An Aristotelian argument for Causal Finitism

The Aristotelian account of individuation for beings in the same species proceeds by matter. But to fill out this account, we may need to talk about the times at which the matter is different.

One reason for talking about this is the possibility on some versions of Aristotelianism that a chunk of matter can survive substantial change, and hence can compose different substances—albeit at different times. If one wolf kills and eats another, there is in principle no reason why eventually the cannibal wolf’s matter might not entirely be the same as the matter of the victim, then.

So, perhaps, we may want to say that what distinguishes members x and y of the same material species is that they have different matter at the same time. But that’s not quite right. For it could be that x and y don’t ever exist at the same time! We might thus want to say that what grounds the distinction between x and y is:

1. at some time t, either x exists and y doesn’t or x doesn’t exist and y does or x and y both exist and have different matter.

This has at least two problems. First, if I travel backwards in time to a time when I already existed, then I will have different matter from my past self at the same time (since I’ve changed some cells in the meanwhile).

But the second is probably the more serious. According to the story in (1), past, present and future differences in matter all ground the distinction between x and y. But it is implausible that future differences in matter be relevant to my present distinction from you. So we should minimally restrict (1) to talking of past and present times t. But if we do that, then what grounds our difference changes over time, and does so pointlessly, because as soon as our distinction has once been established, that’s surely all we need. In fact, the last point is particularly important given the soul’s survival past death: what makes your soul past death different from mine is presumably the past difference in matter. This suggests that if we want to get at what truly grounds our distinction, we have to go back in time as far as we can, to the very beginnings of our existence, and say:

2. either x and y differ in the time at which they began to exist, or x and y began at the same time with different matter.

There is another reason to prefer (2) to (1). We not only want an account of the distinction of substances within a world, but between possible worlds. But there are many possible worlds where I exist but where my current matter is different from the matter I now have in the actual world (namely, because my diet was different). Thus, (1) has no hope of being extended to an account of transworld distinction. But (2) has some hope of such an extension. At the very least, it gives a sufficient condition for distinctness in the transworld case, while (1) does not even do that.

But now here is an interesting thing. If (2) is the true story about the distinction between material substances of the same species, it follows that:

3. It is impossible for there to be two material substances of the same species that have no beginning in time.

But if Causal Finitism (the doctrine that one effect cannot have infinitely many causes) is false, it seems like it should be possible to have an organism that has lived for an infinite amount of time, and likewise possible to have two such organisms in one species. So (2) gives us a new reason to accept Causal Finitism.

However, personally, I don’t like the Aristotelian account of distinctions between substances.

A tweak to the Aristotelian account of individuation

The standard Aristotelian story about individuation of finite substances is two-fold:

1. What makes x and y distinct when x and y are members of different species is their difference in form

2. What makes x and y distinct when x and y are members of the same species is their difference in matter.

But I think a slight tweak is in order. Suppose Alice and Spot are both members of different species and have a difference of matter. By the standard story, what accounts for their distinction is just their having different form. But it seems right to say that their difference in matter is also sufficient to distinguish them. The distinction between Alice and Spot is overdetermined by a difference in species and a difference in matter.

If so, then intead of (1) and (2), we should have an inclusively disjunctive account:

3. What makes x and y distinct is that they have a difference in form or have a difference in matter or both.

To make this account work even better, I will stipulate that the difference between an immaterial substance (say, an angel) and a material substance (say, a human) also counts as a difference in matter. Thus, there are two sorts of differences of matter: two things having different matter, or one thing having matter and the other not.

An argument for the three-species view

Some contemporary Thomists have the idea that there are exactly three metaphysical species—three kinds differentiated by qualitatively different natures—of living things: plants (maybe broadly understood as non-sentient living things), mere animals, and rational animals.

Here’s a line of thought that yields two-thirds of the view, starting with a premise that most medieval Aristotelians would have accepted:

1. Our (metaphysical) species is rational animal.

2. Therefore, if there were a rational fish, it would be a member of our species.

3. And, a fortiori any rational ape would be a member of our species.

4. So, all rational fish would be the same species as all rational apes.

5. If all rational fish would be the same species as all rational apes, all non-rational fish are the same species as all non-rational apes.

6. The above generalizes from fish to all other animals.

7. So, all rational animals are the same species and all non-rational animals are the same species.

I don’t have an argument for 5, but it seems pretty plausible.

