How Essentialism Strengthens Modal Realism — Epoche B2
Inconstant Essences: Counterpart Theory and the Statue Starting from a case A sculptor takes a lump of clay and works it into a statue. Suppose the lump comes into existence as she begins and both statue and lump are destroyed together in the same accident [1] . Allan Gibbard set out this case in "Contingent Identity" (1975 [2] ), naming the statue Goliath and the lump Lumpl [3] . They occupy the same place at every moment of their existence, are made of the same matter, and weigh the same. There seems to be one object here, not two. Yet they differ in what could have happened to them. Squash the clay flat and the lump survives; the statue does not. So Goliath and Lumpl seem to have different properties, and by Leibniz's Law two things with different properties are not identical. The puzzle is sharp because both halves are compelling: one object, two modal profiles. This essay uses the case to argue a thesis about David Lewis's counterpart theory [4] . The thesis is not that counterpart theory gives a non-essentialist paraphrase of essentialist talk — that much is well known. It is that counterpart theory handles the case only because it makes an object's essential properties inconstant , varying with the counterpart relation in play; that inconstancy is not a blemish but the working part; and that its cost is not the objection Kripke famously pressed, which Lewis answers [5] , but a consequence Lewis himself accepts and his opponents cannot [6] . Counterpart theory and Kripkean essentialism are therefore not two analyses of one subject matter. They are a proposal to replace it and a defence of keeping it. Clearing away a confusion first It is sometimes said that Lewis gives a "mereological account of accessibility" that might be combined with an essentialist ontology. Two things have gone wrong there. Accessibility relations belong to Kripke-style model theory for modal logic, where necessity is truth at all worlds accessible from a given world; Lewis's modal realism has no such relation, because for Lewis every world is on a par and "necessarily" simply means "at every world". And Lewis is not an essentialist about individuals in the traditional sense at all. Nothing is gained by asking how his mereology strengthens essentialism. The genuine question in the neighbourhood is what his machinery does instead of essences, and whether it does enough. Worlds, parts, counterparts Lewis's modal realism, set out in On the Plurality of Worlds (1986), holds that there are many concrete worlds, ours among them, each a maximal spatiotemporally connected whole, and none causally or spatiotemporally related to any other. Ordinary things are parts of worlds, and worlds are mereological sums of their parts. Because being spatiotemporally related is what makes parts worldmates, nothing is a part of two worlds. That last point forces the central innovation. If Humphrey is a part of this world only, he is not present in any world where he wins the election. So what makes it true that he might have won? Lewis's answer, given first in "Counterpart Theory and Quantified Modal Logic" (1968), is that some inhabitant of another world is Humphrey's counterpart : an individual there who resembles him more closely, in the relevant respects, than anything else in that world does. To say Humphrey might have won is to say that some counterpart of his wins. The counterpart relation is a relation of comparative similarity. It is not identity, and it inherits the features of similarity: it is not transitive, it admits of degree, and — this is the point that matters — which respects count as relevant is not fixed once and for all. Inconstancy, and what it buys Because the relevant respects are not fixed, one and the same object has different counterparts under different ways of counting. Lewis makes this explicit in chapter 4 of On the Plurality of Worlds , arguing directly against the assumption that the counterpart relation is constant across contexts. He had already used two relations for one object in "Counterparts of Persons and Their Bodies" (1971), where what counts as a counterpart of a person differs from what counts as a counterpart of that person's body. Apply this to Goliath and Lumpl. Lewis's verdict is that they are identical — there is one thing there — but that the one thing can be considered as a statue or as a lump, and these are two counterpart relations. Considered under the statue relation, its counterparts are all statue-shaped; the flattened things in other worlds are not among them, so it could not have been flattened. Considered under the lump relation, its counterparts include flattened lumps, so it could have been flattened. The apparent violation of Leibniz's Law dissolves, because "could have been flattened" was never a single property that the object either has or lacks. It is not a property of the object simpliciter but of the object under a counterpart relation, and the description we use signals which relation is meant. Notice what this costs. On the Kripkean picture an object has an essence: a set of properties it has necessarily, fixed by what it is and not by how we refer to it. Kripke argues in Naming and Necessity that a given table could not have been made from a different block of wood, and takes this to be a fact about the table. On Lewis's picture there is no such fact, only facts about what shares which similarities with what, plus a context that selects among them. Essences are inconstant. The objection everyone cites, and why it fails Kripke's objection is that counterpart theory changes the subject. In a footnote he puts it with a memorable example: Humphrey could not care less whether someone else, no matter how much resembling him, would have been victorious in another possible world. What Humphrey cares about is what might have happened to him . Lewis has a good reply. He agrees that the modal property belongs to Humphrey. It is Humphrey, and nobody else, who has the prope