This post is an attempt to understand and evaluate Peter van Inwagen's "Can Mereological Sums Change Their Parts," J. Phil. (December 2006), 614-630. A preprint is available online here.
The Wise Pig and the Brick House: My Take
On Tuesday the Wise Pig takes delivery of 10,000 bricks. On the following Friday he completes construction of a house made of exactly these bricks and nothing else. Call the bricks in question the 'Tuesday bricks.' I would 'assay' the situation as follows. On Tuesday there are some unassembled bricks laying about the building site. By Unrestricted Composition, these bricks compose a classical mereological sum. Call this sum 'Brick Sum.' (To save keystrokes I will write 'sum' for 'classical mereological sum.' ) By Uniqueness of Composition, there is exactly one sum that the Tuesday bricks compose. On Friday, both the Tuesday bricks and their (unique) sum exist. But as I see it, the Brick House is identical neither to the Tuesday bricks nor to their sum. Thus I deny that the Brick House is identical to the sum of the things that compose it. I give two arguments for this non-identity.
Nonmodal 'Historical' Argument: Brick Sum has a property that Brick House does not have, namely the property of existing on Tuesday. Therefore, by the Indiscernibility of Identicals, Brick Sum is not identical to Brick House.
Modal Argument: Suppose that the actual world is such that Brick Sum and Brick House always existed, exist now, and always will exist: every time t is such that both exist at t. This does not alter the plain fact that the house depends for its existence on the bricks, while the bricks do not depend for their existence on the house. Thus there are possible worlds in which Brick Sum exists but Brick House does not. (Note that Brick Sum exists 'automatically' given the existence of the bricks.) These worlds are simply the worlds in which the bricks exist but in an unassembled state. So Brick Sum has a property that Brick House does not have, namely, the modal property of being possibly such as to exist without composing a house. Therefore, by the Indiscernibility of Identicals, Brick Sum is not identical to Brick House.
In sum (pardon the pun!), The Brick House is not a mereological sum. (If it were, it would have existed on Tuesday as a load of bricks, which is absurd.) This is not to say that there is no sum 'corresponding' to the Brick House: there is. It is just that this sum -- Brick Sum -- is not identical to Brick House. So what I am saying implies no rejection of Unrestricted Composition. The point is rather that a material artifact such as a house cannot be identified with the mereological sum of the things it is made of. This is because sums abstract or prescind from the mutual relations of parts in virtue of which parts form what we might call 'integral wholes' as opposed to a mere mereological sums. Unassembled bricks do not a brick house make: you have to assemble them properly. And the assembly, however you want to assay it, is an added ontological ingredient that escapes consideration by a general purely formal part-whole theory such as classical mereology.
I assume with van Inwagen that Brick House can lose a brick (or gain a brick) without prejudice to its identity. But, contra van Inwagen, I do not take this to imply that mereological sums can gain or lose parts. And this for the simple reason that Brick House and things like it are not identical to sums of the things that compose them. I would say, pace van Inwagen, that mereological sums can no more gain or lose parts than (mathematical) sets can gain or lose elements.
The Wise Pig and the Brick House: Van Inwagen's Take
I agree with van Inwagen that "The Tuesday bricks are all parts of the Brick House and every part of the Brick House overlaps at least one of the Tuesday bricks." (616-617) But he takes this obvious truth to imply that " . . . 'a merelogical sum' is the obvious thing to call something of which the Tuesday Bricks are all parts and each of whose parts overlaps at least one of the Tuesday Bricks." (617) Well, he can call it that but only if he uses 'mereological sum' in a way different that the way it is used in classical mereology.
Now if we acquiesce in van Inwagen's usage, and we grant that things like houses can change their parts, then it follows that mereological sums can change their parts. But why should we acquiesce in van Inwagen's usage of 'mereological sum'?
Is Everything a Mereological Sum?
As I use 'mereological sum,' not everything is such a sum. The Brick House is not a sum. It is no more a sum than it is a set. There are sums and there are sets, but not everything is a sum just as not everything is a set. There is a set consisting of the Tuesday Bricks, and there is a singleton set of the Brick House. But neither of these sets is identical to the Brick House. Neither of them has anything to fear from the pulmonary exertions of the Big Bad Wolf -- not because they are so strong, but because they are abstract objects removed from the flux and shove of the causal order. Sums of concreta, unlike sets of concreta, are themselves concrete -- but the Brick House is not a sum. Van Inwagen disagrees. For him, "Everything is a mereological sum." (618)
His argument for this surprising claim is roughly as follows. PvI's presentation is tedious and technical but I think I will not be misrepresenting him if I sum up the gist of it as follows:
1. Everything, whether simple or composite, has parts. (This is a consequence of the following definition: x is a part of y =df x is a proper part of y or x = y. Because everything is self-identical, everything has itself as a part, an improper part to be sure, but a part nonetheless. Therefore:
2. Everything is a mereological sum of its parts. Therefore:
3. Everything is a mereological sum. Therefore:
4. ". . . mereological sums are not a special sort of object." (622) In this respect they are unlike sets."'Mereological sum' is not a useful stand-alone general term." (622) 'Set' is.
What's At Issue Here?
I confess to not being clear about what exactly is at issue here. One could of course use 'mereological sum' in the way that van Inwagen proposes, a way that implies that everything is a mereological sum, and that implies that there is no conceptual confusion in the notion of a mereological sum changing its parts. But why adopt this usage? How does it help us in the understanding of material composition?
What am I missing?