Aristotelian abstraction

On the Aristotelian account of abstraction, we abstract the forms of things via perception. But here is a problem. First of all, we sometimes have better knowledge of things not perceived than of things perceived. Let’s say you read a detailed scientific book about pangolins, though you’ve never encountered one, while I once saw a koala in a zoo, but don’t much know anything more about them than that they are cute marsupials. It seems quite problematic to say I have the form of the koala in my mind, but you do not have the form of the pangolin. For that would make the mental possession of the form of the thing an unimportant flourish to what really epistemically matters, since clearly you are better off epistemically for reading the book about pangolins than I am for seeing the koala.

Of course, presumably, the author of the pangolin book presumably saw the pangolin. But that doesn’t seem to matter much, either. There are many dinosaur species where the paleontologist knows more about the species than I know about koalas, and yet no human ever perceptually interacted with a dinosaur, but typically only with minerals that have displaced their carcasses.

What should someone committed to the Aristotelian story about abstraction say? Two options come to mind, a modest and an expansive one.

Modest option: It really doesn’t really matter much epistemically whether one has the form of a pangolin or a koala in one’s mind. What matters is the propositional knowledge. However, it is essential to our possession of the propositional knowledge that our thoughts have intentionality, that they refer to the world. And it is crucial to securing intentionality that we have Aristotelian abstraction at the interface between the world and the mind. The triceratops expert’s intentionality with respect to triceratopses is derivative from the causal chain from triceratopses to their corpses to their fossils to the light reflecting from the fossils into the expert’s eyes to (eventually somehow) the expert’s thoughts. Where the causal chain crosses from the world to the mind, we need a transmission of form to ensure intentionality for the whole chain. Maybe the transmission happens when the minerals that have replaced the bones transmit their mineral forms to the expert’s mind, in some mysterious way mediated by the light.

Expansive option: Everything in the world carries the forms of everything nondivine that is causally upstream from itself. The triceratops corpse somehow has the form of the triceratops in it, and so do the bones of the triceratops, and so do the minerals that replace the bones, and so does the light modulated by reflection from the minerals, and so do the electrical impulses in the nerves from the retinal receptors to the brain. It is easier to extract the form when it comes from seeing a live koala than when it comes from seeing fossils, so that a layman can do the former while the scientist is needed to do the latter. Similarly, when you read a book about pangolins, the ink on the page, being causally modulated by the author’s knowledge, carries the form of the pangolin (in addition to any forms naturally contained in the ink, say those of the particles constituting the ink).

Medievals already said something like this about the modulated light, so it’s just a matter of extending the story. And while the problem I am concerned about is one that does not require any science or technology beyond what the medievals had—the medievals knew about the gaining of expertise from books (if anything, they might have overestimated it!)—in a modern setting we it feels like an Aristotelian has to do this. After all, it is hard to deny that one can gain the same kind of knowledge of koalas by looking at them through high-end augmented reality goggles as from directly seeing them with our eyes. Thus, on a form-transmission story, the electrical potentials of the capacitors in the computer memory in the goggles have to somehow carry the form of the koala. But given the many ways that computer memory can be realized (think of magnetized rings versus capacitors versus markings on a CD), it seems plausible that any effect will have to have to be admitted to carry the form of its cause. It is tempting to say the form is only found in substances where there is sufficient data to reconstruct significant information about the causally-upstream object the form is of, but I think is not tenable. Presumably each bacterium is a substance, and we could have a type of biological memory in augmented reality glasses where each bit of information is stored in a different bacterium.

This story coheres very nicely with the essentiality of origins. It is a kind of a reversal of the principle of proportionality of causation on which the reality of the effect is actually or eminently found in the cause: the formal reality of a cause is found in the effect. I think it’s a defensible story. But I also find it hard to believe.

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.

Avoiding temporal parts of elementary particles

It would be appealing to be able to hold on to all of the following:

1. Four-dimensionalism.

2. Elementary particles are simples.

3. There is only kind of parthood and it is timeless parthood.

4. Uniqueness of fusions: a plurality of parts composes at most one thing.

But (1)–(4) have a problem in cases where one object is transformed into another object made of the same elementary particles. For instance, perhaps, an oak tree dies and then an angel meticulously gathers together all the elementary particles the oak ever has and makes a pine out of them, which he shortly destroys before it can gain any new particles. Then the elementary particles of the oak seem to compose the pine, contrary to (4).

One common solution for four-dimensionalists is to deny (2). Elementary particles have temporal parts, and you can’t make the old temporal parts of the oak’s particles live again in the pine. But there are problems with this solution. First, you might believe in a patchwork principle which should allow the old temporal parts to get re-used again. Second, it is intuitive to think that elementary particles are parts of the oak. But on the temporal part solution, this violates the transitivity of parthood, since the elementary particles will have temporal parts that outlive the oak. Third, the temporal parts of particles seem to be just as physical as the particles, and you might think that it’s the job of physics and not metaphysics to tell us what physical objects there are, so positing the temporal parts steps on the physicist’s toes in a problematic way. Fourth, and I am not fully confident I understand all the ramifications here, we need some kind of primitive relation joining the temporal parts of the particle into a single particle, since otherwise we cannot distinguish the case where two electrons swap properties and positions (and thereby reverse the sign of the wavefunction) from the case where they don’t.

The second common solution is to deny (3), distinguishing parthood from an irreducible parthood-at-t, and then say that trees are merely composed-at-t from elementary particles. I find an irreducible parthood-at-t kind of mysterious, but perhaps it’s not too terrible.

I want to offer a different solution, with an unorthodox four-dimensionalist Aristotelianism. Like orthodox Aristotelianism, the unorthodox version introduces a further entity, a form. And now we deny that a tree is composed of the elementary particles. Instead, we say that a tree is composed of form and elementary particles. One minor unorthodox feature here is that we don’t distinguish the parthood of a form in a substance and the parthood of a particle in a substance: there is just one kind of parthood. The more unorthodox thing will be, however, that we allow elementary particles to outlive their substances. The resulting unorthodox four-dimensionalist Aristotelianism then allows one to accept all of (1)–(4), since the pine is no longer composed of parts that compose the oak, as the oak’s form is not a part of the pine.

But we still have to account for parthood-at-t. After all, it just is true that some electron e is a part of the oak at some but not other times. And this surely matters—it is needed to account for, say, the mass and shape of the oak at different times. How do we that? Well, we might suppose that even if in our unorthodox Aristotelianism particles can outlive their substances, they get something from the substance’s form, even if it’s not identity. Perhaps, for instance, they get their causal powers from the substance’s form. (We then still need to say something about unaffiliated particles—particles not inside a larger substance. Perhaps when a particle, considered as a bit of matter, gets expelled from a larger substance and becomes unaffiliated, it gains its own substantial form. It loses that form when it joins into a larger substance again. At any given time, it gets its causal powers from the substance’s form.) So we can say that e is a part of the oak at t if and only if e gets its causal powers from the oak’s form at t.

Killing coiled and straight snakes

Suppose a woman crushes the head of a very long serpent. If the snake all dies instantly when its head is crushed, then in some reference frame the tail of the snake dies before the woman crushes the head, which seems wrong. So it seems we should not say the snake dies instantly.

I am not talking about the fact that the tail can still wiggle a significant amount of time after the head is crushed, or so I assume. That’s not life. What makes a snake be alive is having a snake substantial form. Death is the departure of the form. If the tail of the headless snake wiggles, that’s just a chunk of matter wiggling without a snake form.

What’s going on? Presumably it’s that metaphysical death—the separation of form from body—propagates from the crushed head to the rest of the snake, and it propagates at most at the speed of light. After all, the separation is a genuine causal process, and we are supposed to think that genuine causal processes happen at the speed of light or less.

So we get a constraint: a part of the snake cannot be dead before light emitted from the head-crushing event could reach the part. But it is also plausible that as soon as the light can reach the part, the part is dead. For a headless snake is dead, and as soon as the light from the head-crushing event can reach a part, the head-crushing event is in the absolute past of the part, and so the part is a part of a headless snake in every reference frame. Thus the part is dead.

So death propagates to the snake exactly at the speed of light from the head-crushing, it seems. Moreover, it does this not along the snake but in the shortest distance—that’s what the argument of the previous paragraph suggests. That means that a snake that’s tightly coiled into a ball dies faster than one that is stretched out when the head is crushed. Moreover, if you have a snake that is rolled into the shape of the letter C, and the head is crushed, the tail dies before the middle of the snake dies. That’s counterintuitive, but we shouldn’t expect reality to always be intuitive.