And the claim that all living non-sentients are the same species doesn’t seem implausible given 7.

I myself reject 1.

What is real change?

I am starting to think that it’s rather mysterious what real change—i.e., non-Cambridge change—is. (Cambridge change is illustrated by examples like: Alice became shorter than her son Bob because Bob grew.)

It is tempting to say:

1. x undergoes non-Cambridge change if and only if there is an intrinsic property that x gains or loses.

But it could well turn out that one can undergo non-Cambridge change with respect to relational, and hence non-intrinsic, properties. The radical, but I think quite possibly correct, example is that it could turn out that all creaturely properties are relational because they all involve participation in God. (Thus, to be green is to greenly participate in God.)

However, there could be less radical cases. For instance, plausibly, shape properties are constituted by relations between an object’s parts and regions of space. But an object’s changing shape is a paradigm example of a non-Cambridge change. Or it might be that a Platonism on which we have an “eye of the soul” that changingly gazes at timeless Platonic objects. It seems like the change in the eye of the soul in coming to gaze on Beauty Itself could be entirely relational and fundamental. In particular, the “gaze” might not be constituted by any non-relational features of the eye of the soul. And yet the change is not a Cambridge change.

It seems to me that this worry gives one some reason to accept this Aristotelian account:

2. x undergoes non-Cambridge change if and only if x has a passive potentiality that is actualized.

I would rather not do that—I have long tried to avoid passive potentialities—but I don’t right now know another alternative to (1). I dislike passive potentialities sufficiently that I am actually tempted to deny that there is an account of the difference between Cambridge and non-Cambridge change. But that would come at a serious cost: it would be hard to account for divine immutability.

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.

Aristotelianism and fundamental particles

A number of contemporary Aristotelians hold to the view that when a fundamental particle becomes or ceases to be a part of an organism, the particle perishes and is replaced by another. The reasoning is that the identity of parts comes from the whole substance, so parts are tied to their substances.

I’ve long inclined to this view, but I’ve also always found it rather hard to believe, feeling that a commitment to this view is a significant piece of evidence against Aristotelianism. I think I may now have found a way to reduce the force of this evidence.

Consider one of the main competitors to Aristotelianism, a non-Aristotelian four-dimensionalism with standard mereology that includes strong supplementation:

1. If y is not a part of x, then y has a part z that does not overlap x.

Together with antisymmetry (if x is a part of y and conversely, then x = y), it immediately follows that:

2. If everything that overlaps x also overlaps y and conversely, then x = y.

Now, suppose that we have a chair made of some fundamental particles. The planks from the chair are ripped off and reassembled into a model trebuchet, with no fundamental particles added or gained. Suppose the fundamental particles are simples. Then any z that overlaps the chair had better overlap at least one fundamental particle u of the chair (the Aristotelian will deny this: it might instead overlap the form) and since fundamental particles are simples it must have u as a part. But u is also a part of the trebuchet. Thus z overlaps the trebuchet, and so anything that overlaps the chair overlaps the trebuchet. And the converse follows by the same argument. Thus, the chair is the trebuchet, which is absurd.

Here is a standard solution to this: fundamental particles are not actually simples, because they have proper temporal parts, and temporal parts are parts. What are the true simples are the instantaneous slices of fundamental particles. Thus a z that overlaps the chair in a fundamental particle u need not overlap the trebuchet as the overlap can happen in disjoint temporal parts of u.

The main competitor to Aristotelianism, thus, has to suppose that fundamental particles are actually made up of their instantaneous slices. Now suppose the Aristotelian accepts this ontology of instantaneous slices of fundamental particles, but denies that there are fundamental particles composed of the slices. Problem solved! We don’t have the problem of fundamental particles persisting beyond the substances that they are parts of, because there are no fundamental particles, just instantaneous slices of fundamental particles.

Is there much cost to this? Granted, we have to deny that there are electrons and the like. But our non-Aristotelian four-dimensionalist mereologist either also denies that there are electrons or else has to construct the electrons out of electron slices, presumably by supposing some sort of a diachronic relation R that relates slices that are to count as part of the same electron. But if we have such a relation, then we can just paraphrase away talk of electrons into talk of maximal sets of electron-slices interrelated by R. If anything, we gain parsimony.

And if we cannot find such a diachronic relation that joins up electron-slices into electrons, then our non-Aristotelian four-dimensionalist has a serious problem, too.

