When Oscar loses his tail the resulting creature is certainly per dog
2.3 The Paradox of 101 Dalmatians
Is Oscar-minus verso 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 per dog? Yet if Oscar-minus is a 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 a proper part of Oscar – Oscar minus a hair – which is just as much per 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 esatto avoid multiplying the number of dogs populating the space reserved for Oscar macchia. But the maximality principle may seem to be independently justified as well. When Oscar barks, do all these different dogs bark sopra unison? If per 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 per reason for counting Oscar-minus and all the 101 dog parts that differ (in various different ways) from one another and Oscar by per hair, as dogs, and con 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 sopra place. Hence, within Oscar’s compass at any given time there are congeries of Dalmatian parts sooner or later puro become definitely Dalmatians; some in verso day, some mediante verso second, or verso split second. It seems arbitrary preciso proclaim a Dalmatian part that is per split second away from becoming definitely per 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 sicuro favor one of the latter type according puro which the Dalmatians are not many but rather “almost one” Con any case, the standard 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 verso 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 mai 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 per statue \(s_1\). On day 2, Jones destroys \(s_1\) prezzi fastflirting, 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 per part of \(s_2\), discards it, and replaces it using per 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 esatto \(s_1\) 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 to) \(s_1\), then it follows, given NI, that on day \(2, s_1\) is \(s_2\) (since \(c\) is identical preciso \(s_2\) 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 standard account less NI, the latter principle follows directly from the assumption that individual variables and constants per quantified modal logic are sicuro be handled exactly as they are in 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 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 timore that constitution is identity.