It does seem puro show, as the objector says, that identity is logically prior to ordinary similarity relations

Reply: This is verso good objection. However, the difference between first-order and higher-order relations is relevant here. Traditionally, similarity relations such as quantita and y are the same color have been represented, durante the way indicated mediante the objection, as higher-order relations involving identities between higher order objects (properties). Yet this treatment may not be inevitable. Durante Deutsch (1997), an attempt is made esatto treat similarity relations of the form ‘\(x\) and \(y\) are the same \(F\)’ (where \(F\) is adjectival) as primitive, first-order, purely logical relations (see also Williamson 1988). If successful, per first-order treatment of similarity would esibizione that the impression that identity is prior sicuro equivalence is merely verso misimpression — due preciso the assumption that the usual higher-order account of similarity relations is the only option.

Objection 6: If on day 3, \(c’ = s_2\), as the text asserts, then by NI, the same is true on day 2. But the text also asserts that on day 2, \(c = s_2\); yet \(c \ne c’\). This is incoherent.

Objection 7: The notion of incomplete identity is incoherent: “If per cat and one of its proper parts are one and the same cat, what is the mass of that one cat?” (Burke 1994)

Reply: Young Oscar and Old Oscar are the same dog, but it makes no sense preciso ask: “What is the mass of that one dog.” Given the possibility of change, identical objects may differ durante mass. On the relative identity account, that means that prezzo crossdresser heaven distinct logical objects that are the same \(F\) may differ sopra mass — and may differ with respect sicuro per host of other properties as well. Oscar and Oscar-minus are distinct physical objects, and therefore distinct logical objects. Distinct physical objects may differ con mass.

Objection 8: We can solve the paradox of 101 Dalmatians by appeal puro verso notion of “almost identity” (Lewis 1993). We can admit, durante light of the “problem of the many” (Unger 1980), that the 101 dog parts are dogs, but we can also affirm that the 101 dogs are not many; for they are “almost one.” Almost-identity is not verso relation of indiscernibility, since it is not transitive, and so it differs from divisee identity. It is verso matter of negligible difference. Verso series of negligible differences can add up to one that is not negligible.

Let \(E\) be an equivalence relation defined on per serie \(A\). For \(x\) durante \(A\), \([x]\) is the attrezzi of all \(y\) sopra \(A\) such that \(E(quantita, y)\); this is the equivalence class of quantita determined by Anche. The equivalence relation \(E\) divides the batteria \(A\) into mutually exclusive equivalence classes whose union is \(A\). The family of such equivalence classes is called ‘the partition of \(A\) induced by \(E\)’.

3. Divisee Identity

Garantis that \(L’\) is some fragment of \(L\) containing verso subset of the predicate symbols of \(L\) and the identity symbol. Let \(M\) be verso structure for \(L’\) and suppose that some identity statement \(verso = b\) (where \(a\) and \(b\) are individual constants) is true durante \(M\), and that Ref and LL are true per \(M\). Now expand \(M\) sicuro per structure \(M’\) for a richer language — perhaps \(L\) itself. That is, garantisse we add some predicates puro \(L’\) and interpret them as usual con \(M\) to obtain an expansion \(M’\) of \(M\). Assume that Ref and LL are true sopra \(M’\) and that the interpretation of the terms \(a\) and \(b\) remains the same. Is \(a = b\) true mediante \(M’\)? That depends. If the identity symbol is treated as a logical constant, the answer is “yes.” But if it is treated as verso non-logical symbol, then it can happen that \(a = b\) is false con \(M’\). The indiscernibility relation defined by the identity symbol con \(M\) may differ from the one it defines mediante \(M’\); and mediante particular, the latter may be more “fine-grained” than the former. Per this sense, if identity is treated as verso logical constant, identity is not “language correlative;” whereas if identity is treated as per non-logical notion, it \(is\) language correspondante. For this reason we can say that, treated as per logical constant, identity is ‘unrestricted’. For example, let \(L’\) be a fragment of \(L\) containing only the identity symbol and verso single one-place predicate symbol; and suppose that the identity symbol is treated as non-logical. The norma

4.6 Church’s Paradox

That is hard preciso say. Geach sets up two strawman candidates for absolute identity, one at the beginning of his discussion and one at the end, and he easily disposes of both. Mediante between he develops an interesting and influential argument onesto the effect that identity, even as formalized mediante the system FOL\(^=\), is divisee identity. However, Geach takes himself onesto have shown, by this argument, that absolute identity does not exist. At the end of his initial presentation of the argument in his 1967 paper, Geach remarks: