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.

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.

Microphysics and philosophy of mind

Much (but not all) contemporary philosophy of mind is written as if microphysics were fundamental physics. But as far as I know, only on those interpretations of quantum mechanics that disallow indeterminacy as to the number of particles can microphysics be fundamental physics. The most prominent such interpretation is Bohmianism. On most other interpretations, the most we can say about the number of particles is that we are in a superposition between states with different numbers of particles. But reality has to have determinate numbers of fundamental entities. The picture of reality we get from both relativity theory and mainstream interpretations of quantum mechanics other than Bohmianism and its close cousins is that fundamental physical reality consists of global entities such as the spacetime manifold or the wavefunction of the universe rather than microscopic entities like particles. (I am attracted to a non-mainstream interpretation on which the fundamental physical entities may include mid-sized things like dogs and trees.)

Sometimes, pretending microphysics is fundamental physics is excusable. For certain discussions, it doesn’t matter what the fundamental physics is—the arguments work equally well for global and local fundamental entities. In other cases, all that matters is relative fundamentality. Thus, facts about chemistry might be held to be more fundamental relative to biology, and facts about microphysics might be fundamental relative to chemistry, even if the microphysics facts themselves are not fundamental simpliciter, being reducible, say, to facts about global fields.

But even when the arguments do not formally rely on fundamental physics being microphysics, it is risky in a field so reliant on intuition to let one’s intuitions be guided by acting as if fundamental physics were microphysics. And doing this is likely to mis-focus one’s critical attention, say focusing one more on the puzzle of why the functioning of various neurons produces a unified consciousness than on the puzzle of how the functioning of a handful of global entities results in the existence of billions of minded persons.

Towards a postcorpuscular ontology

My intuition is that quantum physics presents a picture of reality on which fundamental particles rarely if ever exist simpliciter. Most of the time, the world is in a superposition of the particle existing and not-existing, though perhaps with a much heavier weight being given to the one state rather than the other. Perhaps just at the moment of quantum collapse a particle simply exists. But immediately afterwards, there will be some interaction at the tail end of the wavefunction that makes the particle’s “existence” be in a superposition. And superposed existence is not real existence, since superposed existence comes in degrees, while real existence does not (at least not in the relevant sense of “degrees”).

If my intuition is right, then over the past hour, I take it that on a quantum picture at most instants of time no particles of my body were really existing. Maybe occasionally some particles flashed into being due to some collapse, but at most times there weren’t any particles there.

This means that at most times over the past hour one of the following was true:

1. I didn’t exist

2. I existed immaterially

3. I existed materially without having any particles.

Option (1) leads to ethical and theological difficulties. On that view, I am constantly popping in and
out of existence. But if so, then I am constantly dying and being resurrected. And that robs death and resurrection of their deep moral significance.

Option (2) leads to the interesting question whether I always exist immaterially, or only when none of my particles exist. If always, we get a very strong dualism. If sometimes, then we get a very funny semi-dualism: most of the time I’m immaterial.

Option (3) seems to me to be the most plausible. But on option (3), we should not think of material existence as a function of being constituted by particles. The kind of picture of material existence we get from van Inwagen, where living things come into existence by having their constituent particles get caught up in a life is untenable. Perhaps, instead, material existence is a function of having a certain kind of relationship to the wavefunction of the universe (perhaps a relationship of partly constituting or being partly constituted by that wavefunction).

If my argument is right, then Aristotelian metaphysicians should stop worrying very much about the pesky problem of what happens to the identities of fundamental particles when they get incorporated into our bodies. If there are ever any particles at all, then on quantum grounds independent of Aristotelian metaphysics, they are evanescent beings that do not persist long enough—for their existence soon becomes superposed—to cause much of a problem on that score. I suppose it could still be a problem if they come back into existence later. But it is dubious whether the numerically same particles can come back into existence. Indeed, the whole business of the particles “in the body” is so dubious on quantum grounds, that there is little theoretical cost to such seemingly absurd solutions as saying that there are no electrons in the body—for it seems we should anyway think that most of the time there aren’t any electrons in the body.

In the above, I allowed that perhaps when we have the right eigenstate, for a very short time a particle exists. But even that, I think, is dubious. The change from the system being in an eigenstate of particle number and not being in an eigenstate of particle number seems to be a merely quantitative change in the wavefunction, and hence we have little reason to think it corresponds to substantial generation or corruption.