Aristotelianism and transformative technology

The Aristotelian picture of us is that like other organisms, we flourish in fulfilling our nature. Our nature specifies the proper way of interacting with the world. We do not expect an organism’s nature to specify proper ways of interacting with scenarios far from its niche: how bats should fly in weightless conditions; how cats should feed in an environment with unlimited food supply; how tardigrades should live on the moon.

But with technology, we have shifted far from the environment we evolved for. While adaptability is a part of our nature, some technological innovations seem to go beyond the adaptability we expect, in that they appear to impact central aspects of the life of the social beings we are: innovations like the city, writing, and fast and widely accessible global communication. We should not expect for our nature specify how we should behave with respect to these new social technologies. We should have a skepticism that our nature contains sensible answers to questions about how we should behave in these cases.

Thus we appear to have an Aristotelian argument for avoiding the more transformative types of technology, since we are more likely to have meaningful answers to questions about how to lead our lives if our lives are less affected by social transformations. To be on the safe side, we should live in the country, and have most of our social interaction with a relatively small number of neighbors in person.

The theistic Aristotelian, however, has an answer to this. While evolution cannot foresee the Internet, God can, and he can give us a normative nature that specifies how we should adapt to vast changes in the shape of our lives. We do not need to avoid transformative technology in general, though of course we must be careful lest the transformation be for ill.

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’.

More on the centrality of morality

I think we can imagine a species which have moral agency, but moral agency is a minor part of their flourishing. I assume wolves don’t have moral agency. But now imagine a species of canids that live much like wolves, but every couple of months get to make a very minor moral choice whether to inconvenience the pack in the slightest way—the rest is instinct. It seems to me that these canids are moral agents, but morality is a relatively minor part of their flourishing. The bulk of the flourishing of these canids would be the same as that of ordinary wolves.

Aristotle argued that the fact that rationality is how we differ from other species tells us that rationality is what is central to our flourishing. The above thought experiment shows that the argument is implausible. Our imaginary canids could, in fact, be the only rational species in the universe, and their moral agency or rationality (with Aristotle and Kant, I am inclined to equate the two) is the one thing that makes them different from other canids, but yet what is more important to their flourishing is what they have in common with other canids.

At the same time, it would be easy for an Aristotelian theorist to accommodate my canids. One needs to say that the form of a species defines what is central to the flourishing, and in my canids, unlike in humans, morality is not so central. And one can somehow observe this: rationality just is clearly important to the lives of humans in a way in which it’s not so much these canids.

In this way, I think, the Aristotelian may have a significant advantage over a Kantian. For a Kantian may have to prioritize rationality in all possible species.

In any case, we should not take it as a defining feature of morality that it is central to our flourishing.

One might wonder how this works in a theistic context. For humans, moral wrongdoing is also sin, an offense against a loving infinite Creator. As I’ve described the canids, they may have no concept of God and sin, and so moral wrongdoing isn’t seen as sin by them. Could you have a species which does have a concept of God and sin, but where morality (and hence sin) isn’t central to flourishing? Or does bringing God in automatically elevate morality to a higher plane? Anselm thought so. He might have been right. If so, then the discomfort that one is liable to feel at the idea of a species of moral agents where morality is not very important could be an inchoate grasp of the connection between God and morality.

Aristotelian sciences

There is an Aristotelian picture of knowledge on which all knowable things are divided exhaustively and exclusively into sciences by subject matter. This picture appears wrong. Suppose, after all, that p is a fact from one science—say, the natural science fact that water is wet—and q is a fact from another science—say, the anthropological fact that people pursue pleasure. Then the conjunction p and q does not belong to either of these science, or any other science.

One might cavil that a conjunction isn’t another fact over and beyond the conjuncts, that to say p and q is to say p and to say q. I am sceptical, but it’s easy to fix. Just replace my counterexample with something that isn’t a conjunction but is logically equivalent to it, say the claim that it’s not the case that either p or q is false.

Of snakes and cerebra

Suppose that you very quickly crush the head of a very long stretched-out serpent. Specifically, suppose your crushing takes less time than it takes for light to travel to the snake’s tail.

Let t be a time just after the crushing of the head.

Now causal influences propagate at most at the speed of light or less, the crushing of the head is the cause of death, and at t there wasn’t yet time for the effects of the crushing to have propagated to the tip of the tail. Furthermore, assume an Aristotelian account of life where a living thing is everywhere joined with its form or soul and death is the separation of the form from the matter. Then at t, because the effects of crushing haven’t propagated to the tail, the tail is joined with the snake’s form, even though the head is crushed and hence presumably no longer a part of the snake. (Imagine the head being annihilated for greater clarity.)

