Frege and Hilbert on the foundations of geometry (1994 talk)
| Abstract | I examine Frege’s explanation of how Hilbert ought to have presented his proofs of the independence of the axioms of geometry: in terms of mappings between (what we would call) fully interpreted statements. This helps make sense of Frege’s objections to the notion of different interpretations, which many have found puzzling. (The paper is the text of a talk presented in October 1994.). | |||||||||
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Jamie Tappenden (2000). Frege on Axioms, Indirect Proof, and Independence Arguments in Geometry: Did Frege Reject Independence Arguments? Notre Dame Journal of Formal Logic 41 (3):271-315.
Stewart Shapiro (1996). Space, Number and Structure: A Tale of Two Debates. Philosophia Mathematica 4 (2):148-173.
Patricia A. Blanchette (2007). Frege on Consistency and Conceptual Analysis. Philosophia Mathematica 15 (3):321-346.
Jan von Plato (1997). Formalization of Hilbert's Geometry of Incidence and Parallelism. Synthese 110 (1):127-141.
Jan Platvono (1997). Formalization of Hilbert's Geometry of Incidence and Parallelism. Synthese 110 (1):127-141.
G. Aldo Antonelli & Robert C. May (2000). Frege's New Science. Notre Dame Journal of Formal Logic 41 (3):242-270.
William Demopoulos (1994). Frege, Hilbert, and the Conceptual Structure of Model Theory. History and Philosophy of Logic 15 (2):211-225.
Kai F. Wehmeier (1997). Aspekte der Frege–Hilbert-Korrespondenz. History and Philosophy of Logic 18 (4):201-209.
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