[...]... thank Diane O’Leary, who provided encouragement and metaphysical direction at times in my career when it was most needed My cursory overview has left one important theme unmentioned, one that will no doubt strike anyone who reads these essays A good proportion of them involve a direct engagement with some segment or other of David Lewis’s formidable metaphysical corpus In this way, I am in the position... reprint it here 1 Thanks to Kit Fine, Daniel Nolan, Brian Weatherson, Timothy Williamson, Dean Zimmerman, an audience at the 2001 Mighty Metaphysical Mayhem conference at Syracuse, and especially Tamar Gendler and Ted Sider for helpful comments and discussion 2 Metaphysical Essays In this vein, Quine observes that ‘Quantification depends upon there being values of variables, same or different absolutely... 9 I have Max Black, ‘The Identity of Indiscernibles’, in J Kim and E Sosa (eds.), Metaphysics: An Anthology (Oxford: Basil Blackwell, 1999) (first pub in Mind, 51 (1952), 153–64) in mind here 7 4 Metaphysical Essays ordered pair consisting of distinct spheres One of the clauses in the definition of ‘xIy’ will be ‘∀z(z is 2 miles from x ≡ z is 2 miles from y) But this is not satisfied by the ordered pair... predicate ‘is identical to’, if it exists in the language, counts as non-logical vocabulary 15 I shall not pursue here the question of whether the need for second-order variables is a deep one 14 6 Metaphysical Essays enough to speak in a general way about all properties and relations whatsoever? Let us suppose that they are liberal about what counts as a property and what counts as a relation (This is... conception, the principles can be given a settheoretic gloss, namely: (LL) ∀x∀y(x = y ⊃ ∀z(x is a member of z ⊃ y is a member of z)) (II) ∀x∀y((∀z(x is a member of z iff y is a member of z)) ⊃ x = y) 8 Metaphysical Essays Assuming our set theory takes it as axiomatic that everything has a unit set,19 then, quite obviously, we will be committed to regarding the identity of indiscernibles as a fairly trivial... with a rich 24 25 26 Op cit 69 And on the set-theoretic gloss of properties, it is more than an analogy I leave it open whether some other argument against haecceitistic properties might work 10 Metaphysical Essays range of qualitative, non-haecceitistic predicates But it is not an effective way to make trouble for a liberal view of properties, one that allows the properties instantiated by each sphere... 30 Williamson, ‘Vagueness, Identity, and Leibniz’s Law’ in Giaretta, Bottani, and Carrera (eds.), Individuals, Essence, and Identity: Themes of Analytic Metaphysics (Dordrecht: Kluwer, 2001) 12 Metaphysical Essays truth-value relative to a pair of assignments A and A* such that A assigns x to ‘a’, A* assigns y to ‘a’, A being exactly like A* in every other way.31 3 D EV I A N T V I EW S : R E L AT... number of these’ as ‘Find the number of objects in my hand’ As Frege reminds us, such instructions as the former are typically elliptical for an instruction far more mundane than the latter 14 Metaphysical Essays as an ‘extensional context’? What is it to mean to say that two terms ‘corefer’? All of these notions are built upon the notions of simple identity and difference Abandon those notions and... offers one gloss on the mystery of the Trinity: there are three persons: Christ is not the same person as God the Father (and so on) There is one divinity: Christ is the same God as the Father 16 Metaphysical Essays Therefore, β is black all over at t is invalid A vital feature of the notion of identity is its amenability to Leibniz’s law Within an extensional language, inferences of the form α is F... 44 Geach, ‘Replies’, p 295 Similarly, suppose I have changed my name from ‘Hawthorne’ to ‘O’Leary-Hawthorne’ and then back again There are two surman Which of them am I the same surman as? 45 18 Metaphysical Essays Suppose a clay statue is at t1 made of a lump, call it ‘Lump1,’ and at t2 made of a slightly different lump (through erosion or small replacements), call it ‘Lump2.’ Let ‘Jerry’ name the .