Let us return to that impressive product of porcine ingenuity, Brick House. Brick House, whose completion by the Wise Pig occurred on Friday, is composed entirely of the 10,000 Tuesday Bricks. I grant that there is a sum, call it 'Brick Sum,' that is the classical mereological sum of the Tuesday Bricks. Brick Sum is 'generated' -- if you care to put it that way -- by Unrestricted Composition, the classical axiom which states that "Whenever there are some things, then there exists a fusion [sum] of those things." (D. Lewis, Parts of Classes, p. 74) I also grant that Brick Sum is unique by Uniqueness of Composition according to which "It never happens that the same things have two different fusions [sums]." (Ibid.) But I deny Lewis' Composition as Identity. Accordingly, Brick Sum cannot be identical to the Tuesday Bricks. After all, it is one while they are many.
Now the question I am debating with commenter John is whether Brick House is identical to Brick Sum. This ought not be confused with the question whether Brick House is identical to the Tuesday Bricks. This second question has an easy negative answer inasmuch as the former is one while the latter are many. Clearly, one thing cannot be many things.
The question, then, is whether Brick House is identical to Brick Sum. Here is a reason to think that they are not identical. Brick Sum exists regardless of the arrangement of its parts: they can be scattered throughout the land; they can be piled up in one place; they can be moving away from each other; they can be arranged to form a wall, or a corral, or a house, or whatever. All of this without prejudice to the existence and the identity of Brick Sum. Now suppose Hezbollah Wolf, a 'porcicide' bomber, enters Brick House and blows it and himself up at time t on Friday evening. At time t* later than t, Brick Sum still exists while Brick House does not. This shows that they cannot be identical; for if they were identical, then the destruction of Brick House would be the destruction of Brick Sum.
This argument, however, rests on an assumption, namely, that Brick Sum exists both at t and at t*. This won't be true if Four Dimensionalism is true. If bricks and houses are occurrents rather than continuants, if they are composed of temporal parts, then we cannot say, strictly and philosophically, that Brick Sum at t still exists at t*. And if we cannot say this, then the above argument fails.
But all is not lost since there remains a modal consideration. Brick House and Brick Sum both exist at time t in the actual world. But there are plenty of possible worlds in which, at t, the latter exists but not the former. Thus it might have been the case at t that the bricks were arranged corral-wise rather than house-wise. So Brick Sum has a property that Brick House lacks, namely, the modal property of being such that its parts could have been arranged in non-house-wise fashion. Therefore, by the Indiscernibility of Identicals, Brick House is not identical to Brick Sum.
So even if the historical discernibility argument fails on Four Dimensionalism, the modal discernibility argument seems to work even assuming Four Dimensionalism.
Please note that my thesis is not that Brick House is a sum that violates Uniqueness of Composition, but that Brick House is not a classical mereological sum. If Brick House were a sum, then it would be Brick Sum. But I have just argued that it cannot be Brick Sum. So it cannot identified with any classical sum. It is a whole of parts all right, but an unmereological whole. What does that mean? It means that it is a whole that cannot be adequately understood using only the resources of classical mereology.