Darwin and Einstein against the shared-form interpretation of Aristotle

Assume an Aristotelian account of substantial form on which forms are found in the informed things. A classic question is whether substantial forms are shared between members of the same kind or whether each individual has their own numerically (but maybe not qualitatively) distinct form.

Here’s a fun argument against the shared-form view. For evolution to work with substantial forms, sometimes organisms of one metaphysical kind must produce organisms of another kind. For instance, supposing that wolves are a different metaphysical kind from dogs, and dogs evolved from wolves, it must have happened that two wolves reproduced and made a dog. (I suspect wolves and dogs are metaphysically the same kind, but let’s suppose they aren’t for the sake of the argument.) If we are to avoid occasionalism about this, we have to suppose that the two wolves had a causal power to produce a dog-form under those circumstances.

Plausibly dogs evolved from wolves in Siberia, but there was also a Pleistocene wolf population in Japan, and imagine that the causal power to produce a dog was found in both wolf populations. Suppose, counterfactually, that a short period of time after a pair of wolves produced a dog in Siberia, a pair of Japanese wolves also produced a dog. On a shared-form view, when the Siberian wolves produced a dog, they did two things: they produced a dog-form and they made a dog composed of the dog-form and matter. But when the Japanese wolves produced a dog, the dog-form already existed, so they only thing they could do is make a dog composed of matter and that dog-form.

The first oddity here is this. Our (perhaps imaginary) Japanese wolves didn’t know that there was already a dog in Siberia, so when they produced a dog, they exercised exactly the same causal powers that their Siberian cousins did. But their exercise of these causal powers had a different effect, because it did not produce a new form, since the form already existed, and instead it made the form get exemplified in some matter in Japan. It is odd that the exercise of the same causal power worked differently in the same local circumstances.

Second, there is an odd action-at-a-distance here. The dog-form was available in Siberia, and somehow the Japanese wolves in the story made matter get affected by it thousands of kilometers away.

In fact, to make things worse, we can suppose the Japanese wolves only lagged a two or three milliseconds after their Siberian cousins. In that case, the Siberian wolves caused the existence of the dog-form, which then affected the coming-into-existence of a dog in Japan in a faster-than-light way. Indeed, in some reference frames, the Japanese dog came into existence shortly before the dog-form came into existence in Siberia. In those reference frames we have backwards causation: the Siberian wolves make a dog-form and that dog form organizes matter in Japan earlier.

If, on the other hand, every dog has a numerically distinct form, there is no difficulty: the Japanese wolves’ activity can be entirely causally independent of the Siberian ones’.

Tables and organisms

A common-sense response to Eddington’s two table problem is that a table just is composed of molecules. This leads to difficult questions of exactly which molecules it is composed of. I assume that at table boundaries, molecules fly off all the time (that’s why one can smell a wooden table!).

But I think we could have an ontology of tables where we deny that tables are composed of molecules. Instead, we simply say that tables are grounded in the global wavefunction of the universe. We then deny precise localization for tables, recognizing that nothing is localized in our quantum universe. There is some approximate shape of the table, but this shape should not be understood as precise—there is no such thing as “the set of spacetime points occupied by the table”, unless perhaps we mean something truly vast (since the tails of wavefunctions spread out very far very fast).

That said, I don’t believe in tables, so I don’t have skin in the game.

But I do believe in organisms. Similar issues come up for organisms as for tables, except that organisms (I think) also have forms or souls. So I wouldn’t want to even initially say that organisms are composed of molecules, but that organisms are partly composed of molecules (and partly of form). That still generates the same problem of which exact molecules they are composed of. And in a quantum universe where there are no sharp facts about particle number, there probably is no hope for a good answer to that question.

So maybe it would be better to say that organisms are not even partly composed of molecules, but are instead partly grounded in the global wavefunction of the universe, and partly in the form. The form delineates which aspects of the global wavefunction are relevant to the organism in question.

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.)

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.

