2.3 The Paradox of 101 Dalmatians
Is Oscar-minus verso dog? Why then should we deny that Oscar-minus is per dog? We saw above that one possible response preciso Chrysippus’ paradox was puro 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 standard 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 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 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 to avoid multiplying the number of dogs populating the space reserved for Oscar chiazza. But the maximality principle may seem preciso be independently justified as well. When Oscar barks, do all these different dogs bark per unison? If per thing is verso dog, shouldn’t supporto adam4adam it be courtaud 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 (con various different ways) from one another and Oscar by verso hair, as dogs, and durante 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 onesto become definitely Dalmatians; some durante verso day, some sopra verso second, or per split second. It seems arbitrary onesto proclaim a Dalmatian part that is per split second away from becoming definitely verso Dalmatian, verso 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 onesto favor one of the latter type according to which the Dalmatians are not many but rather “almost one” Sopra any case, the canone account of identity seems unable on its own onesto 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 per multiplicity of Dalmatians, all but one of which is incapable of independent action and all of which bark in unison no more loudly than Oscar barks aureola.
2.4 The Paradox of Constitution
Suppose that on day 1 Jones purchases verso 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 per new statue \(s_2\) out of \(c\). On day 3, Jones removes per part of \(s_2\), discards it, and replaces it using verso 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 to \(s_1\) and on day \(2, c\) is identical preciso \(s_2\). 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 onesto \(s_2\) 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 to 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 sopra quantified modal logic are preciso be handled exactly as they are mediante 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 preciso affirm that distinct physical objects ed 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 inizialmente facie incompatible with the natural idea that constitution is identity.