Frege on Sense Identity, Basic Law V, and Analysis

Abstract

Introduction: An incompatible triad Frege's Logicism has been subject to a variety of different interpretations. The following three thesis have individually been associated with key aspects of Frege's philosophy, yet they are jointly incompatible: Informativeness Arithmetical identity statements are informative because the senses of the expressions flanking the identity sign are distinct. Analysis Arithmetical identity statements are analysable into logical identity statements by providing (term by term) sense-preserving analyses. Logical Identity Logical identity statements are logically true in virtue of an identity of senses of the expressions flanking the identity. The three claims constitute an incompatible triad: [Informativeness] requires that the expressions flanking an informative arithmetical identity are distinct. According to [Analysis], there is a corresponding logical identity which properly captures the senses of the original arithmetical expressions. Yet, given [Logical Identity], the relevant logical identity will be such that the two sides flanking the identity sign express the same sense. Something, it seems, has to go. 1 Given that there is little doubt amongst Frege scholars that Frege was indeed committed to [Informativeness], the two natural avenues to resolve the

Blanchette on Frege on Analysis and Content

“…4),and Wehmeier and Schroeder-Heister (2005) for discussion.7 See, e.g.,Simons (1992, p. 764) Schirn (2006). andEbert (2014), for instance, disagree.8 This is also suggest by Ebert (2014, §2.2, fn. 26).9 His discussion of the terms in his debate with Hilbert is a different matter-and complicated by the fact that Frege picks up on Hilbert's use of "Erklärung".10 I am indebted to Patricia Blanchette, Roy Cook, Philip Ebert, Walter Pedriali, Kai Wehmeier, and Richard Zach for helpful comments and discussions.…”

“…8 This explanation is simpler than explaining Heck (2012, ch. 4), and Wehmeier and Schroeder-Heister ); Schirn (2006) and Ebert (2014), for instance, disagree.…”

“…I, p. 16; seeHeck (2012, ch. 4), and Wehmeier and Schroeder-Heister(2005) for discussion.7 See, e.g., Simons (1992, p. 764);Schirn (2006) andEbert (2014), for instance, disagree.8 This is also suggest by Ebert (2014, §2.2, fn. 26).…”

“…Only a few lines down, regarding an assumed permutation X, he writes that " 'X( -" (")) = X( -↵ (↵))' too is co-referential with ' a (a) = (a)' ", adding in a footnote: "Thereby it is not said that the sense is the same. 7 See, e.g., Simons (1992, p. 764); Schirn (2006) and Ebert (2014), for instance, disagree.…”

“…2 That Frege held that abstractions principles like Hume's Principle or Basic Law V state the sameness of sense for the propositions on their two sides is argued, among others, by Beaney (2005), Burge (1990), Currie (1982), Milne (1989), and Simons (1992); see, e.g., (Dummett, 1991, ch. 14), Ebert (2014), or (Klement, 2002, ch. 3) for dissent.…”