2.3 The Paradox of 101 Dalmatians
Is Oscar-minus per dog? Why then should we deny that Oscar-minus is a dog fruzo? We saw above that one possible response preciso 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. Sopra fact, for each of Oscar’s hairs, of which there are at least 101, there is a 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 preciso 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 mediante 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 (durante various different ways) from one another and Oscar by verso 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 con place. Hence, within Oscar’s compass at any given time there are congeries of Dalmatian parts sooner or later esatto become definitely Dalmatians; some durante verso day, some con per second, or a split second. It seems arbitrary esatto proclaim verso 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 preciso favor one of the latter type according onesto which the Dalmatians are not many but rather “almost one” Mediante any case, the canone account of identity seems unable on its own to handle the paradox of 101 Dalmatians.
It requires that we either deny that Oscar minus per hair is a dog – and verso Dalmatian – or else that we must affirm that there is per multiplicity of Dalmatians, all but one of which is incapable of independent action and all of which bark durante unison mai more loudly than Oscar barks aureola.
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 per new statue \(s_2\) out of \(c\). On day 3, Jones removes a part of \(s_2\), discards it, and replaces it using verso 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 esatto \(s_2\). On day \(3, s_2\) is identical to \(c’\). But this conclusion directly contradicts NI. If, on day \(1, c\) is (identical esatto) \(s_1\), 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 verso 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 standard account less NI, the latter principle follows directly from the assumption that individual variables and constants con quantified modal logic are sicuro 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 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 standard account is thus avanti facie incompatible with the natural preoccupazione that constitution is identity.