Now as long as any matter is joined to the form, the critter is alive. It follows that at time t, the snake is alive despite lacking a head. The argument generalizes. If we crush everything but the snake’s tail, including crushing all the major organs of the snake, the snake is alive despite lacking all the major organs, and having but a tail (or part of a tail).

So what? Well, one of the most compelling arguments against animalism—the view that people are animals—is that:

1. People can survive as just a cerebrum (in a vat).

2. No animal can survive as just a cerebrum.

3. So, people are not animals.

But presumably the reason for thinking that an animal can’t survive as just a cerebrum is that a cerebrum makes an insufficient contribution to the animal functions. But the tail of a snake makes an even less significant contribution to the animal functions. Hence:

4. If a snake can survive as just a tail, a mammal can survive as just a cerebrum.

5. A snake can survive as just a tail.

6. So, a mammal can survive as just a cerebrum.

Objection: Only physical effects are limited to the speed of light in their propagation, and the separation of form from matter is not a physical effect, so that instantly when the head is crushed, the form leaves the snake, all at once at t.

Response: Let z be the spacetime location of the tip of the snake’s tail at t. According to the object, at z the form is no longer present. Now, given my assumption that crushing takes less time than it takes for light to travel to the snake’s tail, and that in one reference frame w is just after the crushing, there will also be a reference frame according to which z is before the crushing has even started. If at z the form is no longer present, then the form has left the tip of the tail before the crushing.

In other words, if we try to get out of the initial argument by supposing that loss of form proceeds faster than light, then we have to admit that in some reference frames, loss of form goes backwards in time. And that seems rather implausible.

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.

The inappropriateness of matter explanation of death

A standard Aristotelian explanation of when an organism dies—when its form separates from the body—is that this happens precisely when the organism’s body is no longer “fit” for the form, say because it completely fails to support the basic functions of the type of organism that the form specifies.

If I am right in my series of posts about pointy beginnings and ends (starting with this one), this is a problematic idea. For according to the arguments in the posts, in almost every reference frame, towards the very end of my life, my form (which is my soul) informs a tiny subatomic bit of matter. But no subatomic piece of my matter is supportive of the distinctive functioning of a human being: it is equally supportive of an oak tree, a frog, a human, or just a particle. If I survive until a moment when I am reduced to such a tiny organism, then the “fitness” criterion seems rather meaningless or at best trivial—for as far as this criterion goes, I could survive even if everything was destroyed in me other than a subatomic piece of my left little toe, since the subatomic pieces of my left little toe are no different from the subatomic pieces of any other part of me.

I still suspect that fitness of the body for the form plays some sort of a role in determining the time of death. Plausibly the causal powers of an organism, grounded in the form, are such that when the body stops being capable of supporting the functioning of the organism, the organism’s power to sustain its existence starts to fade, and the organism shrinks (as per my pointiness posts) and dies. However that shrinking is gradual, and not necessitated simply by the unfitness of the matter, but by the unfitness of the matter and the form’s causal powers which explain how quickly the unfitness of the matter is followed by death.

But maybe there is a way out of this argument using this line of thought.

Metaphysical semiholism

For a while I’ve speculated that making ontological sense of quantum mechanics requires introducing a global entity into our ontology to ground the value of the wavefunction throughout the universe.

One alternative is to divide up the grounding task among the local entities (particles and/or Aristotelian substances). For instance, on a Bohmian story, one could divide up 3N-dimensional configuration space into N cells, one cell for each of the N particles, with each particle grounding the values of the wavefunction in its own cell. But it seems impossible to find a non-arbitrary way to divide up configuration space into such cells without massive overdetermination. (Perhaps the easiest way to think about the problem is to ask which particle gets to determine the value of the wavefunction in a small neighborhood of the current position in configuration space. They all intuitively have “equal rights” to it.)

It just seems neater to suppose a global entity to do the job.

A similar issue comes up in theories that require a global field, like an electromagnetic field or a gravitational field (even if these is to be identified with spacetime).

