t₂ the matter of the pig were annihilated, the pig would still exist—reduced to an abnormal immateriality—for that one instant of t₂, and then, barring a second miracle, it would slide into non-being at t₃.

What about us? Well, Aquinas argues for our soul’s natural immortality on the grounds that the human soul has a proper operation that does not depend on the matter, namely pure thought. I have never before been impressed by the move from a proper operation independent of matter to natural immortality, but in my above (neo-Aristotelian but not very Thomistic) setting I see it having significant force. First, we have this question: What are the activation conditions for the human’s power-to-continue-existing? It makes sense that for a being whose only non-existential operations are material, the activation conditions should be purely material. But if a being has a proper operation not dependent on the matter, then it makes perfect sense for the activation conditions of its power-to-continue-existing not to include material conditions. In fact, something stronger can be said. It seems absurd for a thing to have a power to continue thinking whose activation conditions outstrip its power to continue existing. It would be like a power to play soccer without a power to move. So, it seems, if Aquinas is right that we have an immaterial operation, then we have the power to continue existing even absent a body. Of course, God can stop cooperating with any power we have, and if he stopped cooperating with our power-to-continue-existing, then we would stop existing (unless God miraculously sustained us in existence independently of that power!), but naturally we would continue to exist. Assuming, of course, Thomas is right about us having a proper operation that does not depend on matter, which is a different question.

(And unlike Thomas, I think we have immortality, not just our souls.)

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.

Leaving space

Suppose that we are in an infinite Euclidean space, and that a rocket accelerates in such a way that in the first 30 minutes its speed doubles, in the next 15 minutes it doubles again, in the next 7.5 minutes it doubles, and so on. Then in each of the first 30 minutes, and the next 15 minutes, and the next 7.5 minutes, and so on, it travels roughly the same distance, and over the next hour it will have traveled an infinite distance. So where will it be? (This is a less compelling version of a paradox Josh Rasmussen once sent me. But it’s this version that interests me in this post.)

The causal finitist solution is that the story is impossible, for the final state of the rocket depends on infinitely many accelerations, and nothing can causally depend on infinitely many things.

But there is another curious solution that I’ve never heard applied to questions like this: after an hour, the rocket will be nowhere. It will exist, but it won’t be spatially related to anything outside of itself.

Would there be a spatial relationship between the parts of the rocket? That depends on whether the internal relationships between the parts of the rocket are dependent on global space, or can be maintained in a kind of “internal space”. One possibility is that all of the rocket’s particles would lose their spatiality and exist aspatially. Another is that they would maintain spatial relationships with each other, without any spatial relationships to things outside of the rocket.

While I embrace the causal finitist solution, it seems to me that the aspatial solution is pretty good. A lot of people have the intuition that material objects cannot continue to exist without being in space. I don’t see why not. One might, of course, think that spatiality is definitive of materiality. But why couldn’t a material object then continue to exist after having lost its materiality?

Individuating substances by their matter

According to traditional Aristotelianism, what makes you and me be distinct entities is that although we are of the same species, we’re made of distinct chunks of matter.

Here is a quick initial problem with this. The matter in us changes. It is quite possible that someone has different matter at age 1 and at age 20, and so by the Aristotelian individuation criterion, they are a different entity of the same species at ages 1 and 20, which is false.

One way out of this is to embrace presentism. But presentism is incompatible with the Aristotelian conviction that truth supervenes on being.

Another move is to narrow down the individuation criterion to say that:

1. Conspecifics x and y are made distinct by their being simultaneously made of different chunks of matter.

There are two problems with this move.

First, time travel. If at age 20, with different matter, you enter a time machine and travel back to meet yourself back when you were 1, then 20-year-old you and 1-year-old you are made of different chunks of matter at the same time. And while many problems about time travel are solved by moving from external to internal time, that doesn’t work here. For one cannot say that matter individuates x and y at the same internal time, since internal time is a concept that only makes sense when you are dealing with a single substance.

Second, relativity theory and teleportation (which is also kind of like time travel). Suppose that by age 20 you have different matter from what you had at age 1. Then God teleports 20-year-old you 100 light-years away instantly or nearly instantly (with respect to some reference frame). Then there will be a reference frame with respect to which it is true that the teleported 20-year-old you is simultaneous with 1-year-old you. So either simultaneity with respect to that reference frame doesn’t count—and that leads us to a privileged reference frame, contrary at least to the spirit of relativity—or else you are not yourself, which is absurd.

