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Four puzzling paragraphs: Frege on ‘≡’ and ‘=’

  • María de Ponte ORCID logo EMAIL logo , Kepa Korta and John Perry
From the journal Semiotica


In §8 of his Begriffsschrift (1879), Gottlob Frege discusses issues related to identity. Frege begins his most famous essay, “On Sense and Denotation” (1892), published 13 years later, by criticizing the view advocated in §8. He returns to these issues in the concluding paragraph. Controversies continue over these important passages. We offer an interpretation and discuss some alternatives. We defend that in the Begriffsschrift, Frege does not hold that identity is a relation between signs. §8 of the Begriffsschrift is motivated by the conflict between two different criteria for sameness of conceptual content of sentences. To resolve that conflict, Frege introduces ‘≡’ in §8 and, thus, circumstances with names as constituents. To the same end, in “On Sense and Denotation,” Frege introduces senses and Thoughts and abandons both ‘≡’ and circumstances. He solves what we call the Co-instantiation problem, and disregards, but does not solve, the Name problem.

Corresponding author: María de Ponte, ILCLI and Philosophy Department, University of the Basque Country, Donostia, Spain, E-mail:

Funding source: Spanish Government

Award Identifier / Grant number: FFI2015-63719-P (MINECO/FEDER, UE); PID2019-106078GB-I00 (MCI/AEI/FEDER, UE)

Funding source: Basque Government

Award Identifier / Grant number: IT1032-16


This paper was inspired by our dissatisfaction with the discussion of these problems in an early draft of Perry’s Frege’s Detour (2019), and inspired the discussion in later drafts. We are grateful to the members of the Zoom group, and the audience of the World Philosophy Congress at Beijing (August 2918), where we presented an early version of it. The first two authors benefitted from grants by the Spanish Government (FFI2015-63719-P (MINECO/FEDER, UE); PID2019-106078GB-I00 (MCI/AEI/FEDER, UE)) and the Basque Government (IT1032-16). We are very thankful for the comments of an anonymous reviewer. We are particularly very grateful to Tadeusz Ciecierski for his invitation and his help and patience during the process.


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Received: 2021-01-22
Accepted: 2021-01-31
Published Online: 2021-03-18
Published in Print: 2021-05-26

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