Here is another, rather different task for a global entity in an Aristotelian context. At many times in evolutionary history, new types of organisms have arisen, with new forms. For instance, from a dinosaur whose form did not require feathers, we got a dinosaur whose form did require feathers. Where did the new form come from? Or suppose that one day in the lab we synthesize something molecularily indistinguishable from a duck embryo. It is plausible to suppose that once it grows up, it will not only walk and quack like a duck, but it will be a duck. But where did it get its duck form from?

We could suppose that particles have a much more complex nature than the one that physics assigns to them, including the power to generate the forms of all possible organisms (or at least all possible non-personal organisms—there is at least theological reason to make that distinction). But it does not seem plausible to suppose that encoded in all the particles we have the forms of ducks, elephants, oak trees, and presumably a vast array of non-actual organisms. Also, it is somewhat difficult to see how the vast number of particles involved in the production of a duck embryo would “divide up” the task of producing a duck form. This is reminiscent of the problem of dividing up the wavefunction grounding among Bohmian particles.

I am now finding somewhat attractive the idea that a global entity carries the powers of producing a vast array of forms, so that if we synthesize something just like a duck embryo in the lab, the global entity makes it into a duck.

Of course, we could suppose the global entity to be God. But that may be too occasionalistic, and too much of a God-of-the-gaps solution. Moreover, we may want to be able to say that there is some kind of natural necessity in these productions of organisms.

We could suppose several global entities: a wavefunction, a spacetime, and a form-generator.

But we could also suppose them to be one entity that plays several roles. There are two main ways of doing this:

1. The global entity is the Universe, and all the local entities, like ducks and people and particles (if there are any), are parts of it or otherwise grounded in it. (This is Jonathan Schaffer’s holism.)

2. Local entities are ontologically independent of the global entity.

I rather like option (2). We might call this semi-holism.

But I don’t know if there is anything to be gained by supposing there to be one global entity rather than several.

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.

What has form?

On the question of what has a substantial form, I have tended to think something similar to van Inwagen’s answer to the question of what wholes there are. Namely, I assign form to:

1. organisms, and

2. fundamental objects in physics that are good candidates for being substances.

Regarding 2, if the correct physics is particle-based (which I doubt, in light of the apparent possibility of the world being in a superposition of states with different numbers of particles), these will be particles, or at least those particles that aren’t part of an organism. If the correct physics is field-based, the substances in physics will be fields (or maybe just one field-like object, namely “the global wavefunction”).

A lot of Aristotelians have substances, with forms, that are intermediate between (1) and (2), such as hydrogen atoms or water molecules or chunks of iron, and maybe astronomical objects like stars or galaxies. While I don’t have a knock-down argument against such substances, I also don’t see any reason to posit them.

My reasons for positing form for organisms and fundamental physical objects are quite different. For organisms, the reasons are largely normative. Parrots and oak trees can flourish or languish; they have ends and proper functions. In the case of humans, the normativity extends much further. Furthermore, we need well-defined boundaries for organisms for ethical reasons—there is reason not to harm an organism, especially but not only a human one—and there need to be well-defined persistence conditions for humans for moral responsibility. Something needs to ground all this. And the best candidate is form.

It is a central commitment of Aristotelianism that all of physical reality is grounded in physical substances and their accidents. But it is false that all of physical reality is grounded in organisms. There was a time when the physical universe had no organisms. So we need other substances. The fundamental objects of physics are the best candidates. They are active and have very clear kind-boundaries. The electromagnetic field is a different kind of thing from the gravitational field (which is just spacetime, according to Einstein). Photons are clearly different from electrons. (Though if it turns out that particle number is indeterminate, then particles won’t be the fundamental objects of physics.)

Granted, it is not obvious (and somewhat counterintuitive) that organisms have well-defined kind-boundaries and identity conditions. And it is not obvious (and somewhat counterintuitive) that fundamental physical objects have norms. But here I just take these to be consequences of the theory. Organisms have well-defined kind-boundaries and identity conditions, but we don’t know where they lie. Fundamental physical objects have normative properties, but I suspect they are perfect instances of their kind, and always do exactly what they should (C. S. Lewis says something like that in Mere Christianity).

Neither of my two reasons applies much to objects like atoms, molecules, chunks of stuff, or astronomical objects. There is no strong independent reason to suppose that they have normative properties in their own right, and their boundaries are, if not quite as fuzzy as those of organisms, pretty fuzzy. How far apart do I get to move a hydrogen atom from two oxygen atoms before I destroy a water molecule? How many sodium and chloride ions do I add to water to change it from water with impurities to a salt solution? (I suppose the concept of impurity pulls in the direction of thinking there are normative properties. But here is a reason to think this is mistaken. If impure water is languishing, then we have reason to distill water independently of any practical benefit to any organism, just for the sake of the water itself. That seems absurd.)

