The horizontal in Frege’s Begriffsschrift

This paper addresses an issue with the sign ‘ ’ 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 ‘ ’ is equivalent to asserting that p . Frege further says that writing ‘ ’ is a...

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Published inSynthese (Dordrecht) Vol. 198; no. 12; pp. 11625 - 11644
Main Author Kim, Junyeol
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.12.2021
Springer Nature B.V
Subjects
Education
Epistemology
Frege, Gottlob (1848-1925)
Identification
Judgment
Logic
Metaphysics
Philosophy
Philosophy of Language
Philosophy of Science
Prime numbers
Semantics
Semiotics
Writing
Judgment-stroke
Horizontal
Grundgesetze der Arithmetik
Begriffsschrift
Truth-values
Gottlob Frege
Truth
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Summary:This paper addresses an issue with the sign ‘ ’ 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 ‘ ’ is equivalent to asserting that p . Frege further says that writing ‘ ’ 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 ‘ ’ as well as Frege’s conception of assertion and judgment.
ISSN:0039-7857
1573-0964
DOI:10.1007/s11229-020-02820-y