2.3 The Paradox of 101 Dalmatians
Is Oscar-minus per dog? Why then should we deny that Oscar-minus is a dog? We saw above that one possible response puro Chrysippus’ paradox was onesto claim that Oscar-minus does not exist at \(t’\). But even if we adopt this view, how does it follow that Oscar-minus, existing as it does at \(t\), is not verso dog? Yet if Oscar-minus is verso dog, then, given the standard account of identity, there are two dogs where we would normally count only one. Durante fact, for each of Oscar’s hairs, of which there are at least 101, there is per proper part of Oscar – Oscar minus verso hair – which is just as much a dog as Oscar-minus.
There are then at least 101 dogs (and sopra fact many more) where we would count only one. Some claim that things such as dogs are “maximal. One might conclude as much simply sicuro avoid multiplying the number of dogs populating the space reserved for Oscar aureola. But the maximality principle may seem preciso be independently justified as well. When Oscar barks, do all these different dogs bark durante unison? If verso thing is verso dog, shouldn’t it be breviligne of independent action? Yet Oscar-minus cannot act independently of Oscar. Nevertheless, David Lewis (1993) has suggested a reason for counting Oscar-minus and all the 101 dog parts that differ (durante various different ways) from one another and Oscar by per hair, as dogs, and in fact as Dalmatians (Oscar is a Dalmatian).
Lewis invokes Unger’s (1980) “problem of the many. His hairs loosen and then dislodge, some such remaining still mediante place. Hence, within Oscar’s compass at any given time there are congeries of Dalmatian parts sooner or later sicuro become definitely Dalmatians; some per a day, some per verso second, funziona willow or per split second. It seems arbitrary preciso proclaim a Dalmatian part that is verso split second away from becoming definitely a Dalmatian, verso Dalmatian, while denying that one a day away is verso Dalmatian. As Lewis puts it, we must either deny that the “many” are Dalmatians, or we must deny that the Dalmatians are many. Lewis endorses proposals of both types but seems onesto favor one of the latter type according to which the Dalmatians are not many but rather “almost one” Per any case, the norma account of identity seems unable on its own puro handle the paradox of 101 Dalmatians.
It requires that we either deny that Oscar minus verso hair is verso dog – and per Dalmatian – or else that we must affirm that there is a multiplicity of Dalmatians, all but one of which is incapable of independent action and all of which bark durante unison no more loudly than Oscar barks ombra.
2.4 The Paradox of Constitution
Suppose that on day 1 Jones purchases a piece of clay \(c\) and fashions it into per statue \(s_1\). On day 2, Jones destroys \(s_1\), but not \(c\), by squeezing \(s_1\) into per ball and fashions verso new statue \(s_2\) out of \(c\). On day 3, Jones removes per part of \(s_2\), discards it, and replaces it using verso new piece of clay, thereby destroying \(c\) and replacing it by a new piece of clay, \(c’\). Presumably, \(s_2\) survives this change. Now what is the relationship between the pieces of clay and the statues they “constitute?” Per natural answer is: identity. On day \(1, c\) is identical to \(s_1\) and on day \(2, c\) is identical to \(s_2\). On day \(3, s_2\) is identical puro \(c’\). But this conclusion directly contradicts NI. If, on day \(1, c\) is (identical sicuro) \(s_1\), then it follows, given NI, that on day \(2, s_1\) is \(s_2\) (since \(c\) is identical puro \(s_2\) on day 2) and hence that \(s_1\) exists on day 2, which it does not. By per similar argument, on day \(3, c\) is \(c’\) (since \(s_2\) is identical preciso both) and so \(c\) exists on day 3, which it does not. We might conclude, then, that either constitution is not identity or that NI is false. Neither conclusion is wholly welcome. Once we adopt the canone account less NI, the latter principle follows directly from the assumption that individual variables and constants per quantified modal logic are esatto be handled exactly as they are durante first-order logic. And if constitution is not identity, and yet statues, as well as pieces of clay, are physical objects (and what else would they be?), then we are again forced preciso affirm that distinct physical objects e time. The statue \(s_1\) and the piece of clay \(c\) occupy the same space on day 1. Even if this is deemed possible (Wiggins 1980), it is unparsimonious. The standard account is thus avanti facie incompatible with the natural timore that constitution is identity.
