Frege and saving substitution

Bryan Pickel,Brian Rabern

doi:10.1007/s11098-020-01576-y

Bryan Pickel, Brian Rabern

Open Access

https://doi.org/10.1007/s11098-020-01576-y

Copy DOI

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.

Highlights

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)
Given that (4) follows from (1) and (3) and yet is false on some uniform disambiguations, the Fregean should take this as prima facie evidence that the relevant notion of validity is not closed under classical propositional logic
We have examined the argument that Goodman and Lederman provisionally consider for the invalidity of SUBSTITUTION and argued that one of its premises—that (3) is valid—is false

Summary

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). (1*) If George Eliot is Mary Anne Evans and Twain knows that George Eliot wrote Middlemarch, Twain knows that Mary Anne Evans wrote Middlemarch This sentence is not an instance of SUBSTITUTION and its falsity is no threat to the validity of the law. We will focus on one natural way to extend the notion of validity as applied to unambiguous languages On this approach, a schema is valid only if all uniform disambiguations of its instances are true (or at least not false).. Disambiguation (1a) is true because its antecedent is false if ‘George Eliot’ and ‘Mary Ann Evans’ are taken to have their customary referent, namely the woman herself—the conjunct ‘Twain knows that George Eliot wrote Middlemarch’ is false.. In this way the Fregean can save the principle of SUBSTITUTION.

The argument and validity

The argument and schmalidity

Fregean factivity

Conclusion