2.3 The Paradox of 101 Dalmatians
Is Oscar-minus a dog? Why then should we deny that Oscar-minus is a dog? We saw above that one possible response esatto Chrysippus’ paradox was preciso 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 per dog, then, given the standard account of identity, there are two dogs where we would normally count only one. Sopra fact, for each of Oscar’s hairs, of which there are at least 101, there is per proper part of Oscar – Oscar minus a hair – which is just as much verso dog as Oscar-minus.
There are then at least 101 dogs (and con 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 puro be independently justified as well. When Oscar barks, do all these different dogs bark con unison? If verso thing is a dog, shouldn’t it be capable of independent action? Yet Oscar-minus cannot act independently of Oscar. Nevertheless, David Lewis (1993) has suggested per reason for counting Oscar-minus and all the 101 dog parts that differ (con various different ways) from one another and Oscar by a 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 con place. Hence, within Oscar’s compass at any given time there are congeries of Dalmatian parts sooner or later to become definitely Dalmatians; some per per day, some con per second, or verso split second. It seems arbitrary puro proclaim a Dalmatian part that is verso split second away from becoming definitely verso Dalmatian, a Dalmatian, while denying that one verso 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 sicuro which the Dalmatians are not many but rather “almost one” Durante any case, the canone account of identity seems unable on its own onesto handle the paradox of 101 Dalmatians.
It requires that we either deny that Oscar minus a hair is per dog – and a 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 mediante unison giammai more loudly than Oscar barks alone.
2.4 The Paradox of Constitution
Suppose that on day 1 Jones purchases verso piece of clay \(c\) and fashions it into a statue \(s_1\). On day 2, Jones destroys \(s_1\), but not \(c\), by squeezing \(s_1\) into verso ball and fashions verso new statue \(s_2\) out of \(c\). On day 3, Jones removes a 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?” Verso natural answer is: identity. On day \(1, c\) is identical onesto \(s_1\) and on day \(2, c\) is identical puro \(s_2\). On day \(3, s_2\) is identical preciso \(c’\). But this conclusion directly contradicts NI. If, on day \(1, c\) is (identical onesto) \(s_1\), then it follows, given NI, that on day \(2, s_1\) is \(s_2\) (since \(c\) is identical sicuro \(s_2\) on day 2) and hence that \(s_1\) exists on day 2, which it does not. By verso similar argument, on day \(3, c\) is \(c’\) (since \(s_2\) is identical to 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 standard account less NI, the latter principle follows directly from the assumption that individual variables and constants sopra 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 esatto affirm that distinct physical ciò che è catholic singles objects di nuovo 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 intenzione that constitution is identity.