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 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 verso dog, then, given the canone account of identity, there are two dogs where we would normally count only one. Mediante fact, for each of Oscar’s hairs, of which there are at least 101, there is per proper part of Oscar – Oscar minus per hair – which is just as much a dog as Oscar-minus.

There are then at least 101 dogs (and per 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 macchia. But the maximality principle may seem sicuro be independently justified as well. When Oscar barks, do all these different dogs bark con unison? If verso thing is per dog, shouldn’t it be athletique 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 (sopra various different ways) from one another and Oscar by a hair, as dogs, and in fact as Dalmatians (Oscar is per 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 sicuro become definitely Dalmatians; some per verso day, some con a second, or a split second. It seems arbitrary puro proclaim per Dalmatian part that is per split second away from becoming definitely a Dalmatian, per Dalmatian, while denying that one per 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 esatto favor one of the latter type according puro which the Dalmatians are not many but rather “almost one” Mediante 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 verso hair is verso 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 con unison per niente more loudly than Oscar barks bolla.

2.4 The Paradox of Constitution

Suppose that on day 1 Jones purchases per 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 a new piece of clay, thereby destroying \(c\) and replacing it by verso 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 sicuro \(s_1\) and on day \(2, c\) is identical onesto \(s_2\). On day \(3, s_2\) is identical puro \(c’\). But this conclusion directly contradicts NI. If, on day \(1, c\) is (identical puro) \(s_1\), 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 a similar argument, on day \(3, c\) is \(c’\) (since \(s_2\) is identical esatto 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 con quantified modal logic are preciso 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 esatto 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) Ricerca wamba, it is unparsimonious. The canone account is thus avanti facie incompatible with the natural ispirazione that constitution is identity.