Once one has an adverbial ontology, like the one I used to help with the Incarnation, one no longer needs the parts of a substance in one's ontology. "I have two hands." That's made true by my being two-handed. "My right hand has five fingers." That's made true by my having a right hand five-fingeredly. More explicitly, there is a mode m in virtue of which I have a right hand. (According to my Incarnation post, I have m indirectly, as m is a mode of my humanity.) Then we have two moves we can make. We could say that there are five modes of m, which each of which is a different way of the hand's being fingered. If we go that route, then we are forced into identity of indiscernibles for fingers, and by extension for any other parts. I welcome that consequence myself, since I'm anyway pulled to identity of indiscernibles by my theory of transworld identity. But alternately we could simply posit a mode of being five-fingered, perhaps a mode relational to the number five.
To my mind there are three main uses of parts:
- Some properties of wholes are grounded in properties of parts. "I have the property of having heart-beat in virtue of having as a part a heart that in turn has the property of beating."
- Parts have location and help explain partial location. "I am partly in this room and partly in that, because one of my legs is here and the other there."
- Some parts are widely thought to be able to move between substances. "Several hours after you ate the apple, a carbon atom that used to be a part of an apple tree has become a part of you."
The adverbial mode ontology does the first two tasks well.
1: There is a mode in virtue of having which I have heart-beat. But I have that mode indirectly: that mode modifies my being hearted, which in turn modifies my humanity. So properties are divided up. But an advantage of the mode way is that we get to uniformly divide properties not just by parts, but by functional subsystems. Some functional subsystems correspond to parts, but likely not all. In a computer running several processes at once on the same processor core, the processes may correspond to different functional systems—say, one doing Fourier transforms of microphone data and another watching for user input events—but the processes may be implemented by overlapping sets of physical parts (and a computer has no others), and we could easily imagine that there is no distinct set of parts corresponding to each process. It seems likely that something like that happens in the brain, and even if it does not, the possibility should be accounted for in our ontology. The adverbial mode ontology apportions properties had in virtue of a functional subsystem in the same way that it apportions those properties had in virtue of a physical part, and that strikes me as exactly right.
2: This is really just a special case of 1. "My right leg is located in this room" is true in virtue of my being right-leg-possessed this-roomly.
But unless we posit that modes can move between substances—I've heard Rob Koons speculate in that direction and Aquinas's account of transsubstantiation famously allows modes to survive the destruction of their underlying substance—it's harder to handle 3. On general Aristotelian grounds, I think one can just bite the bullet. The identity of a part, if there are parts, is going to be dependent on the whole. There is no carbon atom that was a part of the apple tree and is now a part of you. There are (in the eternalist sense of "are"), at best, two carbon atoms, one that was identity dependent on the tree and the other that is identity dependent on you, and the first caused the second. This is counterintuitive.
So what our adverbial ontologists should say about 3 is that the apple tree has some mode m1 that makes it count as having had a certain carbon atom once, and you have some mode m2 that makes you count as having a certain carbon atom. There is a continuity of location (see 2) between the one mode (perhaps with some other intervening modes, depending on the ontological status of the apple as such) and the other. Moreover, m1 is a cause of m2. Or, if we prefer (and I think we should), the apple tree as modified by m1 caused you to have m2. I.e., there is a mode c1 of causation had by m1, which is a causation of m2, or of me as having m2. But the numerical identity of the particles, that we need to give up on. However, since giving up on parts dissolves the problem of material constitution, and since every other solution to the problem of material constitution has something else counterintuitive about it, we are in this regard no worse off here than any view on which there are parts.
A challenge for the view is to distinguish between those modes that correspond to parts and those modes that don't. But one might just reject the distinction. Or one might go like this. It might be that all and only the modes that have a location mode are parts. But don't non-part subsystems have a location mode? Maybe not. Rather, they may be modes--or joint modes (maybe a mode can be a mode of more than one mode--or maybe even more than one substance--and maybe that is how relations are to be handled)--of one or more parts, and the parts are what have a location mode. The non-part subsystems, then, have a location in a derivative sense.