While one can swallow the idea that time travel is impossible, spacelike teleportation seems clearly possible.

Here is another move: we replace (1) with:

2. Conspecifics x and y are made distinct by their originating in distinct chunks of matter.

And 20-year-old you, no matter how they travel in space and/or time, has originated in the same chunk of matter as 1-year-old you.

This move has a cost: it requires that we be somewhat non-realist about substantial change. Full-blown realism about substantial change requires the matter to stay in existence while the substance changes. But if matter can stay in existence when its substance perishes, then that matter could be re-formed into another substance of the same species, which would violate the origination-restricted indviduation criterion. On (2), we have to accept the theory that the matter of a thing perishes when the substance does. This removes one of the major motivations behind positing matter: namely, that matter is supposed to explain why a corpse looks like the living body (viz., because it is allegedly made of the same matter).

Note, too, that (2) has a serious ambiguity once we have insisted that matter does not survive substantial change. By the chunk of matter that a substance originates in, do we mean the last chunk of matter before the substance’s existence or the first chunk of matter in the substance?

If we mean the last chunk of matter before the substance’s existence, there are two problems. First, it seems ad hoc to single out one aspect of the causes of the substance—the earlier matter—as doing the individuating. It seems better to individuate by means of the causes, applying the converse of the essentiality of origins. Second, it seems possible for an object to come into existence without prior matter. (If God exists, this is clear, since God creates ex nihilo. If God doesn’t exist, then very likely the world came into existence ex nihilo.) But then it seems quite possible for two objects of the same species to come into existence without prior matter. (Though if one wants to dispute this, one might point to the fact that a literal reading of the biblical creation account has God making the first two humans out of chunks of preexisting matter—soil and rib respectively. Maybe there is a deep metaphysical reason why this has to be so, and perhaps the initial ex nihilo created things had to be all of different species. But I just don’t find the latter requirement that plausible.)

So perhaps in (2) we mean the first chunk of matter in the substance. But if matter does not survive substantial change, then it seems plausible that the identity of the substance is prior to the identity of its initial matter, and hence the identity of the substance cannot come from its initial matter. This isn’t a very strong argument. Maybe the initial matter is prior to the substance, and has an identity of its own, while later matter is posterior to the substance.

So, our best version of the Aristotelian individuation account is this:

3. Conspecifics x and y are made distinct by their each having a different first chunk of matter.

Finally, it is interesting to note that (2) and (3) are only plausible if it is impossible for a material substance to have no beginning. But our best account for why a material substance cannot have a beginning is causal finitism. So those who like the Aristotelian account of individuation—I am not one of them—have another reason to accept causal finitism.

Sameness without identity

Mike Rea’s numerical-sameness-without-identity solution to the problem of material constitution holds that the statue and the lump have numerical sameness but do not have identity. Rea explicitly says that numerical sameness implies sharing of all parts but not identity.

Does Rea here mean: sharing of all parts, proper or improper? It had better not be so. For improper parthood is transitive.

Proposition. If improper parthood is transitive and x and y share all their parts (proper and improper), then x = y.

Proof: But suppose that x and y share all parts. Then since x is a part of x, x is a part of y, and since y is a part of y, y is a part of x. Moreover, if x ≠ y, then x is a proper part of y and y is a proper part of x. Hence by transitivity, x would be a proper part of x, which is absurd, so we cannot have x ≠ y. □

So let’s assume charitably that Rea means the sharing of all proper parts. This is perhaps coherent, but it doesn’t allow Rea to preserve common sense in Tibbles/Tib cases. Suppose Tibbles the cat loses everything below the neck and becomes reduced to a head in a life support unit. Call the head “Head”. Then Head is a proper part of Tibbles. The two are not identical: the modal properties of heads and cats are different. (Cats can have normal tails; heads can’t.) This is precisely the kind of case where Rea’s sameness without identity mechanism should apply, so that Head and Tibbles are numerically the same without identity. But Tibbles has Head as a proper part and Head does not have Head as a proper part. But that means Tibbles and Head do not share all their proper parts.