There is one way out of all of the above: to accept a Bohmian interpretation of quantum mechanics. If I am right, then much contemporary metaphysics is being done on the implicit assumption that something like Bohmianism is right. But why assume that?

Perdurance and particles

A perdurantist who believes that particles are fundamental will typically think that the truly fundamental physical entities are instantaneous particle-slices.

But particles are not spatially localized, unless we interpret quantum mechanics in a Bohmian way. They are fuzzily spread over space. So particle-slices have the weird property that they are precisely temporally located—by definition of a slice—but spatially fuzzily spread out. Of course, it is not too surprising if fundamental reality is strange, but maybe the strangeness here should make one suspicious.

There is a second problem. According to special relativity, there are infinitely many spacelike hyperplanes through spacetime at a given point z of spacetime, corresponding to the infinitely many inertial frames of reference. If particles are spatially localized, this isn’t a problem: all of these hyperplanes slice a particle that is located at z into the same slice-at-z. But if the particles are spatially fuzzy, we have different slices corresponding to different hyperplanes. Any one family of slices seems sufficient to ground the properties of the full particle, but there are many families, so we have grounding overdetermination of a sort that seems to be evidence against the hypothesis that the slices are fundamental. (Compare Schaffer’s tiling requirement on the fundamental objects.)

A perdurantist who thinks the fundamental physical entities are fields has a similar problem.

A supersubstantialist perdurantist, who thinks that the fundamental entities are points of spacetime, doesn’t run into this problem. But that’s a really, really radical view.

An “Aristotelian” perdurantist who thinks that particles (or macroscopic entities) are ontologically prior to their slices also doesn’t have this problem.

Perdurance, Relativity and Quantum Mechanics

It is known that perdurantists, who hold that objects persisting in time are made of infinitely thin temporal slices, have to deny that fundamental particles are simple (i.e., do not have (integral) parts). For a fundamental particle is an object persisting in time, and hence will be made of particle-slices.

But what is perhaps not so well-known is that on perdurantism, the temporal slices a particle is made of will typically not be simple either, given some claims from standard interpretations of Quantum Mechanics and Special Relativity. The quick version of the argument is this: the spatial non-localizability of quantum particles requires typical temporal slices to be non-localized simples (e.g., extended simples), but this runs into relativistic problems.

Here is a detailed argument.

A perdurantist who takes Relativity seriously will say that for each inertial reference frame R and each persistent object, the object is made of R-temporal slices, where an R-temporal slice is a slice all of whose points are simultaneous according to R.

Now, suppose that p is a fundamental particle and that p is made up of a family F₁ of temporal slices defined by an inertial reference frame R₁. Now, particles are rarely if ever perfectly localized spatially on standard interpretations of Quantum Mechanics (Bohmianism is an exception): except perhaps right after a collapse, their position is fuzzy and wavelike. Thus, most particle-slices in F₁ will not be localized at a single point. Consider one of the typical unlocalized particle-slices, call it S. Since it’s not localized, S must cover (be at least partially located at) at least two distinct spacetime points a and b. These points are simultaneous according to R₁.

But for two distinct spacetime points that are simultaneous according to one frame, there will be another frame according to which they are not simultaneous. Let R₂, thus, be a frame according to which a and b are not simultaneous. Let F₂ be the family of temporal slices making up p according to R₂. Then S is not a part (proper or improper) of any slice in F₂, since S covers the points a and b of spacetime, but no member of F₂ covers these two points. But:

1. If a simple x is not a part of any member of a family F of objects, then x is not a part of any object made up of the members of that family.

Thus, if S is simple, then S is not a part of our particle p, which is absurd. Therefore, for any reference frame R and particle p, a typical R-temporal slice of p is not simple.

I think the perdurantist’s best bet is supersubstantialism, the view that particles are themselves made out of points of spacetime. But I do not think this is a satisfactory view. After all, two bosons could exist for all eternity in the same place.

Without Relativity, the problem is easily solved: particle-slices could be extended simples.

It is, I think, ironic that perdurantism would have trouble with Relativity. After all, a standard path to perdurantism is: Special Relativity → four-dimensionalism → perdurantism.

I myself accept four-dimensionalism but not perdurantism.

