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.

The Hermes in the marble

A substance’s existence does not ontologically depend on the state of anything beyond the substance. But a typical artifact depends on absences of materials beyond itself. A classic example is a statue that comes into existence when the surrounding marble is removed. The statue’s existence is grounded in part in the absence of the surrounding marble. Similarly, even if a knife blade is made by forging rather than by removal of material, one can destroy the blade by encasing it in a block of steel: the existence of the knife is grounded in part in the absence of surrounding steel.

Thus, it seems, typical artifacts are not substances.

But this argument was too quick. What if the laws of nature are such that the following is true? When the sculptor chips away the surrounding marble to make the Hermes, a non-physical component, a form, of the Hermes comes into existence. That form is united with the Hermes’ matter. And what makes the statue be itself is not the absence of surrounding matter, but the presence of the form. It may be that by the laws of nature the form only comes into existence as a result of the removal of material, but it would be logically possible for the form to come into existence without any removal: the statue causally but not ontologically depends on the absence of surrounding material. God could make the statue within the block of marble, without any removal of material, simply by creating a form for a Hermes-arranged subset of marble molecules.

(One could also have a non-Aristotelian version of this account in terms of Markosian’s brute theory of composition.)

I think the above Aristotelian story is implausible. One reason is that the story conflicts with our intuitions as to the survival conditions for artifacts. A statue is essentially a statue. But the Hermes-shaped bundle of atoms in the block marble, even if distinguished by a metaphysical union with a form, are not a statue. Maybe God could make a form for these atoms, but it wouldn’t be the form of an artifact.

The weird view that particles don't survive substantial change

I have a weird view: when a dog or another substance ceases to exist, all its particles cease to exist, being replaced by new particles with very similar physical parameters (with the new physical parameters being predictable via the laws of nature). Similar things happen when a new substance comes into existence, and when a particle is incorporated into or leaves a substance: no particles survive such things.

I have good Aristotelian reasons for this view. Particles are not substances, since substances cannot have substances as parts, and hence ontologically depend on substances for their existence. Thus, when the substance perishes, the particles do as well.

The view seems preposterously unparsimonious. I disagree. Let’s compare the view to some competitors. First of all, it’s clear to me that some version of four-dimensionalism is true, so let’s start with four-dimensionalist views.

A standard four-dimensionalism is perdurantism: four-dimensional objects are made up of instantaneous temporal parts—infinitely many of them if time is continuous. These instantaneous temporal parts come in and out of existence all the time, with very similar physical parameters to their predecessors. My weird view is compatible with the idea that particles actually all exist only instantaneously, akin to the perdurantist’s temporal parts. Such a view could be more parsimonious than standard perdurantism for two reasons: first, it needn’t posit temporal parts of substances, and, second, it needn’t posit wholes made up of the instantaneous particles.

An alternate version of my weird view says that particles do not survive change of substance, but live as long as they recognizably remain in the same substance. Imagine a particle that is eaten by a dog and some months later sloughed off. On my view, there are three particle-like objects in the story: the pre-dog particle, the in-dog particle, and the post-dog particle. On standard perdurantism, there are as many particle-like objects as moments of time in this story. Granted, some may think it weirder that the temporal boundaries in the existence of particles are determined by their allegiances to substances rather than by instants of time. But there is nothing weird about that if one takes seriously the priority of substances to their parts.

My view is admittedly less parsimonious than a four-dimensionalist view on which substances and particles are temporally extended, have no temporal parts, and particles outlast their substances. But such a four-dimensionalist has an implausible consequence. Many people will find plausible the idea that in some exceptional cases substances can share parts: conjoined twins are a standard example. But on this version of four-dimensionalism, it is now a matter of course that distinct substances share parts. The dog dies and some of its particles become a part of a flower: so the dog and the flower, considered as four-dimensional entities, have these particles as common parts. You and I share probably share parts with dinosaurs. So while my weird view is less parsimonious than a no-temporal-parts four-dimensionalism with particles that outlive substances, it is not less plausible.

The main alternative to four-dimensionalism is presentism. Is a presentist version of my view less parsimonious than a typical competing presentist view? In one sense, not. For at the present time, my view doesn’t posit additional present particles over and beyond those present particles posited by competing presentist views. And only present particles exist according to presentism! But more seriously, my view does posits that particles cease to exist and come into existence more than on typical presentist alternatives. So in that sense it is less parsimonious.

