Abstract
In his logical foundation of arithmetic, Frege faced the problem that the semantic interpretation of his system does not determine the reference of the abstract terms completely. The contextual definition of number, for instance, does not decide whether the number 5 is identical to Julius Caesar. In a late writing, Quine claimed that the indeterminacy of reference established by Frege’s Caesar problem is a special case of the indeterminacy established by his proxy-function argument. The present paper aims to show that Frege’s Caesar problem does not really support the conclusions that Quine draws from the proxy-function argument. On the contrary, it reveals that Quine’s argument is a non sequitur: it does not establish that there are alternative interpretations of our terms that are equally correct, but only that these terms are ambiguous. The latter kind of referential indeterminacy implies that almost all sentences of our overall theory of the world are either false or neither true nor false, because they contain definite descriptions whose uniqueness presupposition is not fulfilled. The proxy-function argument must therefore be regarded as a reductio ad absurdum of Quine’s behaviorist premise that the reference of terms is determined only by our linguistic behavior.
Highlights
Frege’s Caesar problem arises, for example, when we introduce the notion of direction by means of the following contextual definition:(D) The direction of line x = the direction of line y if and only if x and y are parallel.(D) does not decide in all cases whether an identity statement of the form ‘the direction of line a = N’ is true or false; it leaves open, for instance, whether ‘The direction of the Earth’s axis = Julius Caesar’ is true or false
Quine claimed that the indeterminacy of reference established by Frege’s Caesar problem is a special case of the indeterminacy established by his proxy-function argument
The present paper aims to show that Frege’s Caesar problem does not really support the conclusions that Quine draws from the proxy-function argument
Summary
Frege’s Caesar problem arises, for example, when we introduce the notion of direction by means of the following contextual definition:. This problem is usually referred to as ‘Frege’s Caesar problem’ To establish this kind of indeterminacy in a more rigorous form, Frege used in a parallel case his muchacclaimed permutation argument. Quine mentioned that, with regard to abstract terms, the referential indeterminacy established by his proxy-function argument is already familiar from Frege’s Caesar problem:. It is instructive to make this comparison because Frege’s discussion of the Caesar problem reveals that Quine’s proxyfunction argument is a non sequitur: it does not really establish that there are different interpretations of our terms that are correct, but only that these terms are ambiguous The latter kind of referential indeterminacy implies that almost all sentences are either false or neither true nor false, because they contain definite descriptions whose uniqueness presupposition is not fulfilled. It has been criticized by Weiner 1995 and others. 6 See Salmón 2018. 7 See Greimann 2003, 2014 and 2021
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