Philosophia Mathematica 15 (3):321-346 (2007)
AbstractGottlob Frege famously rejects the methodology for consistency and independence proofs offered by David Hilbert in the latter's Foundations of Geometry. The present essay defends against recent criticism the view that this rejection turns on Frege's understanding of logical entailment, on which the entailment relation is sensitive to the contents of non-logical terminology. The goals are (a) to clarify further Frege's understanding of logic and of the role of conceptual analysis in logical investigation, and (b) to point out the extent to which his understanding of logic differs importantly from that of the model-theoretic tradition that grows out of Hilbert's work
Similar books and articles
On the Consistency of the Δ11-CA Fragment of Frege's Grundgesetze.Fernando Ferreira & Kai F. Wehmeier - 2002 - Journal of Philosophical Logic 31 (4):301-311.
Aspekte der frege–hilbert-korrespondenz.Kai F. Wehmeier - 1997 - History and Philosophy of Logic 18 (4):201-209.
Frege's New Science.G. Aldo Antonelli & Robert C. May - 2000 - Notre Dame Journal of Formal Logic 41 (3):242-270.
On Frege's Two Notions of Sense.Guillermo E. Rosado Haddock - 1986 - History and Philosophy of Logic 7 (1):31-41.
Frege Explained: From Arithmetic to Analytic Philosophy.Joan Carol Weiner - 2004 - Chicago, IL, USA: Open Court.
Frege, Hilbert, and the Conceptual Structure of Model Theory.William Demopoulos - 1994 - History and Philosophy of Logic 15 (2):211-225.
Added to PP
Historical graph of downloads
Citations of this work
On the Exhaustion of Mathematical Entities by Structures.Adrian Heathcote - 2014 - Axiomathes 24 (2):167-180.
Frege and the Origins of Model Theory in Nineteenth Century Geometry.Günther Eder - 2019 - Synthese 198 (6):5547-5575.
Frege on Intuition and Objecthood in Projective Geometry.Günther Eder - 2021 - Synthese 199 (3-4):6523-6561.
Frege’s ‘On the Foundations of Geometry’ and Axiomatic Metatheory.Günther Eder - 2016 - Mind 125 (497):5-40.
References found in this work
The Frege-Hilbert Controversy.Michael David Resnik - 1974 - Philosophy and Phenomenological Research 34 (3):386-403.
Frege: An Introduction to his Philosophy.G. CURRIE - 1982 - Tijdschrift Voor Filosofie 46 (2):353-354.
Frege on Axioms, Indirect Proof, and Independence Arguments in Geometry: Did Frege Reject Independence Arguments?Jamie Tappenden - 2000 - Notre Dame Journal of Formal Logic 41 (3):271-315.
Frege, Sense and Mathematical Knowledge.Gregory Currie - 1982 - Australasian Journal of Philosophy 60 (1):5 – 19.