2.3 The Paradox of 101 Dalmatians
Is Oscar-minus verso dog? Why then should we deny that Oscar-minus is verso dog? We saw above that one possible response onesto 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 canone account of identity, there are two dogs where we would normally count only one. Per 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 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 to be independently justified as well. When Oscar barks, do all these different dogs bark mediante unison? If per thing is per dog, shouldn’t it be courtaud of independent action? Yet Oscar-minus cannot act independently of Oscar. Nevertheless, David Lewis (1993) has suggested verso reason for counting Oscar-minus and all the 101 dog parts that differ (con various different ways) from one another and Oscar by verso hair, as dogs, and sopra fact as Dalmatians (Oscar is verso Dalmatian).
Lewis invokes Unger’s (1980) “problem of the many. His hairs loosen and then dislodge, some such remaining still durante place. Hence, within Oscar’s compass at any given time there are congeries of Dalmatian parts sooner or later sicuro become definitely Dalmatians; some con per day, some sopra per second, or a split second. It seems arbitrary sicuro proclaim a Dalmatian part that is a split second away from becoming definitely per Dalmatian, per Dalmatian, while denying that one verso day away is per 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 to favor one Ricerca profilo firstmet of the latter type according to which the Dalmatians are not many but rather “almost one” Con any case, the canone account of identity seems unable on its own preciso handle the paradox of 101 Dalmatians.
It requires that we either deny that Oscar minus per hair is verso dog – and per Dalmatian – or else that we must affirm that there is verso multiplicity of Dalmatians, all but one of which is incapable of independent action and all of which bark durante unison niente affatto more loudly than Oscar barks ombra.
2.4 The Paradox of Constitution
Suppose that on day 1 Jones purchases per 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 a ball and fashions a 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 per 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 sicuro \(s_1\) and on day \(2, c\) is identical to \(s_2\). On day \(3, s_2\) is identical esatto \(c’\). But this conclusion directly contradicts NI. If, on day \(1, c\) is (identical esatto) \(s_1\), then it follows, given NI, that on day \(2, s_1\) is \(s_2\) (since \(c\) is identical onesto \(s_2\) 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 sicuro 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 norma account less NI, the latter principle follows directly from the assumption that individual variables and constants in quantified modal logic are puro be handled exactly as they are sopra 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 puro affirm that distinct physical objects anche 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 davanti facie incompatible with the natural idea that constitution is identity.