Parts and priority

Schaffer says that pluralists think that parts are ontologically prior to their wholes. But this seems wrong, even as restricted to bottom-up pluralists who think the fundamental realities are microphysical.

For consider that (assuming the materialism that bottom-up pluralists typically do) I am a part of the Milky Way Galaxy (both a part-at-a-time and an atemporal part). But it seems quite wrong to say that I am ontologically prior to the Milky Way. My fundamental particles may be ontologically prior to the Milky Way, but I am not.

Further, many bottom-up pluralists accept classical mereology. But now while it seems right, if I put myself in the mindset of a typical non-Aristotelian metaphysician, to say that my atoms, molecules, cells, and organs are prior to me, it seems wrong to think that “weird scattered parts” are prior to me. Imagine for instance ordering all my molecules from bottom to up, and then take the fusion of all the even-numbered molecules. That fusion exists and is a part of me by classical mereology, but it doesn’t seem like the sort of thing that’s prior to me. It seems to be something that emerges from my simples in parallel with me at best.

If this is right, then what are the priority relations between objects for bottom-up pluralists? For unrestricted compositionalists, I think the natural suggestion is this: The simples are prior to all the wholes made of them, and that’s the only priority relation there is. This has some counterintuitive results. For instance, it seems plausible that my molecules are prior to me, or that the individual people of France are prior to France. That’s probably a bullet that the unrestricted compositionalist should bite. For one of the primary arguments for unrestricted composition is worries about vagueness and continuous series, and as soon as we start inserting some additional priority relations, we are likely to get analogous worries. But it is an uncomfortable bullet to bite, because it undercuts many of the intuitive motivations for bottom-up views, such as that the Lego blocks are prior to the Lego sculpture.

A related point applies to top-down priority monistic views, at least assuming classical mereology. Maybe the Milky Way is prior to me, but it doesn’t seem right to say that the fusion of all people whose height in inches is even is prior to me (my height in inches is even). So the top-down priority monist seems to need a complicated story of when a whole is prior to its parts.

If we have highly restricted mereology, it becomes easier to say how the priority relation runs. If, say, van Inwagen is right and all we have are simples and organisms, then we can say that parts are always prior to wholes, and be done with it, as the only cases will be that simples are prior to cells and cells to multicellular organisms. Or we can reverse it and say that multicellural organisms are prior to their cells, cells are prior to their cells (while unaffiliated cells as well as unaffiliated simples are fundamental). In either case, the story is neat and simple.

An argument that organisms aren't wholly material

Here’s an argument for non-materialism about all organisms.

Start with these premises:

1. Organisms exist.

2. If organisms exist, it is possible to have two organisms that have all their matter in common.

3. Antisymmetry of parthood: Two distinct things can’t each be a part of the other.

4. Strong supplementation: If y isn’t a part of x, then y has a part that doesn’t overlap x.

Now suppose that x and y are two organisms that have all their matter in common. By antisymmetry of parthood, they can’t both be mutual parts of each other. Swapping labels if necessary, suppose y isn’t a part of x. Then by strong supplementation, y has a part z that doesn’t overlap x. But any material part of y is a material part of x by (2). Thus, y has a part that isn’t a material part. Hence:

5. It is possible to have an organism with a non-material part.

But this is weak in two ways. First, it doesn’t show that any actual organism has a non-material part. Second, even if we showed that, that wouldn’t show that all organisms have non-material parts. Moreover, I have given no argument for premise 2.

I will fix all these problems together. In a recent post, I gave a plausible construction of a world where there is a dog-like organism and a cat-like organism with all their matter in common. The same construction would give the following conclusion: there is a world where there is a mushroom-like organism and a grass-like organism thathave all their matter in common. Plugging that into the above argument yields:

5. Possibly a mushroom-like or a grass-like organism has a non-material part.

The likeness here is functional: the way of life of the organism is like that of mushroom or a grass plant. Then add:

6. If possibly a mushroom-like organism has a non-material part, all organisms have non-material parts.

7. If possibly a grass-like organism has a non-material part, all organisms have non-material parts.

From 5-7, we get:

8. All organisms have non-material parts.

Why believe 6 and 7? Here’s a thought. You might think that conscious animals have to have souls or something like that. But if a mushroom- or grass-like organism can have a non-material part, probably it actually does, and if it has a non-material part, probably all organisms do.

