Frege and saving substitution
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Frege and saving substitution Bryan Pickel1 • Brian Rabern2
Accepted: 5 October 2020 Ó The Author(s) 2020
Abstract Goodman and Lederman (Philos Stud 177(4):947–952, 2020) argue that the traditional Fregean strategy for preserving the validity of Leibniz’s Law of substitution fails when confronted with apparent counterexamples involving proper names embedded under propositional attitude verbs. We argue, on the contrary, that the Fregean strategy succeeds and that Goodman and Lederman’s argument misfires. Keywords Leibniz’ Law Substitution Frege Sense Ambiguity Opacity Validity
1 Introduction On one formulation of Leibniz’s Law, terms flanking true identities are everywhere intersubstitutable salva veritate: ‘‘given a true statement of identity, one of its two terms may be substituted for the other in any true statement and the result will be true’’ (Quine 1953: 139). This may be regimented as the following schema, where U½a=b is the result of substituting an occurrence of a for b in U. SUBSTITUTION:
ða ¼ b ^ UÞ ! U½a=b
Codifying this, it is tempting to hold that the schema are valid.
SUBSTITUTION
and its instances
& Brian Rabern [email protected] Bryan Pickel [email protected] 1
The University of Glasgow, 69 Oakfield Avenue, Glasgow G12 8LP, UK
2
The University of Edinburgh, 3 Charles St., Edinburgh EH8 9AD, UK
123
B. Pickel, B. Rabern
Yet, it has been argued that instances of SUBSTITUTION cannot be valid because they have false uses involving quotation, modal, and epistemic contexts. Focussing on epistemic contexts, any typical utterance of sentence (1) would likely be taken as false. (1)
If George Eliot is Mary Anne Evans and Twain knows that George Eliot wrote Middlemarch, then Twain knows that Mary Anne Evans wrote Middlemarch.
Although George Eliot is Mary Anne Evans, some who assert ‘George Eliot wrote Middlemarch’ would reject ‘Mary Anne Evans wrote Middlemarch’. It is a genuine discovery that Mary Anne Evans wrote Middlemarch even to those who know that George Eliot did. This has led various theorists to insist that the truth of the antecedent of (1) does not require the truth of the consequent. Thus we have an apparently false reading of (1) and a counterexample to the validity of SUBSTITUTION. According to the traditional Fregean diagnosis, these false uses of (1) do not threaten the validity of SUBSTITUTION. As (1) is normally used, the first occurrences of ‘George Eliot’ and ‘Mary Anne Evans’ refer to their customary referents, the woman herself, whereas the second occurrences (which occur under attitude verbs) refer to the senses of ‘George Eliot’ and ‘Mary Anne Evans’, respectively. The fact that the ambiguous sentence has a false reading is no more a counterexample to SUBSTITUTION, than is the false use of sentence (2) with the first three occurrences of ‘Aristotle’ referring to Aristotle Onassis, the famous shipping magnate, and the fourth referring to the philosopher: (2)
If Aristotle is Aristotle and Aristotle is a shipping magnate, then Aristotle is a s
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