When Oscar loses his tail the resulting creature is certainly a dog

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 sicuro Chrysippus’ paradox was sicuro 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 canone account of identity, there are two dogs where we would normally count only one. Durante fact, for each of Oscar’s hairs, of which there are at least 101, there is a proper part of Oscar – Oscar minus verso hair – which is just as much per 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 onesto avoid multiplying the number of dogs populating the space reserved for Oscar alone. But the maximality principle may seem preciso be independently justified as well. When Oscar barks, do all these different dogs bark sopra unison? If a thing is verso dog, shouldn’t it be trapu 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 per hair, as dogs, and con 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 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 per verso day, some durante per second, or verso split second. It seems arbitrary onesto proclaim per Dalmatian part that is per split second away from becoming definitely per Dalmatian, verso Dalmatian, while denying that one per day away is a 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 esatto which the Dalmatians are not many but rather “almost one” Con any case, the norma account of identity seems unable on its own esatto handle the paradox of 101 Dalmatians.

It requires that we either deny that Oscar minus a hair is per dog – and verso 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 sopra unison giammai more loudly than Oscar barks chiazza.

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 verso 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 segno blackcupid in, \(s_2\) 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 preciso \(s_1\) and on day \(2, c\) is identical sicuro \(s_2\). On day \(3, s_2\) is identical to \(c’\). 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 sicuro \(s_2\) on day 2) and hence that \(s_1\) exists on day 2, which it does not. By per 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 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 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 norma account is thus precedentemente facie incompatible with the natural idea that constitution is identity.