There is a lot in this argument that doesn’t personally convince me. In fact, I am skeptical of premises 2 and 4, and my main reason for accepting 6 and 7 is that I already accept anti-materialism about all organisms. But I think the argument has some force.

Completely overlapping lives

Van Inwagen thinks that the very same particles cannot have their activities constitute two life events. I am not so sure.

Pretend for the sake of simplicity that our world is made of fundamental particles with well-defined positions in three-dimensional space, with n basic quantities Q₁, ..., Q_n (mass, charge, etc.), otherwise interchangeable, and with no particles coming in and out of existence. And suppose we have dogs and cats (or something like them).

Suppose, further, that our world contains Rover the dog and Felix the cat. No particle that is ever a part of one of them is a part of the other. Finally, we have a very odd coincidence. There is a one-to-one correspondence ϕ between the particles that are ever a part of Rover and those that are ever a part of Felix such that particle c is a part of Rover at time t if and only if ϕ(c) is a part of Felix at that time. This last condition can be assured if we assume that Rover and Felix don’t change in what particles they have and they have the same number, but we don’t need such a strong assumption.

Now imagine a six-dimensional world made of fundamental particles, with 2n basic quantities U₁, ..., U_n, V₁, ..., V_n. Now suppose:

1. The first three coordinates of the particle positions and the quantities U₁, ..., U_n over time are physically related by laws exactly like the ones that govern the three coordinates of the particle positions and (respectively) the quantities Q₁, ..., Q_n in our world are.

Thus, if we project the six-dimensional space of this world to our three-dimensional space by ignoring coordinates 4–6, and relabel U_i as Q_i, the behavior of the particles will look just like the familiar behavior of particles in our world.

Then add:

2. The last three coordinates of the particle positions and the quantities V₁, ..., V_n over time are physically related by laws exactly like the ones that govern the three coordinates of the particle positions and (respectively) the quantities Q₁, ..., Q_n in our world are.

In other words, likewise if we ignore coordinates 1–3, and relabel V_i as Q_i, the behavior of the particles will be like that of our world’s particles.

Note that the U_i and Q_j quantities don’t interact, and the particle positions with respect to coordinates 1–3 and coordinates 4–6 don’t interact. This is like two non-interacting universes in one, except that the particles are shared between them.

Now suppose that there is a one-to-one correspondence f between the particles of our world and those of the six-dimensional world such that:

3. If at time t, particle c is at (x,y,z) and has basic quantity values Q₁ = a₁, ..., Q_n = a_n, then at t in the six-dimensional world, particle f(c) is at (x,y,z,u,v,w) for some u, v and w, and has basic quantity values U₁ = a₁, ..., U_n = a_n.

And there is also also another one-to-one correspondence g such that:

4. If at time t, particle c is at (x,y,z) and has basic quantity values Q₁ = a₁, ..., Q_n = a_n, then at t in the six-dimensional world, particle g(c) is at (u,v,w,x,y,z) for some u, v and w, and has basic quantity values V₁ = a₁, ..., V_n = a_n.

In theory, these correspondences f and g could be the same. But they are not. There is a twist:

5. If c is ever a particle of Rover, then g(c) = f(ϕ(c)) and if c is ever a particle of Felix, then g(c) = f(ϕ⁻¹(c))

where ϕ is our correspondence between Rover and Felix’s particles. This twist implies that g maps Felix’s and Rover’s particles to particles that f respectively maps Rover’s and Felix’s to.

We can mathematically arrange all this.

Now, fix a time t. If the cs are Rover’s particles at t, let the es consist of the particles corresponding to them under the mapping f. Note that the es are also the particles corresponding to Felix’s particles under the mapping g.