Here may be what Rea should say: if x and y are numerically the same, then any part of the one is numerically the same as a part of the other. This does, however, have the cost that the sharing-of-parts condition now cannot be understood by someone who doesn’t already understand sameness without identity.

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.

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.

Artifacts, Aristotelianism and naturalism

One of the main reasons I don’t believe in (complex) artifacts is that the existence of an artifact would have to depend on our intentions. Whether some stones make up a sculpture depends on whether they were piled with the intention of making a sculpture or just tossed in a heap to provide raw materials. And it is incredible that just because one thinks about something in a particular way while executing a series of physical actions, a material object comes into being, and if one doesn’t think in this way, but executes the same series of physical actions, there are just raw materials in a heap rather than a thing. This just seems like magic.

It has, however, just occurred to me that I may have been thinking too much like a naturalist. We human beings already have a broad array of amazing non-natural powers. By promising, I create an obligation for myself, and by requesting, I create a reason for you. By reproducing, two humans produce a new thinking being. Why couldn’t human beings (and perhaps other tool-using animals) also be gifted with the basic power to create a form for a bunch of physical objects, a power which they exercise by executing some physical movements with particular intentions, much as I change my own normative status by using my vocal chords with particular intentions?

That our intentions should affect what material objects there are is also a bit less magical when one has an Aristotelian ontology. For on an Aristotelian ontology, “material objects” are not purely material: they have immaterial form. Yes, all this is a bit magical. But on Aristotelian ontology, all beings are a little magical, and we are especially so, being minded.

That said, I still find it hard to believe that we can create artifacts.

But all this suggests an interesting argument against naturalism:

1. We can bring complex artifacts into existence.

2. Mereological universalism is false.

3. If naturalism is true, we can bring complex artifacts into existence if and only if mereological universalism is true.

4. So, naturalism is not true.

But I am still not sure (1) is true.

Materiality revisited

I’ve long been puzzled by materiality.

Here’s a thought: What if materiality isn’t characterized by anything deeply metaphysical, but by a physical quality? Perhaps to be material just is to have something like inertia, or mass, or energy?

(I think that to have zero of some quality like mass is still to have mass. A mass of x is a determinate of the determinable mass even if x = 0. Photons have mass, while numbers don’t.)

Substantial change

The following seems to me to be a central tenet of classical Aristotelianism:

1. The identity of a parcel of matter is grounded in form.

But it seems to me that matter is introduced by Aristotelianism primarily to solve the problem of distinguishing (a) one substance changing into another (or into several others) from (b) one substance perishing and a new substance coming to be. The solution seems to be that in case (a) the matter persists, but not so in case (b).

But if the identity of a parcel of matter comes from form, then it is very puzzling indeed how a parcel of matter can remain selfsame while a change of form occurs. In other words, there is a tension between (1) and the motive for the introduction of matter into the ontology.

I am inclined to hold on to (1) in some sense, but reject the idea that matter solves the problem of substantial change.

Here is my currently best deflationary solution to the problem of substantial change. Certain kinds of causal interactions are described as “transfers of qualities”. For instance, when billiard ball A strikes billiard ball B in such a way that A stops moving and B begins moving, the momentum of A is “transferred” to B. However, we certainly do not want a metaphysics of momentum transfer on which there exists an entity m that previously was in A and later the numerically same m is present in B. That would be taking the talk of “transfer” too literally. Similarly, we talk of heat transfer.

I do not have an account of quality transfer, but a rough necessary condition for it is that there is a causal interaction where A causes B to gain a property that it itself is losing. There is an obvious difference between the momentum transfer story and the case where A is miraculously stopped by God from moving while B is simultaneously and miraculously set by God in motion.

Now, a special case of quality transfer is when a causal interaction not only transfers a quality but also creates one or more new substances. For instance, suppose a gecko chased by a predator drops its tail, whose writhing confuses the predator. In doing so, the gecko transfers some of its mass, extension, color, motion and other qualities to a new substance (or aggregate of substances), a substance that comes to exist as a result of the same causal interaction.