An argument for something close to property dualism

1. There are fundamental irreducible mental properties.

2. There are fundamental irreducible physical properties.

3. Necessarily, anything that has a physical property is a physical thing.

4. Recombination: Fundamental irreducible properties are all mutually compatible.

5. So, it is possible for something to have both a mental and a physical property. (1, 2 and 4)

6. So, it is possible for a physical thing to have a mental property. (3 and 5)

This seems to imply at least the logical possibility of property dualism. But not quite: for property dualism, you need that a purely physical thing has a mental property. And I think there are no purely physical things, because each substance has an immaterial form.

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.

Disembodied trees

Here’s an interesting thesis:

1. If x has the ys among its parts, and for each z among the ys, x can survive losing z without gaining anything, then x can survive simultaneously losing all the ys without gaining anything.

There are obvious apparent counterexamples. A boat that has sufficient redundancy can survive the loss of any plank, but cannot survive losing them all. An oak tree can lose any cell but cannot lose all cells.

But counterexamples aside, wouldn’t (1) be a nice metaphysical thesis to have? Then essential parts wouldn’t be made of inessential ones. You can see all the nasty ship-of-Theseus questions that would disappear if we had (1).

I think an Aristotelian can embrace (1), and can get around the counterexamples by biting some big bullets. First, like some contemporary Aristotelians, she can deny that artifacts like boats (or bullets) exist. Second, she can say that oak trees can survive the loss of all their matter, becoming constituted by form alone, much as some philosophers say happens to human beings after death (before the resurrection). The second part seems a bigger bullet to bite, as one would need a story as to why in fact oak trees perish when they lose all their cells, even if they don’t have to. But perhaps that’s just contingently how it happens, though an all powerful being could make an oak tree survive the destruction of all its cells.

The big question here is exactly what philosophical advantages embracing (1) has.

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.

Group impairment and Aristotelianism

Aristotelians have a metaphysical ground for claims about what is normal and abnormal in an individual: the form of a substance grounds the development of individuals in a teleological ways and specifies what the substance should be like. Thus a one-eyed owl is impaired—while it is an owl, it falls short of the specification in its form.

But there is another set of normalcy claims that are harder to ground in form: claims about the proportions of characteristics in a population. Sex ratios are perhaps the most prevalent example: if all the foals born over the next twenty years were, say, male, then that would be disastrous for the horse as a species. And yet it seems that each individual foal could still be a perfect instance of its kind, since both a male and a female can be a perfect instance of horsehood. Caste in social insects is another example: it would be disastrous for a bee hive if all the females developed into workers, even though each one could be a perfect bee.

The two cases are different. The sex of a horse is genetically determined, while social insect caste is largely or wholly environmental. Still, both are similar in that the species not only has norms as to what individuals should be like but also what the distribution of types of individuals should be. There is not only the possibility of individual but of group impairment. But what is the metaphysics behind these norms?

Infamously, Aristotle interpreters differ on whether forms are individual or common: whether two members of the same species have a merely exactly similar or a numerically identical form. Here is a place where taking forms to be common would help: for then the form could not only dictate the variation between the parts of each organism’s body but also the variation between the organisms in the species. But taking forms to be common would be ethically disastrous, because it would mean that all humans have the same soul, since the soul is the form of the human being.

Here’s my best solution to the puzzle. The form specifies the conditions of the flourishing of an individual. But these conditions can be social in addition to individual. Thus, a perfectly healthy and well-nourished male foal would not be flourishing if it lacks a society with potential future mates. And while each worker bee can internally be a fulfilled worker bee, it is not flourishing if its work does not in fact help support a queen. These social conditions for flourishing are constitutive. It’s not that the lack of a queen will cause the worker bee to die sooner (though for all I know, it might), but that the lack of a queen is constitutive of the worker bee being poorly off.

Once we see that there can be constitutive social conditions for flourishing, it is natural to think that there will be constitutive environmental conditions for flourishing. And this could be the start of an Aristotelian philosophy of ecology.

The usefulness of having two kinds of quantifiers

A central Aristotelian insight is that substances exist in a primary way and other things—say, accidents—in a derivative way. This insight implies that use of a single existential quantifier ∃x for both substances and forms does not cut nature at the joints as well as it can be cut.

Here are two pieces of terminology that together not only capture the above insight about existence, but do a lot of other (but closely related) ontological work:

1. a fundamental quantifier ∃u over substances.

2. for any y, a quantifier ∃_yx over all the (immediate) modes (tropes) of y.

