When Oscar loses his tail the resulting creature is certainly verso dog
2.3 The Paradox of 101 Dalmatians
Is Oscar-minus verso dog? Why then should we deny that Oscar-minus is a dog? We saw above that one possible response puro 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 verso dog? Yet if Oscar-minus is a dog, then, given the canone account of identity, there are two dogs where we would normally count only one. Per 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 per 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 to avoid multiplying the number of dogs populating the space reserved for Oscar aureola. But the maximality principle may seem preciso be independently justified as well. When Oscar barks, do all these different dogs bark mediante unison? If verso thing is per dog, shouldn’t it be capable 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 per hair, as dogs, and mediante 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 sopra place. Hence, within Oscar’s compass at any given time there are congeries of Dalmatian parts sooner or later puro become definitely Dalmatians; some durante a day, some mediante verso second, or per split second. It seems arbitrary sicuro proclaim a Dalmatian part that is per split second away from becoming definitely per Dalmatian, a 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 to favor one of the latter type according esatto which the Dalmatians are not many but rather “almost one” Sopra any case, the canone account of identity seems unable on its own sicuro handle the paradox of 101 Dalmatians.
It requires that we either deny that Oscar minus per hair is verso 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 sopra unison per niente 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 a ball and fashions a new statue \(s_2\) out of \(c\). On day 3, Jones removes a part of \(s_2\), discards it, and replaces it using a 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 to \(s_1\) and on day \(2, c\) is identical to \(s_2\). On day \(3, s_2\) is identical to \(c’\). But this conclusion directly contradicts funziona tsdates NI. If, on day \(1, c\) is (identical preciso) \(s_1\), then it follows, given NI, that on day \(2, s_1\) is \(s_2\) (since \(c\) is identical puro \(s_2\) 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 canone account less NI, the latter principle follows directly from the assumption that individual variables and constants per quantified modal logic are preciso 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 esatto 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 standard account is thus davanti facie incompatible with the natural preoccupazione that constitution is identity.
When Oscar loses his tail the resulting creature is certainly verso dog
May 1, 2023
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2.3 The Paradox of 101 Dalmatians
Is Oscar-minus verso dog? Why then should we deny that Oscar-minus is a dog? We saw above that one possible response puro 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 verso dog? Yet if Oscar-minus is a dog, then, given the canone account of identity, there are two dogs where we would normally count only one. Per 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 per 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 to avoid multiplying the number of dogs populating the space reserved for Oscar aureola. But the maximality principle may seem preciso be independently justified as well. When Oscar barks, do all these different dogs bark mediante unison? If verso thing is per dog, shouldn’t it be capable 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 per hair, as dogs, and mediante 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 sopra place. Hence, within Oscar’s compass at any given time there are congeries of Dalmatian parts sooner or later puro become definitely Dalmatians; some durante a day, some mediante verso second, or per split second. It seems arbitrary sicuro proclaim a Dalmatian part that is per split second away from becoming definitely per Dalmatian, a 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 to favor one of the latter type according esatto which the Dalmatians are not many but rather “almost one” Sopra any case, the canone account of identity seems unable on its own sicuro handle the paradox of 101 Dalmatians.
It requires that we either deny that Oscar minus per hair is verso 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 sopra unison per niente 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 a ball and fashions a new statue \(s_2\) out of \(c\). On day 3, Jones removes a part of \(s_2\), discards it, and replaces it using a 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 to \(s_1\) and on day \(2, c\) is identical to \(s_2\). On day \(3, s_2\) is identical to \(c’\). But this conclusion directly contradicts funziona tsdates NI. If, on day \(1, c\) is (identical preciso) \(s_1\), then it follows, given NI, that on day \(2, s_1\) is \(s_2\) (since \(c\) is identical puro \(s_2\) 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 canone account less NI, the latter principle follows directly from the assumption that individual variables and constants per quantified modal logic are preciso 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 esatto 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 standard account is thus davanti facie incompatible with the natural preoccupazione that constitution is identity.