The Shifting Sands of Identity: Reconsidering Perdurantism and Mereological Nihilism — Epoche C1
The question, and why it is not silly Take the several hundred thousand billion billion atoms currently arranged in the shape of a table in front of you and ask whether, in addition to those atoms, there exists one further thing that they compose. Peter van Inwagen named this the Special Composition Question — under what conditions do some objects compose a further object? — and the point of asking it is that the obvious answers all fail. "Whenever they are stuck together" cannot be right, since two people shaking hands are stuck together and compose nothing; "whenever they act as a unit" is either vague or false. This note concerns two answers that are neither vague nor obvious, and the relation between them. Mereological universalism — mereology being the formal theory of the part-whole relation — says that composition always occurs: for any objects whatever, there exists a further object that is their fusion, where a fusion of some things is an object that has each of them as a part and each of whose parts overlaps at least one of them. Writing $x \sqsubseteq y$ for "$x$ is part of $y$" and $x \circ y$ for "$x$ and $y$ share a part", the axiom reads $$\forall X\, \exists y\, \Big( \forall x\,(x \in X \rightarrow x \sqsubseteq y) \;\wedge\; \forall z\,(z \sqsubseteq y \rightarrow \exists x\,(x \in X \wedge z \circ x)) \Big).$$ The second conjunct is what stops the fusion from being bloated with irrelevant material. Mereological nihilism says that composition never occurs: the only things that exist are mereological simples, objects with no proper parts, and what we call a table is not an object at all but some simples arranged tablewise. The difference is countable, which is worth seeing because the count drives the central argument below. Given $n$ simples, universalism yields one object for every non-empty selection from them, and there are $2^n - 1$ such selections — each simple is either in or out, giving $2^n$ combinations, minus the empty one, which composes nothing. For three simples that is seven objects: three simples, three pairs, one triple. Nihilism yields three. No intermediate view has yet been mentioned, and the next section explains why that is not an oversight. The argument that eliminates the middle ground Common sense wants a restricted answer: some things compose (the atoms of the table) and others do not (my nose and the Eiffel Tower). David Lewis argued, and Sider developed the argument at length, that no such answer can be sustained. The argument runs in four steps, and each step needs its reason. If composition is restricted, there is a continuous series of cases running from composition to non-composition. Take some simples that plainly compose nothing — scattered across the galaxy — and some that plainly do compose a table. One can describe a finite sequence of intermediate cases in which the simples are moved a Planck length at a time, each case differing minutely from its neighbour. This is a claim about what is possible, and it is hard to deny. There is no sharp cut-off. A restricted view must say that at some adjacent pair in the series, composition switches on. But nothing about the microscopic difference between those two cases could ground so momentous a difference, and a brute metaphysical discontinuity at an arbitrary point is precisely what such a view was meant to avoid. So a restricted view must make it vague, in some cases, whether composition occurs. This is the natural retreat, and it is where the argument bites. But whether composition occurs cannot be vague, because that would make the number of objects vague. Here is the reason. If it is indeterminate whether some simples compose something, then it is indeterminate how many things there are — and the sentence "there are exactly $k$ things" contains no vague vocabulary at all. It is built from quantifiers, identity, negation and conjunction and nothing else. On the standard semantic account, vagueness arises from indecision among candidate meanings for our words; if a sentence contains no word whose meaning is undecided, it cannot be indeterminate in truth value. The conclusion is not that universalism is true. It is that composition is unrestricted or never . Universalism and nihilism are the two survivors, and everything between them has been removed. This is the single most important thing the original version of this note left out, and it reverses the shape of its argument: chipping away at universalism does not push us towards a moderate view, because there is nowhere moderate to stand. If the vagueness argument is sound, weakening universalism is ipso facto strengthening nihilism, which is the original's thesis — but obtained from a real argument rather than an intuition. What perdurantism says, and what Sider actually holds Persistence is a separate question, and the essay's use of it needs correcting in two places. An object endures if it persists by being wholly present at each moment of its career, so that the whole of you was here yesterday and the whole of you is here today. An object perdures if it persists by having distinct temporal parts at distinct times, so that what was here yesterday was a temporal part of you and no part of you is wholly present at more than one moment. On the perdurantist picture an object is extended in time much as it is extended in space, and the whole four-dimensional item is often called a spacetime worm. The first correction: Sider's Four-Dimensionalism defends the existence of temporal parts, but it does not defend the worm view of ordinary objects. Sider argues for the stage view, on which ordinary objects such as tables and people are instantaneous stages rather than worms, and on which "the table was flat yesterday" is made true not by an earlier part of the table but by an earlier stage that stands in a temporal counterpart relation to it. The original text presented the worm picture as Sider's own; it is the picture he argues against in his fi