Thus, parsimony cuts against my view on presentism, but it may actually favor it on four-dimensionalism.

Materiality and spatiality

I’ve been fond of the theory that materiality is just the occupation of space. But here is a problem for that view.

I have argued previously that we should distinguish between the internal space (or geometry) of an object and external space. Here is quartet of considerations:

• Imagine a snake one light-year in length out in empty space arranged in a square. Then imagine that God creates a star in the middle of the square. The star instantly disturbs the geometry of space and makes the distances between parts on opposite sides of the square be different from what they previously where. But this does not make any intrinsic change to the snake until physical influence can reach the snake from the star, which will take about 1/8 of a year (the sides of the square will be 1/4 light-years, so the closest any part of the snake is to the center is 1/8 light years). The internal geometry of the snake differs from the external one.

• We have no difficulty imagining a magical house whose inside is larger than its outside.

• Christ in the Eucharist has very different (larger!) internal size and geometry from the external size and geometry of where he is Eucharistically located.

• Thought experiments about time travel and the twin paradox suggest that we should distinguish internal time from external time. But space is like time.

Now, if internal and external space can come apart so much, then it is plausible that an object could have internal space or geometry in the absence of any connection to external space. Furthermore, if a material object ceased to have an occupation relation to external space but retained its internal geometry, it would surely still be material. Only a material object can be a cube. But a cubical object could remain a cube in internal geometry even after losing all relation to external space. But if so, then materiality is not the occupation of external space.

In fact, even independently of the above considerations about internal and external space, it just doesn’t seem that objects are material in virtue of a relation to something beyond them—like external space.

So, it seems, objects aren’t material in virtue of the occupation of external space. Could they be material in virtue of the occupation of internal space? Not substances! A substance does not occupy its internal space. It has that internal space, and is qualified by it, but it seems wrong to say that it is in it in the sense of occupation. (Perhaps the proper parts of material substances do occupy the substance’s internal space.) But some substances, say pigs or electrons, are material. So materiality isn’t a function of the occupation of internal space, either. And unless we find some third sort of space, we can’t say that materiality is a function of the occupation of space.

Perhaps, though, we can say this. Materiality is the possession or occupation of space. Then material substances are material by possessing internal space, and the proper parts of material substances are material by occupying the substance’s internal space. On this view, the materiality of me and my heart are analogically related—a fine Aristotelian idea.

But I have a worry. Point particles may not exist, but they seem conceivable. And they would be material. But a point particle doesn’t seem to have an internal space or geometry. I am not sure what to say. Perhaps, a point particle can be said to be material by occupying external space (in my proposed account of materiality, I didn’t specify that the space was internal). If so, then a point particle, unlike a square snake, would cease to be material if it came to be unrelated to external space. Or maybe a point particle does have an internal zero-dimensional space. It is hard to see what the spatiality of this “space” would consist in, but then we don’t have a good account of the spatiality of space anyway. (Maybe the spatiality of an internal space consists in a potentiality to be aligned with external space?) And, finally, maybe point particles that are points both externally and internally (particles that have non-trivial internal geometry but that are externally point-like aren’t a problem for the view) either aren’t material or aren’t possible.

Minimizing the number of fundamental relations between concreta

An interesting metaphysics project that could use more work is to minimize the number of fundamental non-intentional relations between substances. How few can we do with? I think it would be really great if one could reduce the number of such relations to a handful of relations, or at least determinable families of relations. There is only one candidate really clear to me: causation. I think it would be an interesting research project to adopt the working hypothesis that causation is the one and only such relation and see how things go.

A lot of people will want to add parthood to this list, but I don't think a substance can be a part of another substance. (Parts are grounded in wholes, and substances are not grounded in other things.) Spatial relations like being seven meters apart (on relationalism about locations) and being located at (on substantivalism about locations) are a family of plausible candidates.

From bundles to bare particulars and back again

Here's a compelling narrative. Start with the bundle theory of substance: substances are nothing but bundles of properties. Then observe that this suffers from serious problems. If a substance is nothing but a bundle of properties, it is unclear how a substance could have had other properties than it does. Further, intuitively it should be possible to have two indiscernible substances--ones with all the same properties. This motivates a move to bare particular theory. According to bundle theory, substances were constituted by one kind of thing: properties. Bare particular theory makes substances be constituted by both properties and a special entity, the bare particular. Introducing the bare particular solves the modal problem, since we can say that the identity of substances is grounded in the identity of the bare particulars, so you can have a substance in one world with different properties than the very same substance in another world, as long as the same bare particular is found in both. Further, there is no difficulty with indiscernibles, as long as you have two bare particulars.

