What Is Identity? Frege’s Argument in ‘Über Sinn und Bedeutung’ Scrutinized and Newly Interpreted with Glances at Grundgesetze

Abstract In this essay, I subject Frege’s line of argument in the opening passage of ‘Über Sinn und Bedeutung’ to critical scrutiny, reveal its weaknesses and show what someone might nonetheless learn from it if pondering over the nature of identity and the cognitive value of identity statements. I argue that (a) Frege’s epistemological argument against the metalinguistic view of identity is inconclusive, (b) he fails to argue for the plausibility and strength of the objectual view of identity, (c) any acknowledgement by Frege that, in general, the cognitive value of true statements of the form “ $$a = b$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>a</mml:mi> <mml:mo>=</mml:mo> <mml:mi>b</mml:mi> </mml:mrow> </mml:math> ” is not negatively affected by the arbitrariness of the name-object relation would have amounted to a concession that the metalinguistic view of identity statements is epistemologically on a par with the objectual view, i.e. that both views allow a plausible explanation of the fact that such statements, unlike statements of the form “ $$a = a$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>a</mml:mi> <mml:mo>=</mml:mo> <mml:mi>a</mml:mi> </mml:mrow> </mml:math> ”, often contain a piece of valuable knowledge. I argue that in his mature period after 1892, Frege was right in calling into question the “coincidence view of (ordinary) proper names” according to which the sense of a proper name coincides with the sense of a “privileged” coreferential definite description. I also comment on the sense of a concept-script proper name as well as on Frege’s transformation of a metalinguistic, but non-definitional stipulation of coreferentiality into an objectual identity in Grundgesetze I. In the penultimate section, I discuss the question of whether the objectual view of identity was a conditio sine qua non for Frege’s attempt to establish the analyticity of (true) non-trivial arithmetical equations.