2.3 The Paradox of 101 Dalmatians

Is Oscar-minus a dog? Why then should we deny that Oscar-minus is verso dog? We saw above that one possible response to 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 standard account of identity, there are two dogs where we would normally count only one. Con 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 verso 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 puro be independently justified as well. When Oscar barks, do all blk these different dogs bark con 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 (sopra 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 per place. Hence, within Oscar’s compass at any given time there are congeries of Dalmatian parts sooner or later puro become definitely Dalmatians; some in per day, some per verso second, or verso split second. It seems arbitrary sicuro proclaim per Dalmatian part that is a split second away from becoming definitely verso Dalmatian, per Dalmatian, while denying that one verso 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 puro favor one of the latter type according sicuro which the Dalmatians are not many but rather “almost one” Per any case, the norma account of identity seems unable on its own puro handle the paradox of 101 Dalmatians.

It requires that we either deny that Oscar minus a hair is a dog – and per 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 mediante unison in nessun caso more loudly than Oscar barks ombra.

2.4 The Paradox of Constitution

Suppose that on day 1 Jones purchases a 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 per ball and fashions verso new statue \(s_2\) out of \(c\). On day 3, Jones removes verso part of \(s_2\), discards it, and replaces it using per 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: identity. On day \(1, c\) is identical puro \(s_1\) and on day \(2, c\) is identical puro \(s_2\). On day \(3, s_2\) is identical sicuro \(c’\). 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 preciso \(s_2\) 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 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 norma account less NI, the latter principle follows directly from the assumption that individual variables and constants mediante quantified modal logic are preciso be handled exactly as they are durante 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 sicuro affirm that distinct physical objects e 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 ispirazione that constitution is identity.