Note that this narrative isn't quite the standard narrative about bare particulars. The standard narrative introduces bare particulars to solve the problem of predication, by making the bare particular be the subject of predication. That standard narrative, however, falls prey to a problem that Andrew Bailey points out: we don't want to say that the bare particular has the ordinary properties of the host substance (for then we get reduplication), but if it does not, then it's not the subject of predication.

So let's stick to my from-bundles-to-bare-particulars narrative. But at this point there is a really interesting move possible, one that was pointed out in my undergraduate metaphysics class by a brilliant freshman, Rose Brugger. According to bare particular theory, substances are constituted by two kinds of things: properties and a bare particular. But Brugger suggested that we take the bare particular to just be an individuating property. Namely, a haecceity.

The result is a really interesting theory. It is a kind of bundle theory. However, first, the motivations for bare particular theory continue to be satisfied: we can ground identity between substances in identity of the haecceity. Second, we solve the puzzle of the mysterious "bareness" of the bare particular: the haecceity isn't some weird propertyless individual, but just a property, albeit a special one. Third, the resulting theory is more parsimonious, because it posits one fewer fundamental category: all it needs are substances and their constituent properties, without a separate category of bare particulars.

The resulting theory is superior to both standard bundle theory and standard bare particular theory, being only slightly more complex than standard bundle theory but solving a number of problems.

A theory of time

This isn't meant to be a very good theory, but it's a start. The primitive notion I want to explicate is this notion of temporal priority between events: A is at least in part earlier than the start of B. I will abbreviate this to "A is earlier than B". And then we say that A is earlier than B if and only if there is a chain of at least partial causation starting at A and ending at B.

A consequence of this theory is that it is not possible to have simultaneous causation: if A causes B, then A is earlier than B. That's a count against it, but perhaps not a fatal one.

Another consequence of this theory is that it gives no account of simultaneity between events. That may not be such a bad thing.

A limitation is that we have no notion of a time, just of temporal ordering of events. That may be fine. But the costs are adding up.

I am more troubled by the fact that this rules out time travel and, more generally, temporally backwards causal influences. This makes me want to reject the theory.

But I can reprise the theory, not as a theory of the temporal priority between events, but of the temporal priority between accidents (or maybe just modes?) of a single substance. Just say that an accident A of a substance S is earlier than an accident B of S if and only if there is a chain of at least partial causation between accidents of S starting at A and ending at B.

We still have to rule the possibility of temporally backwards causation within the life of a single substance. But that's less costly, I think, than ruling out temporally backwards causation between events in general.

We still have the problem of not having simultaneous causation or any account of simultaneity for that matter. And no notion of times.

We can introduce times as follows. In some worlds, it will happen that there are nomic relationships between the accidents of a substance that are simply parametrized in terms of some parameter t such that accident A is earlier than accident B (in the above causal sense) if and only if t(A)<t(B). In such a case, we can call values of this parameter times. In worlds where there is no such neat parametrization, there may be temporal priority, but no times.

We get divine internal atemporality now as a corollary of the claim that God has no accidents.

But there are still a lot of costs. For one, the lack of a notion of simultaneity makes it hard to make sense of the transcendental unity of apperception. Maybe that's just too bad for that unity?

Love of substances

Thesis: Necessarily, it is appropriate to love x in the primary (or focal) sense of "love" if and only if x is a substance.

Why? Maybe because of the Augustinian and Thomistic doctrine of the interchangeability of being and love, and the Aristotelian doctrine that substances are what has being in the primary sense.

If the Thesis is true, this has metaphysical and ethical consequences. Metaphysical consequence: All persons are substances. Ethical consequence: We shouldn't love countries, nations, ecosystems, galaxies, ideas, etc. in the primary sense of "love". If, further, we add the Aristotelian claim that the only real substances there are beings that have life, we get the useful fact that we shouldn't love our non-living material possessions in the primary sense of "love". (I am open, however, to particles being substances. It's odd to say that I should love particles in the primary sense. But less odd when one considers the fact that they do have a sort of "life", and even less odd when one adds that love needs to be proportioned to the dignity of the beloved, so that particles, though lovable in the primary sense, are lovable in only a little way.)