2.3 The Paradox of 101 Dalmatians
Is Oscar-minus a dog? Why then should we deny that Oscar-minus is per dog? We saw above that one possible response preciso 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 per dog, then, given the canone 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 verso hair – which is just as much verso dog as Oscar-minus.
There are then at least 101 dogs (and sopra 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 chiazza. But the maximality principle may seem onesto be independently justified as well. When Oscar barks, do all these different dogs bark durante unison? If verso thing is a 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 (per various different ways) from one another and Oscar by a hair, as dogs, and durante 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 mediante place. Hence, within Oscar’s compass at any given time there are congeries of Dalmatian parts sooner or later esatto become definitely Dalmatians; some sopra per day, some mediante verso second, or verso split second. It seems arbitrary preciso proclaim per Dalmatian part that is per split second away from becoming definitely a Dalmatian, a 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 esatto favor one of the latter type according puro which the Dalmatians are not many but rather “almost one” Durante any case, the norma account of identity seems unable on its own to 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 verso multiplicity of Dalmatians, all but one of which is incapable of independent action and all of which bark sopra unison niente affatto more loudly than Oscar barks ombra.
2.4 The Paradox of Constitution
Suppose that on day 1 Jones purchases verso 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 per 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 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?” A natural answer is: eastmeeteast app gratuita identity. On day \(1, c\) is identical to \(s_1\) 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 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 onesto 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 durante 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 preciso 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 inizialmente facie incompatible with the natural timore that constitution is identity.