Life and non-life

Assume a particle-based fundamental physics. Then the non-living things in the universe outnumber the living by many orders of magnitude. But here is a striking fact given a restricted compositionality like van Inwagen’s, Toner’s or mine on which all there are is in the universe are particles and organisms: the number of kinds of living things outnumbers the number of kinds of non-living things by several orders of magnitude. The number of kinds of particles is of the order of 100, but there are millions of biological species (they may not all correspond to metaphysical species, of course).

Counting by individuals, living things are exceptional. But counting by kinds, physical things are exceptional. Only a tiny portion of the universe is occupied by life. But on the other hand, only a tiny portion of the space of kinds of entities is occupied by non-life.

I am not sure what to make of these observations. Maybe it is gives some credence to an Aristotelian rather than Humean way of seeing the world by putting the the kinds of features as teleology that are found in living things at the center of metaphysics.

Partial location, quantum mechanics and Bohm

The following seems to be intuitively plausible:

1. If an object is wholly located in a region R but is not wholly located in a subregion S, then it is partially located in R−S.
2. If an object is partially located in a region R, then it has a part that is wholly located there.

The following also seems very plausible:

3. If the integral of the modulus squared of the normalized wavefunction for a particle over a region R is 1, then the particle is wholly located in the closure of R.
4. If the integral of the modulus squared of the normalized wavefunction for a particle over a region R is strictly less than one, then the particle is not wholly located in the interior of R.

But now we have a problem. Consider a fundamental point particle, Patty, and suppose that Patty's wavefunction is continuous and the integral of the modulus squared of the wavefunction over the closed unit cube is 1 while over the bottom half of the cube it is 1/2. Then by (3), Patty is wholly contained in the cube, and by (4), Patty is not wholly contained in the interior bottom half of the cube. By (1), Patty is partially located in the closed upper half cube. By (2), Patty has a part wholly located there. But Patty, being a fundamental particle, has only one part: Patty itself. So, Patty is wholly located in the closed upper half cube. But the integral of the modulus squared of the wavefunction over the closed upper half cube is 1−1/2=1/2, and so (4) is violated.

Given that scenarios like the Patty one are physically possible, we need to reject one of (1)-(4). I think (3) is integral to quantum mechanics, and (1) seems central to the concept of partial location. That leaves a choice between (2) and (4).

If we insist on (2) but drop (4), then we can actually generalize the argument to conclude that there is a point at which Patty is wholly located. Either there is exactly one such point--and that's the Bohmian interpretation--or else Patty is wholly multilocated, and probably the best reading of that scenario is that Patty is wholly multilocated at least throughout the interior of any region where the modulus squared of the normalized wavefunction has integral one.

So, all in all, we have three options:

• Bohm
• massive multilocation
• partial location without whole location of parts (denial of (2)).

This means that either we can argue from the denial of Bohm to a controversial metaphysical thesis: massive multilocation or partial location without whole location of parts, or we can argue from fairly plausible metaphysical theses, namely the denial of massive multilocation and the insistence that partial location is whole location of parts, to Bohm. It's interesting that this argument for Bohmian mechanics has nothing to do with the issues about determinism that have dominated the discussion of Bohm. (Indeed, this argument for Bohmian mechanics is compatible with deviant Bohmian accounts on which the dynamics is indeterministic. I am fond of those.)

I myself have independent motivations for embracing the denial of (2): I believe in extended simples.

Are elementary particles extended simples?

This argument is valid and every premise is plausible:

1. An elementary particle is located at every point where its wavefunction is non-zero.
2. An elementary particle is simple.
3. A simple located at every point of a region with non-zero volume is an extended simple.
4. Typical elementary particles have a wavefunction that is non-zero at every point of a region with non-zero volume.
5. So, typical elementary particles are extended simples.

Why so few kinds for so many particles?

There are something like 10⁸⁰ individual particles and only something like 10² kinds of particles. It seems an incredible coincidence; so many particles, all drawn from so few kinds, even though surely the space of metaphysical possibility contains infinitely many kinds. It's like a country all of whose citizens have names that start with A, B or M.

But perhaps one could explain this by the massively multilocated particle hypothesis (MMPH), namely that to each kind there corresponds only one individual, but highly multilocated, particle (Feynman proposed something like this)? It isn't surprising, after all, if all the names of the villagers in a village start with A, B or M when there are only three villagers.

Still, MMPH does bring in a new mystery: Why are there so very few particles? But perhaps that is a less pressing question?

