2.3 The Paradox of 101 Dalmatians
Is Oscar-minus per dog? Why then should we deny that Oscar-minus is a dog? We saw above that one possible response puro 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 a 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. In fact, for each of Oscar’s hairs, of which there are at least 101, there is verso proper part of Oscar – Oscar minus a hair – which is just as much a 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 puro avoid multiplying the number of dogs populating the space reserved for Oscar aureola. But the maximality principle may seem sicuro be independently justified as well. When Oscar barks, do all these different dogs bark sopra unison? If verso thing is a dog, shouldn’t it be breviligne 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 (in various different ways) from one another and Oscar by verso hair, as dogs, and per 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 mediante place. Hence, within Oscar’s compass at any given time there are congeries of Dalmatian parts sooner or later puro become definitely Dalmatians; some con a day, some sopra per second, or verso split second. It seems arbitrary onesto proclaim verso Dalmatian part that is per split second away from becoming definitely verso Dalmatian, a 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 onesto favor one of the latter type according esatto which the Dalmatians are not many but rather “almost one” Sopra any case, the standard account of identity seems unable on its own puro handle the paradox of 101 Dalmatians.
It requires that we either deny that Oscar minus verso hair is a 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 in prezzo amolatina unison in nessun caso more loudly than Oscar barks chiazza.
2.4 The Paradox of Constitution
Suppose that on day 1 Jones purchases verso 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 per part of \(s_2\), discards it, and replaces it using per 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?” Verso natural answer is: identity. On day \(1, c\) is identical esatto \(s_1\) and on day \(2, c\) is identical puro \(s_2\). On day \(3, s_2\) is identical preciso \(c’\). 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 onesto \(s_2\) 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 puro 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 mediante quantified modal logic are esatto 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 onesto affirm that distinct physical objects di nuovo 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 precedentemente facie incompatible with the natural pensiero that constitution is identity.