Eliminating or reducing parthood

Parthood is a mysterious relation. It would really simplify our picture of the world if we could get rid of it.

There are two standard ways of doing this. The microscopic mereological nihilist says that only the fundamental “small” bits—particles, fields, etc.—exist, and that there are no complex objects like tables, trees and people that are made of such bits. (Though one could be a microscopic mereological nihilist dualist, and hold that people are simple souls.)

The macroscopic mereological nihilist says that big things like organisms do exist, but their commonly supposed constituents, such as particles, do not exist, except in a manner of speaking. We can talk as if there were electrons in us, but there are no electrons in us. The typical macroscopic mereological nihilist is a Thomist who talks of “virtual existence” of electrons in us.

Both the microscopic and macroscopic nihilist get rid of parthood at the cost of ridding themselves of large swathes of objects that common sense accepts. The microscopic nihilist gets rid of the things that are commonly thought to be wholes. The macroscopic nihilist gets rid of the things that are commonly thought to be parts.

But there is a third way of getting rid of parthood that has not been sufficiently explored. The third kind of mereological nihilist would neither deny the existence of things commonly thought to be wholes nor of things commonly thought to be parts. Instead, she would deny the parthood relation that is commonly thought to hold between the micro and the macro things. Parts of the space occupied by me are also occupied by my arms, my legs, my heart, the electrons in these, etc. But these things are not parts of me: they are just substances that happen to be colocated with me. I’ll call this “parthood nihilism”.

This is compatible with a neat picture of organ transplants. If my kidney becomes your kidney, nothing changes with respect to parthood. All that changes is the causal interactions: the kidney that previously was causing certain distributional properties in me starts to cause certain distributional properties in you.

An obvious question is what about property inheritance? Whenever my hand is stained purple, I am partly purple. We don’t want this to be just a coincidence. The common-sense parts theorist has a nice explanation: I inherit being partly purple from my hand being partly purple (note that they’re only properly partly purple—they aren’t purple inside the bones, say). My partial purpleness derives from the partial purpleness of a part of me.

But the parthood nihilist can accept accept this kind of property inheritance and give an account of it: the inheritance is causal. My hand’s being partly purple causes me to be partly purple, which is a distributional property of an extended simple). I guess on the standard view, property inheritance is going to be a kind of grounding: my being partly purple occurs in virtue of my hand’s being a part of me and its being partly purple. On the present nihilism, we have simultaneous causation instead of grounding.

Here’s another difficulty: what about gravity (and relevantly similar forces). I have a mass of 77kg. If my mass is m₁ and yours is m₂ and the distance between us is r, there is a force pulling you towards me of magnitude Gm₁m₂/r². But why isn’t that force equal in magnitude to (m₁ + m₁₁ + m₁₂ + m₁₃ + ...)m₂/r², where m₁₁, m₁₂, m₁₃, ... are the masses of what common sense calls “my parts” (about five kilograms for my head, four for my left arm, four for my right arm, and so on)? After all, wouldn’t all these objects be expected to exert gravitational force?

The first two kinds of nihilists have easy answers to the problem. The microscopic nihilist says that only particles have mass as only particles exist. The macroscopic one says that I am all there is here—the head, arms, etc. don’t exist. The standard common-sense view has a slightly more complicated answer available: gravitational forces only take into account non-inherited mass. But parthood nihilist can give a variant of this: it’s a law of nature that only fundamental particles produce gravitational forces.

There is a fourth kind of view. This fourth kind of view is no longer a mereological nihilism, but mereological causal reductivism. On the fourth kind of view, for x to be a part of y just is for x to be identical with y or for x to be a proper part of y. And for x to be a proper part of y just is for a certain causal relation to hold between x’s properties and y’s properties.

Spelling out the details of this causal relation is difficult. Roughly, it just says that all of x’s properties and relations cause corresponding properties and relations of y. Thus, x’s being properly partly located in Pittsburgh causes y to be properly partly located in Pittsburgh, while x’s being wholly located in Pittsburgh causes y to be at least partly located in Pittsburgh; x’s being green on its left half causes y’s being green in the left half of the locational property that x causes y to have; and so on.

As I said, it’s difficult to spell out the details of this causal relation. But it is no more difficult than the common-sense parts theorist’s difficulty in spelling out the details of property inheritance. Wherever the common-sense parts theorist says that there is a part-to-whole inheritance between properties, our reductionist requires a causal relation.

The reductionism changes the order of explanation. Suppose my hand is the only green part of me and it gets amputated. According to the common-sense parts theorist, I am no longer partly green because the green hand has stopped being a part of me. According to the reductionist, on the other hand, the hand’s no longer contributing to my greenness makes it no longer a part of me.

The reductionist and parthood nihilist, however, have an extra explanatory burden. Why do all these causal relations cease together? Why is it that when my right hand stops causing me to be partially green, my right hand also stops causing me to have five right fingers? The common-sense parts theorist has a nice story: when the part stops being a part, all the relevant grounding relations stop because a portion of the ground is the fact that the part is a part.

But there is also a causal solution. The common-sense parts theorist has to give a story as to when it is that certain kinds of causal interaction—say, a surgeon using a scalpel—cause a part to stop being a part. For each such kind of causal interaction, the reductionist and parthood nihilist can say that there is a cessation of all the causal relations that the common-sense parts theorist would say go with inheritance.

All in all, I think the reductionist has a simpler fundamental ideology than the standard common-sense inheritance view: the reductionist can reduce parthood to patterns of causation. Her theory is overall not significantly more complicated than the common-sense inheritance theory, but it is more complicated than either microscopic or macroscopic nihilism. But she gets to keep a lot more of common-sense than the nihilists do. In fact, maybe she gets to keep all of common-sense, except for pretty theoretical claims about the direction of explanation, etc.

The parthood nihilist has most of the advantages of reductionism, but there is some common-sense stuff that she denies—she denies that my arm is a part of me, etc. Overall parthood nihilism is not significantly simpler than reductionism, I think, because the parthood nihilist’s account of how all the relevant causal relations cease together will include all the complications that the reduction includes. So I think reductionism is superior to parthood nihilism.

But I still like macroscopic nihilism more than reductionism.