Particle accretion and excretion in Aristotelian ontology

In Aristotelian ontology the matter and parts of a substance get their being from their substance. But now we have a problem: we constantly accrete (say, when eating) and excrete (say, when sloughing off skin-cells) particles. These particles seem to exist outside of us, then they exist as part of us, and then one day they come to exist outside of us again. How could their being come from our form, when they existed before they joined up with us—sometimes, presumably, even before we existed at all?

But suppose an ontology for physics on which fields are more fundamental than particles, and particles are like a bump or wave-packet in a field. Then we have a very nice solution to the problem of accretion and excretion.

Imagine two ropes. Rope A is tied by one end to a hook on the wall and the other end of rope A is tied to the end of rope B. And you're holding the other end of rope B. You rapidly move your end of the rope up and down. A wave starts traveling along rope B, then over the knot, and finally along rope A. We are quite untroubled by this description of this ordinary phenomenon.

In particular, it is correct to say that the same wave was traveling along rope A as along rope B. Yet surely the being of a wave in a medium comes from the medium and its movement. So we have a very nice model. Rope A has excreted the wave and rope B has accreted the wave. (You might object that in Aristotelian ontology, ropes aren't substances. Very well: replace them with strings of living kelp.) If the knot is negligible enough, then the shape of the wave will seamlessly travel from rope A into rope B.

I think one reason an Aristotelian is apt to be untroubled by the description is because we don't take waves in a rope ontologically very seriously, just as we shouldn't take kings in chess very seriously. They're certainly not fundamental. Perhaps they don't really exist, but we have merely adopted a mode of speech on which it's correct to talk as if they existed.

However, if a field ontology is correct, we shouldn't take particles any more seriously than waves in a rope. And then we can start with the following model. Among the substances in the world, there are fields, gigantic objects that fill much of spacetime, such as the electromagnetic field. And there are also localized substances, which are tiny things like an elephant or a human or a bacterium. The fields have holes in them, holes perfectly filled by the localized substances. The localized substances exist within the fields much like a diver exists in the ocean—the diver exists in a kind of hole in the ocean's water.

Next, pretty much the same kinds of causal powers that are had by the fields are had by the localized substances. Thus, while strictly speaking there is no electromagnetic field where your body is found, you—i.e., the substance that is you—act causally just as the electromagnetic field would. A picture of the field you might have is of a string whose central piece had rotted out and was seamlessly replaced with a piece of living kelp that happened to have the same material properties as the surrounding string. But you don't just do duty for the electromagnetic field. You do duty for all the fundamental fields.

Because you have pretty much the same kinds of causal powers as the fields that surround you, waves can seamlessly pass through you, much as they can through a well-installed patch in a rubber sheet. You accrete the waves and then excrete them. Some wave packets we call "particles".

Objection: When I digest something, it becomes a part of me. But when a radio wave passes through me, it doesn't become a part of me even for a brief period of time.

Response 1: We shouldn't worry about this. In both cases we're talking about non-fundamental entities. There are many ways of talking. For practical reasons, it's useful to distinguish those wave packets that stick around for a long time from those that pass in and out. So we say that the former are denizens of us and the latter are visitors.

Response 2: Perhaps that's right. Maybe we don't exist in holes in the fields, but rather the fields overlap us. However, when the fields are in us, we take over some, but not all, of their causal powers. The radio wave that travels through me does so by virtue of the electromagnetic field's causal powers, while the particles of the piece of cheese that I digest and which eventually slough off with my dead skin travel through me by virtue of my causal powers. The picture now is more complicated.

Big or small?

Isn't it interesting that we are currently don't know whether the fundamental physical entities are the tiniest of things—particles—or the largest of things—fields—or both?

Particles

I used to worry for Aristotelian reasons about the particles making up my body. The worry went something like this: Elementary particles are fundamental entities. Fundamental entities are substances. But no substance has substances as parts. The last is, of course, a very controversial bit. However there are good Aristotelian reasons for it.