We can now define:

• a is a substance iff ∃u(u = a)

• b is a (immediate) mode of a iff ∃_ax(x = b)

• f is a substantial form of a substance a iff a is a substance and ∃_ax(x = f): substantial forms are immediate modes of substances

• b is a (first-level) accident of a substance a iff u is a substance ∃_ax∃_xy(y = b & y ≠ x): first-level accidents are immediate modes of substantial forms, distinct from these forms (this qualifier is needed so that God wouldn’t coount as having any accidents

• f is a substantial form iff ∃u∃_ux(x = f)

• b is a (first-level) accident iff ∃u∃_ux∃_xy(y = b).

This is a close variant on the suggestion here.

Snake annihilation and partial death

The following five principles seem to be rationally incompatible:

1. Every part of a living organism is informed by its form.

2. If any part of an organism is informed by its form, the organism is alive.

3. An snake would be dead if everything but the tailmost one percent of its length were annihilated.

4. Simultaneity is relative, as described by Special Relativity.

5. Being informed by a form is not relative to a reference frame.

To see the incompatibility, consider this case. A snake of ordinary proportions is lying stretched out in a line and is then instantaneously completely annihilated. Notice an interesting fact about this snake:

6. Every bit of this snake is informed by the form of the snake whenever it exists.

This follows from (1) and the setup of the situation. Note that (6) will not be true in the case of snakes that meet a more ordinary end than by complete instant annihilation: those snakes leave behind parts that are no longer informed (they may be parts only in a manner of speaking, but I think nothing in my argument hangs on this). It is to make (6) true that I supposed the snake annihilated instantaneously.

Now, by (4), the claim that the snake is must have been said with respect to some reference frame F₁. But it follows from Special Relativity and the geometry of linear snakes that there will be a reference frame F₂ relative to which the snake is annihilated gradually from the head to the tail rather than simultaneously. There will thus be a time t₂ such that relative to F₂ at t₂ the snake has been annihilated except for the tailmost one percent. At t₂ relative to F₂, that tailmost one percent is informed by the form of the snake by (5) and (6). By (2), the snake is alive at t₂ relative to F₂. But by (3), it is dead at t₂ relative to F₂. So, the snake is both alive and dead at t₂ relative to F₂, which is absurd.

I am not sure what to do about this argument. I feel pushed to deny (2). Perhaps something could be dead simpliciter but still have living parts. But that’s an uncomfortble position.

Good-bye, (Aristotelian) matter

Of course, there are material things like oaks and people, and it’s distinct from immaterial things like angels. But for a long time I’ve been wondering why my fellow Aristotelians think that there is matter, a component of material things. In the process of reflection, I have given up on matter as a fundamental ontological category. Of course, for theological and common-sense purposes, I need to have the concept of a material substance, but here I hope there is some reduction, such as that a material substance is a substance that has at least one geometric property. My Aristotelianism now inclines to be more like Leibniz’s than like the historical Aristotle’s or Aquinas’s. Material substances, on my view, are much like Leibniz’s monads; they are like Aristotle’s gods or Aquinas’s angels, plus whatever properties or causal powers are needed for them to count as material. I am my own form, and in this form there inhere accidents.

What philosophical work does matter play, particularly in Aristotelian theories?

1. Many Aristotelians say that something remains through substantial change, namely matter.

The persistence of matter through substantial change is said to do justice to the intuition that the corpse is the remains of the living creature: that there is something in the corpse that was in the living creature. But it is notoriously difficult to remain faithful to the Aristotelian emphasis that identity always comes from form and allow that anything in the corpse is identical to anything in the prior living body. Absent a solution to this, the Aristotelian has to say that there is one bunch of matter prior to death, a bunch of matter informed by the form of the living body, and a different bunch of matter after death, informed by the forms of the substances making up the corpse. But that does not do justice to the common-sense intuition.

In the vicinity, too, there is the question of why it is that the corpse is physically like the living body. But this is not to be accounted for by matter, but by accidents such as shape, mass and color. Accidents are possessed by substances. Either accidents can or cannot survive the destruction of their underlying substance. If they can, then we have an explanation of why the corpse is physically like the living body. If they cannot, then adding that there is matter in both—and even that it is the same matter—does not help: we simply have to bite the bullet and say that the accidents of the living body have the power to cause similar accidents in the corpse.

