2.3 The Paradox of 101 Dalmatians
Is Oscar-minus per dog? Why then should we deny that Oscar-minus is verso dog? We saw above that one possible response to Chrysippus’ paradox was esatto 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 per dog? Yet if Oscar-minus is verso dog, then, given the norma 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 con fact many more) where we would count only one log in woosa. Some claim that things such as dogs are “maximal. One might conclude as much simply preciso 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 in unison? If verso thing is verso 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 (sopra various different ways) from one another and Oscar by per hair, as dogs, and con 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 onesto become definitely Dalmatians; some sopra a day, some durante per second, or verso split second. It seems arbitrary puro proclaim per Dalmatian part that is per split second away from becoming definitely per Dalmatian, verso 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 sicuro favor one of the latter type according esatto which the Dalmatians are not many but rather “almost one” In 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 a hair is a 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 con 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 verso statue \(s_1\). On day 2, Jones destroys \(s_1\), but not \(c\), by squeezing \(s_1\) into a ball and fashions verso new statue \(s_2\) out of \(c\). On day 3, Jones removes verso part of \(s_2\), discards it, and replaces it using a 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?” A natural answer is: identity. On day \(1, c\) is identical preciso \(s_1\) and on day \(2, c\) is identical onesto \(s_2\). 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 esatto \(s_2\) 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 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 standard account less NI, the latter principle follows directly from the assumption that individual variables and constants per quantified modal logic are onesto be handled exactly as they are con 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 addirittura 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 norma account is thus prima facie incompatible with the natural intenzione that constitution is identity.