The technical neo-Aristotelian term for the gecko’s loss of its tail is excretion. Excretion comes in two sorts. The kind of excretion in the case of the gecko’s autotomy is productive excretion, where qualities, notably including mass and extension (understood broadly to include temporal extension for aspatial temporal things), are transfered to one or more substances that are produced in the same causal interaction. Another kind of excretion is accretive excretion, where qualities are transferred to one or more substances that exist independently of this causal interaction. For instance, if an animal were to swallow a living plant, perhaps the plant in the animal’s digestive system could be accretively excreting: its qualities, notably including mass and extension, would come to be gradually lost to the plant while gained by the animal. (This is a bit more complicated in real life, I expect: I doubt the digested bits immediately become parts of the animal.)

Substantial corruption of a material substance, then, is total excretion, a causal interaction where all of a substance’s extension and mass is excreted to one or more substances. This comes in two basic varieties: substantial change where the the beneficiary substances result from the same causal interaction and accretive substantial corruption where the beneficiary substances exist independently of this causal interaction (and typically are preexistent). And one can have a combination case where some of the beneficiaries result from the interaction and some are not dependent on it.

But there is nothing metaphysically deep about substantial corruption.

Change in transubstantiation

The two main parts of the doctrine of transubstantiation that get philosophically discussed are that after consecration we have:

• Real Presence: Christ's body and blood is really there.
• Real Absence: bread and wine is no longer there.

But there may be another part: that the bread and wine change into the body and blood rather than simply being replaced by the body and blood. Certainly the Council of Trent uses the language of "conversion" of bread and bread wine, but it is not completely clear to me that they mean to define there to be something more than replacement. Aquinas talks unclearly (to me) of the substantial change as a kind of "order" in the two substances.

Besides the general puzzle of how change differs from replacement, there are at least two philosophical difficulties about the change. The first is that on some versions--not mine--of Aristotelian metaphysics, what makes substantial change be a change is the persistence of matter. But there is no matter persisting here (indeed, Aquinas' remark emphasizes this). The second is that what the bread and wine change into, namely Christ's body, is already there. But it seems that if x changes into y, then y doesn't exist prior to the change.

Leibniz considers a theory on which the bread and wine change into new parts of Christ's body. This solves the second problem, but at the expense of having to say that the bread changes into a mere part of Christ's body, which does not appear to be what the Church means. Trent does say that whole Christ comes to be present. I suppose one could have a hybrid theory on which the bread and wine change into new parts of Christ's body, and the rest of Christ's body then additionally comes to be present, but not by conversion. While I do not have decisive textual evidence, this does not seem to me to be what Trent means. And it is grotesque to think that Christ gets fatter at transubstantiation.

While it could well be that the Council doesn't mean anything beefy about the "conversion", and perhaps all it is an "order" between the two substances (cf. Aquinas), an order constituted by by non-coincidental replacement in the same location. That would simplify things metaphysically. But I want to try for something metaphysically thicker.

Here's the thought. On my Aristotelian metaphysics, nothing persists in substantial change. But when a change of substance x into substance y, a rather special causal power is triggered in x, the causal power of giving rise to y while perishing. The exercise of such a causal power is what makes it be the case that x has changed into y. There isn't any matter persisting in the change, so the first of the two philosophical problems with the Eucharistic change disappears. What about the second? Here's my suggestion. Normally, the existence of Christ's body at later times is caused by its existence at earlier times. But what if we say that the bread miraculously gets a special causal power, the power of causing Christ's body to exist just as the bread perishes? Then the existence of Christ's body after consecration will be causally overdetermined by two things: the bread's exercising that causal power and Christ's body exercising its ordinary causal power to make itself persist.

The bread in perishing is an overdetermining cause of the existence of Christ's body, and that is exactly how substantial change happens on my view. The main metaphysical difference here is that normally substantial change is not overdetermined, while here it is.

A materialist intuition against materialism

The following argument is valid:

1. It is metaphysically impossible for us to become wholly immaterial.

2. If we are wholly material, then functionalism is true.

3. If functionalism is true, then it is metaphysically possible for us to become wholly immaterial.

4. So, we are not wholly material.

I think premise 1 is false, but intuitively 1 is pretty plausible—especially to a materialist.

Premise 2 is made plausible by the way functionalism solves serious problems in other materialist theories.

Premise 3 can be argued for: it is metaphysically possible for an immaterial being to have the same functional properties as I do, and furthermore for the immaterial being’s isomorphic functional states to be caused by my functional states at the last moment of my body’s existence in such a way that the immaterial being is a continuant of me given functionalism.