Here’s the fun thing. With respect to their first three coordinates and the quantities U₁, ..., U_n, the es behave just like Rover’s particles. With respect to their last three coordinates and the quantities V₁, ..., V_n, the es behave just like Felix’s particles.

It seems right to say this: the es in our six-dimensional world have two lives, a canine-style life just like Rover’s and a feline-style life just like Felix’s. There is no interaction or unity between these two lives other than due to their being realized in the very same particles.

Suppose someone insists that there must be only one canine-feline hybrid life here because the particles are the same. Modify the mappings slightly, so that the Rover-like life is realized by particles e₁, ..., e_N while the Felix-like life is realized by particles e₂, ..., e_N + 1. Now the particles are not the same, but they are mostly the same. Now we have the same life event but no longer the same particles (just an overlap, like in the case of conjoint twins). But two particles should make little difference here. The slight change in mapping shouldn’t make a difference between having a canine-type life and a feline-type life on the one hand, and having a hybrid canine-feline life.

Note that I am not doing Aristotelian metaphysics here. By “life events”, I mean the kind of empirical event a biologist might talk about, not a form or anything like that. I doubt that the same matter could have two different substantial forms.

Randomness and identity

Suppose an amoeba biologically symmetrically splits into two cells, A and B. Here are the main options for what happens metaphysically:

1. The parent perishes and the child cells are new organisms.

2. The parent becomes a scattered two-celled organism.

3. The parent becomes A, and B is a new organism.

4. The parent becomes B, and A is a new organism.

Typically, philosophers dismiss options (3) and (4) as arbitrary in cases where the splitting is symmetric. Option (2) is implausible, so that leaves option (1).

But now consider an option that the above argument for (1) does not consider:

5. Indeterministically, the parent has chance 1/2 of becoming A, with B being new, and chance 1/2 of becoming B, with A being new.

(Technically, this is not another option, but a further specification of (3) or (4).) Rule (5) is perfectly symmetric between A and B, so there is no arbitrary preference in the rule—though of course the random result may be said to be arbitrary.

I expect that the main reason (5) is usually not considered is that it is assumed that the answer as to which of (1)–(4) happens supervenes on qualitative biological features of the amoeba and offspring system. But if we have a “further fact” view about identity, or if we are dualists about amoebae—say, because we think that an amoeba has a non-physical soul or form that—then I think (5) is not at all crazy. There could well be indeterministic laws of how the “further fact” behaves or where the soul goes.

Of course, (5) is not the only indeterministic symmetric option that avoids scattered individuals. One could have a view where there is a 1/3 chance for each of options (1), (3) and (4). Or where there is a 2/3 chance of (1) and a 1/6 chance of each of (3) and (4).

Some people will think that amoebae do not have “further facts” or souls, but are entirely physically reducible. I am far from confident of that. But in any case, whether the indeterministic solution works for amoebae, it could well work for humans, whether in actual cases of early twinning or in science-fictional brain splitting thought experiments.

Here is another metaphysical difficulty where an indeterministic answer might work. Consider beginning and end of life issues: when do constituents come together as a new organism and when do organisms depart from life? It feels arbitrary to suppose, say, that when the damage exceeds some threshold, the organism must die there and then. But what if we suppose that there is a continuous distribution—say, something like an exponential one—with parameters continuously depending on the degree of damage, governing the random point at which the organism departs from this life if the damage is not changed? Of course, this kind of a story only makes sense on a non-naturalistic picture where there is some further unobservable fact about life.

I wonder what other metaphysical questions might have random answers.

Does it follow from van Inwagen's answer to the Special Composition Question that all complex things are alive?

The view that all objects are either living or simple appears to be a consequence of van Inwagen’s answer to the special composition question, namely that a proper plurality only composes a whole when the parts have a life together, where a proper plurality is a plurality of two or more things.

But this does not follow. Van Inwagen defines:

1. The xs compose y if and only if “the xs are all parts of y and no two of the xs overlap and every part of y overlaps at least one of the xs”.

