335:"the man who won the 1968 election" can be used non-rigidly. Kripke argues, that if names are rigid designators, then identity must be necessary, because the names ‘a’ and ‘b’ will be rigid designators of an object x if a is identical to b, and so in every possible world, ‘a’ and ‘b’ will both refer to this same object x, and no other, and there could be no situation in which a might not have been b, otherwise x would not have been identical with itself.
454:. (What pairs (x, y) could be counterexamples? Not pairs of distinct objects, for then the antecedent is false; nor any pair of an object and itself, for then the consequent is true.) If ‘a’ and ‘b’ are rigid designators, it follows that ‘a = b’, if true, is a necessary truth. If ‘a’ and ‘b’ are not rigid designators, no such conclusion follows about the statement ‘a = b’ (though the objects designated by ‘a’ and ‘b’ will be necessarily identical).
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are typically not. So we can speak of "Richard Nixon" referring to the same person in all possible worlds, but the description "the man who won the 1968 election" could refer to many different people. According to Kripke, the proper name "Richard Nixon" can only be used rigidly, but the description
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in which that object exists. When a name's referent is fixed by the original act of naming, it becomes a rigid designator. Some examples of rigid designators include proper names (i.e. ‘Richard Nixon’), natural kind terms ( i.e. ‘gold’ or ‘H2O’) and some descriptions.
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This does not mean that we have knowledge of this necessity. Before the discovery that
Hesperus (the evening star) and Phosphorus (the morning star) were the same planet, this fact was not known, and could not have been inferred from
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O. It is possible, of course, that we are mistaken about the chemical composition of water, but that does not affect the necessity of identities. What is not being claimed is that water is necessarily H
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O' pick out the same object in every possible world, there is no possible world in which 'water' picks out something different from 'H
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Burgess, J., ‘On a derivation of the necessity of identity’, Synthese May 2014, Volume 191, Issue 7, pp 1567–1585, p 1567
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The first premise is simply postulated: every object is identical to itself. The second is an application of the
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Waiving fussy considerations deriving from the fact that x need not have necessary existence, it was clear from
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is the thesis that for every object x and object y, if x and y are the same object, it is
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that x and y are the same object. The thesis is best known for its association with
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32:, who published it in 1971, although it was first derived by the logician
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Identity of
Individuals in a Strict Functional Calculus of Second Order
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The derivation in Kripke's 'Identity and
Necessity' is in three steps:
181:{\displaystyle \forall x\forall y(x=y\to (\Box (x=x)\to \Box (x=y)))}
620:‘Identity and Necessity’ p. 154, there is a similar argument in
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Kripke, S. ‘Identity and
Necessity’, in Milton K. Munitz (ed.),
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Leibniz’s law that identity is an ‘internal’ relation:
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581:. New York University Press. pp. 135-164 (1971)
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665:Modal logic
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30:Saul Kripke
18:modal logic
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517:water is H
655:Necessity
538:necessity
468:necessity
424:◻
421:→
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283:_
271:◻
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205:∀
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40:in 1953.
26:necessary
529:See also
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556:Notes
479:water
477:. If
481:is H
191:(3)
96:(2)
52:(1)
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525:O.
16:In
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