L.A. Paul's logical parts
In her paper 'Logical Parts', forthcoming in the december issue of Nous, L.A. Paul presents a nice theory of objects according to which things are mereologically composed of their properties. Here are a couple of potential problems.
First, the theory seems to conflict with Unrestricted Composition and incompatible properties. For suppose that P and Q are incompatible properties, like being square and being round. By Unrestricted Composition, there is a fusion of P and Q (or, if you prefer, of P and Q and Paul's red cup). This fusion has both P and Q as parts, hence, on Paul's theory, it is both P and Q. But if P and Q are incompatible, nothing can be both P and Q.
Second, the theory is threatened by Plato's third man problem. For consider the property of being human. This property is an improper part of itself, so it would have to be human. But it isn't. It doesn't help to restrict the thesis to proper parthood: Being human is a proper part of being human and female. Still, the latter property is not human.
This problem could perhaps be solved by restricting the theory to fusions that contain a spatiotemporal location. That is: Something x is F iff both F and some location are part of x. This matches Paul's definition of instantiation in section 3. However, it seems to conflict with section 4, where Paul argues that persons -- the things that endure through time -- do not contain a spatiotemporal location. But certainly persons do have properties?
Next, consider again Paul's red cup. Some of its parts are molecules. On the logical parts theory, these parts have various properties as parts, such as being a molecule and being tiny. By the transitivity of parthood, the cup itself would have to be a molecule and tiny. But it isn't.
Fourth, Paul seems to be comitted to the view that either her cup is not the fusion of its spatiotemporal parts or there are no spatiotemporal atoms. For if there are spatiotemporal atoms and the cup is their fusion, then every part of the cup has to be a fusion of some of these atoms. Since redness is a part of the cup, redness must be such a fusion. And since my curtains are also red, some of the spatiotempotal atoms of Paul's cup would have to be part of my curtains, which would be quite surprising.
To avoid those two problems, Paul could claim that logical parthood is really a different relation than spatiotemporal parthood. With two part-whole relations we'd have two different mereologies, and none of them would be topic-neutral.
Fifth, what about relations? How are things related to each other? Do they contain parts of relations as part? Then when a is R-related to b, and c to d, how can a still not be R-related to d? And whatever the account for relations looks like, does it apply to the part-whole relation itself?