Now the view that all non-simples are alive follows from van Inwagen’s answer to the special composition question (SCQ) provided that we have to have:

2. Anything that has proper parts is composed of some proper plurality of its proper parts.

3. Whenever something is composed of a plurality of things that have a life together, it is alive.

Indeed, if we have 2 and 3, then anything that has proper parts is composed of proper plurality by 2, which thus have a life together by van Inwagen’s answer to SCQ, and hence the thing composed of them is alive by 3. On the other hand, if there can be something that has proper parts but isn’t composed of a proper plurality of proper parts, then there is no way to use van Inwagen’s answer to SCQ to argue that it’s alive. Furthermore, if there is something that is composed of a proper plurality of proper parts that have a life together but isn’t alive, then we have another counterexample to van Inwagen.

Neither 2 nor 3 is completely obvious. You might, for instance, think that where you are, there is also a heap of atoms shaped just like you. If, further, you are a presentist and a materialist, you will think the atoms compose you and compose the heap. Moreover, the atoms have a life together. But the heap of atoms is not alive, unlike you. So (3) on that view is false.

For a view on which (2) is false, imagine a world consisting of four objects, A, B, C and D. Object A has B, C and D as proper parts. Object B has D as a proper part. Object C has D as a proper part. There are no other instances of proper parthood. This is a world where the company axiom of mereology fails (since B and C have D as a proper part and no other proper parts). It would be interesting to characterize in some non-trivial way the mereological theories where (2) is true. A sufficient condition is to assume atomism (Gemini Pro noted this). We can define this by saying every object has a simple part. For then if an object has a proper part, it is easily seen to be composed by its proper parts. But atomism is not a necessary condition. Consider a gunky mereological model whose domain is infinite sets of natural numbers and parthood is inclusion—then (2) is true.

We could also escape this worry by weakening the definition of composition by dropping the requirement that no two of the xs overlap. That makes van Inwagen’s answer to the SCQ put a more stringer requirement on reality, and it becomes trivial that everything that has proper parts is composed of them, and (2) becomes a matter of logic. We still need an argument for (3), however.

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.

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.

If we're not brains, computers can't think

The following argument has occurred to me:

1. We are not brains.

2. If we are not brains, our brains do not think.

3. If our brains do not think, then computers cannot think.

4. So, computers cannot think.

I don’t have anything new to say about (1) right now: I weigh a lot more than three pounds; my arms are parts of me; I have seen people whose brains I haven’t seen.

Regarding (2), if our brains think and yet we are not brains then we have the too many thinkers problem. Moreover, if brains and humans think, then that epistemically undercuts (1), because then I can’t tell if I’m a brain or a human being.

I want to focus on (3). The best story about how computers could think is a functionalist story on which thinking is the operation of a complex system of functional relationships involving inputs, outputs, and interconnections. But brains are such complex systems. So, on the best story about how computers could think, brains think, too.

Is there some non-arbitrary way to extend the functionalist story to avoid the conclusion that brains think? Here are some options:

5. Organismic philosophy of mind: Thought is the operation of an organism with the right functional characteristics.

6. Restrictive ontology: Only existing functional systems think; brains do not exist but organisms do.

7. Maximalism: Thought is to be attributed to the largest entity containing the relevant functional system.

8. Inputs and outputs: The functional system that thinks must contain its input and output facilities.

Unfortunately, none of these are a good way to save the idea that computers could think.

Computers aren’t organisms, so (5) does not help.

The only restrictive ontology on the table where organisms exist but brains do not is one on which the only complex objects are organisms, so (6) in practice goes back to (5).

Now consider maximalism. For maximalism to work and not reduce down to the restrictive ontology solution, these two things have to be the case:

1. Brains exist

2. Humans are not a part of a greater whole.

Option (b) requires a restrictive ontology which denies the existence of nations, ecosystems, etc. Our best restrictive ontologies either deny the existence of brains or relegate them to a subsidiary status, as non-substantial parts of substances. The latter kind of ontology is going to be very restrictive about substances. On such a restrictive ontology, I doubt computers will count as substances. But they also aren’t going to be non-substantial parts of substances, so they aren’t going to exist at all.

