David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Philosophia Mathematica 15 (3):321-346 (2007)
Gottlob 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
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Sébastien Gandon (2009). Toward a Topic-Specific Logicism? Russell's Theory of Geometry in the Principles of Mathematics. Philosophia Mathematica 17 (1):35-72.
Günther Eder (2013). Remarks on Independence Proofs and Indirect Reference. History and Philosophy of Logic 34 (1):68-78.
Adrian Heathcote (2014). On the Exhaustion of Mathematical Entities by Structures. Axiomathes 24 (2):167-180.
Matthias Schirn (2010). Consistency, Models, and Soundness. Axiomathes 20 (2-3):153-207.
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