David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Analysis 65 (285):45–49 (2005)
This paper continues a thread in Analysis begun by Adam Rieger and Nicholas Denyer. Rieger argued that Frege’s theory of thoughts violates Cantor’s theorem by postulating as many thoughts as concepts. Denyer countered that Rieger’s construction could not show that the thoughts generated are always distinct for distinct concepts. By focusing on universally quantified thoughts, rather than thoughts that attribute a concept to an individual, I give a different construction that avoids Denyer’s problem. I also note that this problem for Frege’s philosophy was discovered by Bertrand Russell as early as 1902 and has been discussed intermittently since.
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References found in this work BETA
Gottlob Frege (1991). Posthumous Writings. Wiley-Blackwell.
Bertrand Russell (1903). Principles of Mathematics. Cambridge University Press.
Gottlob Frege, Gottfried Gabriel, Brian Mcguinness & Hans Kaal (1982). Philosophical and Mathematical Correspondence. Revue Philosophique de la France Et de l'Etranger 172 (1):64-64.
Kevin C. Klement (2001). Russell's Paradox in Appendix B of the Principles of Mathematics : Was Frege's Response Adequate? History and Philosophy of Logic 22 (1):13-28.
Citations of this work BETA
Kevin C. Klement (2010). Russell, His Paradoxes, and Cantor's Theorem: Part I. Philosophy Compass 5 (1):16-28.
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