Finally, consider the inputs and outputs option. But brains have inputs and outputs. It seems prejudice to insist that for thought the inputs and outputs have to “reach further into the world” than those of a brain which only reaches the rest of the body. But if we do accept that inputs and outputs must reach further, then we have two problems. The first is that while we are not brains, we could certainly continue to think after the loss of all our senses and muscles. The second is that if our inputs and outputs must reach further into the world, then a hearing-aid is a part of a person which appears false (though recently Hilary Yancey has done a great job defending the possibility of prostheses being body parts in her dissertation here at Baylor).

Fusions and organisms

Suppose you believe the following:

1. For any physical objects, the xs, there is a physical object y with the following properties:
   1. each of the xs is a part of y;
   2. it is an essential property of y that it have the parts it does; and
   3. necessarily, if all the actual proper parts of y exist, then y exists as well.

For instance, on the standard version of mereological universalism, it seems we could just take y to be the fusion of the xs. And on some versions of monism, we could take y to be the cosmos.

But it seems (1) is false if organisms are physical objects and if particles survive ingestion. For suppose that there is exactly one x, Alice, who is a squirrel, and at t₁ we find a y that satisfies (1). And now suppose that at t₂ there comes into existence a nut whose simple parts are not already parts of y, and at t₃ this nut has been eaten and fully digested by Alice. Suppose no parts of y have ceased to exist between t₁ and t₃. Then y exists at t₃ by (c), and has Alice as a part of itself (by (a) and (b)), and the simple particles of the nut are parts of y by transitivity as they are parts of Alice. Hence y has gained parts, contrary to (b), a contradiction.

(Note that the argument can be run modally against a four-dimensionalist version of (1).)

The mereological universalist’s best bet may be to deny that fusions satisfy (c). Normally, we think that the only way for a fusion to perish is for one of its proper parts to perish. But there may be another way for a fusion to perish, namely by certain kinds of changes in the mereological structure of the fusion’s proper parts, and specifically by one of the fusion’s proper parts gaining a part that wasn’t already in the fusion.

Here is another problem for (1), though. Suppose that Alice the squirrel is the only physical object in the universe. Now consider a y satisfying (1)(a)–(b). Then y is distinct from Alice because y has different modal properties from Alice: Alice can survive annihilation of one of her claws while y cannot by (b). But this violates the Weak Supplementation mereological axiom, since all of y’s parts overlap Alice. So we cannot combine fusions as normally conceived of (since the normal conception of them includes classical mereology) with organisms.

A way out of both problems is to say that there are two different senses of parthood at issue: fusion-parthood and organic-parthood, and there is no transitivity across them. This is a serious ideological complication.

Life and self-representation

Here’s another try at an account of life. Maybe:

1. x is alive if and only if x has a non-derivative self-representation.

Consider: Anything that engages in reproduction must represent itself in order to reproduce (note: the growth of a crystal is not reproduction, however, because it does not make another crystal in the image of its own self-representation). Indeed, (1) covers all the organisms we are confident are organisms. And whether a virus represents itself non-derivatively or only derivatively in relation to the transcription mechanisms of a host is unclear, and (1) rightly thus rules that it is unclear whether a virus is alive.

Moreover, God and angels know themselves, and do so non-derivatively, so they count as alive according to (1).

It could be that (1) is a necessary truth, but nonetheless does not capture the concept of life. For there seems to be something more to life than just non-derivative self-representation, even if it turns out that necessarily all and only the non-derivative self-representers are alive. Aquinas thinks life needs operation or activity.

Here is a suggestion that expands on (1):

2. x is alive if and only if x pursues an end for itself in the light of a non-derivative self-representation.

Thus something that merely thinks of itself, without having any ends, won’t be alive. On the other hand, anything that intentionally pursues ends that it non-derivatively represents itself as having satisfies (2). So, once again, God and angels count as alive. And so does any organism, since pursuit of reproduction always satisfies (2).