That the reasons don’t apply doesn’t show that there aren’t other reasons to posit substantial forms for these other candidates. But I don’t see such reasons. And so we can apply Ockham’s razor.

Complexity and skeptical hypotheses

Suppose a strong epistemic preference for simpler theories of the world. One might then think that a simulation hypothesis is automatically more complex than the best physical story about our world, because in addition to all the complexity of our simulated cosmos, it includes the complexity of whatever physical cosmos houses the hardware running the simulation.

But this need not be the case. The best physical story about our world makes our world include vast amounts of information that would not need to be included in the simulation. To simulate the history of the human race, we at most need information on the particles wihtin a sphere of radius about a hundred thousand light-years, so basically just the Milky Way Galaxy, a very small fraction of the particles in the world. And even that is a vast overstatement. One can surely have a low simulation resolution for a lot of stuff, simulating things only on a macroscopic level, and only including particle-level information when the simulated humans peer into scientific instruments. So the information content of the simulation software could be much, much lower than the information content of the physical world that our best theories say we live in.

But what about the simulation hardware itself? Wouldn’t that need to live in a complex physical universe? Maybe, but that universe need not be as complex as our physical theories claim ours to be. It could be a universe that has a level of physical complexity optimized for running the computing hardware. The granularity of that universe could be much coarser than ours. For instance, instead of that universe being made of tiny subatomic particles like ours, requiring many (but fewer and fewer with progress in miniaturization) particles per logic gate, we could suppose a universe optimized for computing whose fundamental building blocks are logic gates, memory cells, etc.

I am dubious, thus, whether we can rule out simulation hypotheses by an epistemic preference for simpler theories. The same goes for Berkeleian skeptical hypotheses on which there is no physical world, but we are disembodied minds being presented with qualia.

And of course the “local five minute hypothesis”, on which the universe is five minutes old and has a radius of five light-minutes, posits a world with intuitively much less complexity than the world of our best theories, a world with vastly fewer particles.

But if we cannot avoid skeptical hypotheses on grounds of complexity, how can we avoid them?

My current view is that we simply have to suppose that our priors are normatively constrained by human nature (which on my Aristotelian view is a form, a real entity), and human nature requires us to have non-skeptical priors. This is a very anthropocentric account.

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.

Species flourishing

As an Aristotelian who believes in individual forms, I’m puzzled about cases of species-level flourishing that don’t seem reducible to individual flourishing. On a biological level, consider how some species (e.g., social insects, slime molds) have individuals who do not reproduce. Nonetheless it is important to the flourishing of the species that the species include some individuals that do reproduce.

We might handle this kind of a case by attributing to other individuals their contribution to reproduction of the species. But I think this doesn’t solve the problem. Consider a non-biological case. There are things that are achievements of the human species, such as having reached the moon, having achieved a four minute mile, or having proved the Poincaré conjecture. It seems a stretch to try to individualize these goods by saying that we all contributed to them. (After all, many of us weren’t even alive in 1969.)

I think a good move for an Aristotelian who believes in individual forms is to say that “No man or bee is an island.” There is an external flourishing in virtue of the species at large: it is a part of my flourishing that humans landed on the moon. Think of how members of a social group are rightly proud of the achievements of some famous fellow-members: we Poles are proud of having produced Copernicus, Russians of having launched humans into space, and Americans of having landed on the moon.

However, there is still a puzzle. If it is a part of every human’s good that “I am a member of a species that landed on the moon”, does that mean the good is multiplied the more humans there are, because there are more instances of this external flourishing? I think not. External flourishing is tricky this way. The goods don’t always aggregate summatively between people in the case of external flourishing. If external flourishing were aggregated summatively, then it would have been better if Russia rather than Poland produced Copernicus, because there are more Russians than Poles, and so there would have been more people with the external good of “being a citizen of a country that produced Copernicus.” But that’s a mistake: it is a good that each Pole has, but the good doesn’t multiply with the number of Poles. Similarly, if Belgium is facing off Brazil for the World Cup, it is not the case that it would be way better if the Brazilians won, just because there are a lot more Brazilians who would have the external good of “being a fellow citizen with the winners of the World Cup.”