Saturday, August 31, 2019

Giorgio Lando's Mereology

I've been reading Giorgio Lando's Mereology, which is his argument for what mereological monism, i.e., the position that Classical Extensional Mereology is the complete and only theory of parthood as such. It's quite good, and very nicely argued. It's very definitely wrong, but it's very nicely argued.

Lando's case has three primary parts, not counting supplementary parts concerned with addressing particular problems and objections, which we can summarize as Paradigm, Principles, and Projection.

(1) Paradigm: Lando puts a lot of weight on starting with a paradigmatic or prototypical kind of parthood, one that is relatively uncontroversial and easy to recognize and in common use. Lando takes the obvious cases of parthood with which we deal to be closely connected to spatial containment; this spatial parthood, as he often calls it, is his paradigmatic form of parthood.

(2) Principles: Taking this paradigmatic form of parthood, we can identify its principles, and Lando argues that CEM is the correct characterization of this kind of parthood, i.e., that parthood paradigmatically follows the basic principles of CEM. To do this, he has to rule out apparent counterexamples even in the context of spatial parthood; he does this a number of ways, but an important way is by making a distinction between selective and nonselective parthood. Selective parthood violates the transitivity principle of CEM; for selective parthood, A can be part of B and B can be part of C without licensing the conclusion that A is part of C. For instance, a biologist will tend to say that the organelles in a cell are parts of the cell but not want to say that they are parts of the tissue made up by the cell. Nonselective parthood is strictly transitive. Lando argues that all selective parthood boils down to nonselective parthood with additional principles.

(3) Projection: Recognizing CEM as encapsulating the governing principles of paradigmatic parthood, we can extend our notion of parthood to include any candidates for parts that also meet the same principles.

This is a reasonable and useful way to argue. The fundamental problem is that it all is dependent on the choice of the paradigm, and while Lando selects the paradigm that gets his conclusion, it is not a particularly good choice of a paradigmatic notion of parthood. Let's consider, for instance, three of his examples that get counted as displaying a "spatial" notion of parthood:

(b) The leg is part of the table.
(c) I want to eat a piece of that cake.
(e) Many components of my car are expensive to replace.

Lando says of all of these that "space is involved"; this is to be taken not in the sense that the things are merely localizable in space but that "a kind of spatial parthood is involved" (p. 19). In particular, there is a correspondence between the instance of parthood and "another instance of parthood that subsists between the corresponding regions of space". He calls this a principle of harmony, and gives another example. If x is a thing and region(x) is the region of space occupied by x, then we can say that the heart is part of the body when region(heart) is part of region(body). I presume that he means region(x) to be a movable designation, because we normally think of bodies as moving in and out of regions of space and not carrying their regions of space around with them. So the idea is that if the heart is part of the body, whatever region the heart may happen to occupy at a given time is part of whatever region the body may happen to occupy at that same time. This means that the idea is actually spatiotemporal. And note that it is the region(heart) being part of region(body) that is actually so. Despite Lando's tendency to collapse the two at times, it is the parthood relation between the regions that has the properties on which Lando is building CEM, not the parthood relation between things like hearts and bodies, which is merely linked to parthood between regions by a claim that they co-occur, a very weak link.

And it's not clear that it's really true. We have no problem saying that if your heart is cut out that part of your body is no longer inside your body; this violates his principle of harmony. Lando would perhaps take this to be a sign of metonymy, but the problem is that all of his actual real-life examples have features like this. Take for instance example (b), the leg and table. I have been putting a table from IKEA together, and you come in, and not having seen what I was doing, pick up the stick of wood that I have put out of my way for a moment as I take a break. "What is this?" you ask. "It is part of the table I am putting together," I reply. This violates the principle of harmony. Indeed, the leg is not even attached to the table.

Take (c), the cake example. "I want a piece of that cake," you say. So I cut you a piece and give it to you. "What are you eating?" asks a friend who comes by. "I am eating a piece of that cake," you say. This violates the principle of harmony, because the piece of cake is no longer even in the vicinity of the cake. And, as with the table leg, the piece of cake is no longer even attached to the cake.

Take (e), the car example. The same thing applies.

Literally all of Lando's examples fail his harmony test if we consider the matter generally. It's true that often there is a harmony, but that does seem to boil down just to the fact that these things are localizable in space.

The most plausible candidates for a 'paradigmatic' or 'prototypical' kind of parthood are all cases where parthood has some sort of functional character to it, broadly construed. When we talk about a foreign object lodged in a tree, and how that differs from the actual parts of the tree, we are recognizing the tree as a whole having a functional integrity that is not purely characterizable in terms of space. What is more, while the degree varies, all of the real-life cases seem actually to be selective. They do allow some kind of transitivity, but only a relative transitivity, they are transitive relative to whatever kind of functional integrity or functional mode of parthood is considered. That's why the biological example makes perfect sense: the organelles of a cell are not parts of the tissue in the way the cells themselves are, so transitivity gets broken. It's not broken completely, because you can still reason transitively, but only as long as you are staying within the same kind of parthood.

As I've said, while he sets things up as if he were talking about ordinary parts and wholes, really what he ends up doing is talking about the mereology of spatiotemporal regions. That makes sense, because spatiotemporal regions are the kinds of things that most obviously have the features Lando needs to make his case -- most notably, we assume almost universally that all regions of spacetime, considered as such, are on a level and pretty much the same kind of thing. This is because a 'spatiotemporal region' is something we get when we take physical objects and abstract away everything except their measurements in space and time as determined relative to other things. There's not much to differentiate parthood if you abstract away everything except an idealized geometrical specification. Thus it is unsurprising that parts receive Lando's seal of authentication to the extent that they act like they are precisely identifiable geometrical objects. The problem for Lando's method, though, is that this kind of parthood is not in any way a plausible candidate for something 'paradigmatic' or 'prototypical'. It is quite clearly something that we got by abstraction and idealization, and it is quite clearly a case that allows us to have things like unrestricted transitivity and unrestricted composition by removing all the reasons not to have them and then taking the barebones of our reasoning to the limit.

If we really started with plausible candidates for paradigmatic cases of parthood we would start with selective parthood, and we would take parthood at least sometimes to require functional or causal elements (parts are not merely there but have something integrating them as parts). This, of course, is what Lando wants to avoid, because it would mean that the mereological monist is probably wrong and that mereology is therefore going to get very, very complicated. But there seems nothing to prevent someone from picking a different 'paradigmatic parthood' from the one that Lando has picked, which so conveniently leads to Lando's conclusions; and the result would in some cases certainly lead to a very different kind of conclusion, and there are many candidates that are much more plausible starting-points.

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