2. Matter may play a role in diachronic identity.

But since immaterial substances like angels can persist over time, matter isn’t needed to solve the problem of diachronic identity. Moreover, the problem of diachronic identity seems to me, as a four-dimensionalist, to be a pseudoproblem (see also this]). It is no more a problem how the same thing can exist in 2017 and in 2018 than it is a problem how someone can exist in the room and in the hall—just put a leg in each, and you’ll see how. Matter does nothing to help with the latter problem, since presumably it isn’t the same chunk of matter that’s in the room as in the hall. So, why should matter help with the former?

3. Matter may play a role in problems of material composition.

Matter may also play a role in some specific solutions to the problem of material composition. One might, for instance, identify the lump with the matter and the statue with the substance composed of it, or the lump with one thing made of the matter and the statue with another thing made of the same matter, and then explain away the commonality of many properties, like mass, by the identity of matter. But either the statue and the lump have numerically the same accident of mass or they do not. If they do, then since accidents inhere in substances, not in matter, the commonality of matter doesn’t do any work. If they do not, then the commonality of matter doesn’t seem to have done much—we still have to explain why the two have an exactly similar accident of mass, given that they have numerically distinct ones.

What matter does do, I think, is help differentiate the classic statue–lump case from the horse–ghost case where Bucephalus’s ghost happens to walk right through the living Seabiscuit, in such a way that the ghost horse and the living horse happen to occupy exactly the same space. For we can say that the ghost case is a case of merely spatial colocation, while the statue–lump case is a case of having the same matter. And intuitively there is a difference between the two cases. Interestingly, though, this isn’t the material composition problem that matter usually gets invoked to solve. And since I don’t believe in statues, or in any other entities that could plausibly be thought to make there be two entities of one chunk of matter, this does little for me.

4. Isn’t hylo-morphism the distinctively Aristotelian solution to the mind-body problem?

Sure. But, even more than the classic Aristotelian solution, my view is a dissolution to the mind-body problem rather than a solution. The form of course affects the accidents that constitute and shape our embodiment. All of this is due to the nexus—ontological, teleological and causal—that exists between the substance and its accidents (both substance–accident and accident–accident). It’s not a case of one thing moving another: it is just the common story of the form affecting the accidents and the accidents affecting one another.

And, yes, of course I agree with the Council of Vienne that the soul is the form of the body. On my view, talk of the soul is talk of the substance qua form and apart from the accidents constituting its materiality, and the substance qua form is a base for all the accidents which constitute us as having bodies. So, the soul is the form of the body.

5. Physics talks of matter.

Sure, but physics probably doesn’t have a fundamental distinction between matter and energy, I think.

Anyway, I don’t deny that there is matter in the sense of substances that are so configured as to count as material. Quite possibly, where you have a heap of sand, you have a heap of material substances, and hence matter. (But perhaps not: perhaps fundamental physical reality is just a handful of fields.)

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All in all, I just see little if any benefit to matter. And there is much mystery about it. Ockham’s razor cuts it away.

Unless, of course, we come to some philosophical problem that can’t be solved without matter, or can’t be solved as well without it…

Substances do not have substantial proper parts

It's an old maxim of Aristotelian metaphysics that substances do not have substantial proper parts. Here's an argument for it, in the case of material substances. Suppose a material substance A has a substance B as a proper part. Now, arguably A is wholly composed of two parts: the matter M and the form F.

Now the form G of B cannot overlap M, as then the form would be partly material. So G must be a part of F. But forms of substances are simples. So G must be all of F. But then we have two substances with the numerically same form, and that seems absurd.

A central assumption in the argument is that forms are simples. There may be a way of making an argument without that assumption. Suppose we say that G, the form of B, is a proper part of F, the form of A. Now if any proper part of a substance is a substance, then my heart is a substance--it's nicely delineated, and one of the best candidates. But I can survive the destruction of my heart (I would just need a machine to circulate the blood). And surely if my heart is destroyed, its form is destroyed as well. But my form doesn't seem to be intrinsically changed by the destruction of my heart. Yet if the form of the heart were a part of my form, then my form would be intrinsically changed by the destruction of the heart.