But I shouldn't have worried much. Elementary particles are not all that likely to be fundamental entities. Quantum mechanics, after all, allows all sorts of superpositions between different particles. But substances either simply exist or simply don't. In the superposition case, they don't simply exist. So they simply don't. But I would expect that the superposition case is more the rule than the exception (if only with small coefficients for all but one one state). I guess we could think that when the wavefunction is in a pure state with respect to the existence of a particle, the particle then pops into existence, and when the state becomes mixed, it pops right out. But notice that the physics behaves in much the same way when we have a pure state and when we have a mixed state that is to a very high approximation pure. So whatever explanatory role the particles play when they pop into existence can be played, it seems, by the wavefunction itself when the particles aren't around. This suggests that the wavefunction is the more explanatorily fundamental entity, not the particles. Of course, the above relies on denying the Bohmian interpretation of quantum mechanics. But it's enough, nonetheless, to establish that elementary particles aren't all that likely to be fundamental entities. And hence they aren't all that likely to be substances.

Of course, it may be that the things that are fundamental physical entities will turn out to be just as problematic for the Aristotelian as the particles were...

Eddington's Two Tables

As far back into my childhood as I remember thinking about such things, I thought of the physical objects around me as made up of particles. I learned last night, in talking to various philosophers, that this attitude in childhood is not universal. In fact, apparently, many educated people have Aristotelian intuitions that material objects are solid and continuous through and through, and while they can think the particle hypothesis, it does not come naturally to them.

This is an interesting case of how theory-laden the "intuitive" can be. To me, it is entirely intuitive to see an object as a bunch of particles, though I wouldn't say that I have a positive intuition that it is so—just a pervasive belief. At the same time, this is a belief I need to think myself out of (and into a suspension of judgment) because I do not think current physics gives one good reason to think there are particles.

This little case study is kind of scary to me. For instance, right now it seems entirely intuitive that space-time be a four-dimensional manifold, with time being ontologically on par with other dimensions. In fact, I've gotten to the point where a philosophical statement that says something like "substance S has accident A at time t" seems clearly incomplete: I want to know which reference frame this is in, and how the accident is spread out in a space-like hypersurface.

But since these intuitions are highly dependent on a physics that might turn out to be wrong (quantum theory and relativity theory are not both true, since they are incompatible), I need to be more open to three-dimensionalist ideas, which I find kind of scary. Three-dimensionalist ideas induce a kind of conceptual vertigo in me—the thought that I am this three-dimensional object in some kind of flow of time is weird, though I do of course think such metaphors sometimes.

Parts and ownership

Some Aristotelians believe the following thesis: When a bit of matter comes to be a part of a substance, it ceases to exist. I.e., the bit of matter comes to be a part of a substance in the way in which a horse comes to be a corpse--the horse and the corpse are distinct entities, the corpse originating in the horse. If they believe this thesis, they have to give some explanation of why particles ingested can still be scientifically detected. They will do this either by saying that the particles no longer exist literally, but "virtually" do, or by saying that new particles just like the old ones come to exist out of the old ones, except the new ones have the essential property of being a part of substance that they have joined. There are two different reasons why one might believe such an outlandish thesis: (1) because one doesn't believe in parthood (Patrick Toner and Alexander Pruss incline in this direction), or (2) because one thinks that parts receive their identity from the whole (there is some textual basis in Aristotle for this).

I want to offer two arguments for this thesis, one metaphysical and Aristotelian, the second ethical and eccentric. I find the first plausible, and much less so the second, but the second is kind of neat, so I'll give it, too:

• Matter receives its identity--that which makes it be the entity that it is--from the substance that it makes up. Therefore, if a bit of matter x is a part of substance A and a bit of matter y is a part of substance B, then if A is distinct from B, it follows that x is distinct from y. Therefore, no bit of matter can be a part of two substances. But everything that exists is a substance or a mode, relation, trope, accident or the like. A proper part of a substance is not a mode, relation, trope, accident or the like. Hence, if a substance has a proper part, that proper part is a substance. But the matter of a proper part A of a substance B would then be a part of both substance A and substance B, which contradicts the thesis that a bit of matter can't be a part of two substances.
• This argument uses two main assumptions:
  1. Without receiving special normative power from you or some higher authority, the only way I can by myself make an item x that you presently literally own to cease to be literally owned by you is by destroying x.
  2. It is impossible for one person to literally own a part of another.
  Suppose now you literally own a carbon atom x (e.g., it's part of a steak that you own), and I without having received any special normative power eat the atom x so that it becomes a part of my body. By (2), I have made it happen that you no longer own x. But by (1), it follows (assuming I have received no grant of authority or the like), the only way I could have done this is by destroying x. Hence, when an atom becomes a part of my body, it is thereby destroyed.