The horizontal in Frege’s Begriffsschrift

This paper addresses an issue with the sign ‘[inline-graphic not available: see fulltext]’ in Frege’s mature version of Begriffsschrift, i.e., the version in ‘Function and Concept’ and Grundgesetze. The sign is a performative for asserting in that writing down ‘[inline-graphic not available: see fulltext]’ is equivalent to asserting that p. Frege further says that writing ‘[inline-graphic not available: see fulltext]’ is also equivalent to identifying the reference of ‘p’ with the truth-value True. It looks as if he holds that asserting that p consists in identifying the True with the reference of ‘p’. Frege’s commitment to it, however, seems to encounter a number of tensions. This paper aims to show that these tensions can be avoided by endorsing a non-assertive conception of identification under which making an identification is not making an identity assertion. The suggested reading leads to an entirely different understanding of the compositionality of the sign ‘[inline-graphic not available: see fulltext]’ as well as Frege’s conception of assertion and judgment.