A Thomistic creationism of sorts

Suppose that God made physical stuff (say, particles) be arranged just like in a butterfly, but he did not give (either directly or by some general policy) a butterfly form. Then we would have something that looks just like a butterfly. And to the extent that butterfly behavior is ultimately predictable just from physics, that bunch of physical stuff would behave like a butterfly. There wouldn't be a butterfly there. In fact, there wouldn't be one thing there: just a bunch of physical stuff.

Now, we are not yet in a position to know how much of the physical behavior of organisms—especially non-human ones—is predicted by the physics. Let us suppose, however, that it turns out that all the physical behavior of non-human animals is predicted by the physics. (Humans have free will, and that's a different business.)

Now let me tell a story. I don't think the story is actually true, though it seems basically[note 1] logically possible:

God created a physical world and had some chemical stuff come together in a way that "reproduced". And then evolution took over, and bundles of physical stuff that were better at survival and reproduction reproduced more, until we had bundles of physical stuff shaped like algae, trilobites, trees, dinosaurs, birds, horses and apes. But there never were any algae, trilobites, trees, dinosaurs, birds, horses or apes. Finally, not too long ago on a cosmic scale, there came to be two bundles of physical stuff that were physically rather like humans. By this point, there was no physical stuff shaped like trilobites or dinosaurs, but there was physical stuff shaped like algae, trees, birds, horses and apes. And God then said: "Let there be algae, trees, birds, horses, apes and many other organisms", and he created forms which informed the algaelike, treelike, birdlike, horselike and apelike bundles of physical stuff, and all sorts of other bundles. Thereupon, there were birds, horses and apes, though things didn't look any different. Finally God said: "Let there be humans", and he created forms which informed the human-like bundles of physical stuff. And there were humans.

This story is fully compatible with naturalistic evolution. Indeed, the only bar to the possibility of this story would be a vitalism on which physical stuff does not behave like living organisms. On this story, there literally never have been any dinosaurs. But there will have been bundles of physical stuff arranged dinosaurwise, and that's all many a biologist thinks a dinosaur is anyway.

But since bunches of physical stuff can't be conscious—they need soul, i.e., form, for that—then on this story there was no consciousness before human beings came on the scene. This is theologically attractive in that it enables us to hold that suffering came into the world through human sin. For we can continue the logically possible story thus:

When God created the forms of all the organisms, he miraculously arranged things so that no organism would suffer, miraculously making a harmonious state. And he put humans in charge of this delicately balanced system. Humans, however, quickly came to freely reject God's sovereignty in the system that he put them in charge of, and he reluctantly removed his miraculous protection from the system in deference to the authority he granted humans. And so humans and other animals came to suffer.

This story is also interesting in that it is yet another way to reconcile naturalistic evolution with the not dogmatically required but still somewhat attractive theological idea that all the organisms there are were directly created by God. For the story makes clear in a Thomistic setting how naturalistic evolution only explains how we got to have the physical stuff shaped and behaving like algae, trees, birds, horses and apes. God's creation is needed to make this stuff into actual algae, trees, birds, horses and apes: forms need to be put in. (Compare how in Genesis we are told that God made Adam from the "dust of the earth", i.e., physical stuff.)

The main reason I don't like this story has to be with my being an eternalist. I think past (and future) objects are real. And I think reality will be more wonderful if it really contains trilobites and dinosaurs, not just physical stuff arranged trilobitewise or dinosaurwise. So while the above story is basically logically possible, I don't think it's actually true, because it seems likely that a God whose goodness spreads itself out creatively would be likely to create forms for physical stuff arranged trilobitewise and dinosaurwise.

But there might, nonetheless, be aspects of the story that we can adopt. In the story, creation was safeguarded by God's taking bundles of physical stuff and giving them form. We can posit this in a more commonsensical evolutionary story. Maybe the gametes of two dinosaur parents involve some mutation that makes the offspring be particularly birdlike. Then God can simply prevent the offspring from being informed by a dinosaur form and then instead make the offspring be informed by a bird form. This is still direct creation of birds from previously existing physical matter. And while higher animals prior to the first human sin were conscious, we can suppose that God in his love miraculously prevented any instance of conscious suffering that wouldn't be on balance good for the animals, say by miraculously preventing pain qualia or in some other way. But this divine miraculous intervention perhaps ended (though perhaps not!) when Adam and Eve rejected God's rule over the earth they were put in charge of.