David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Ratio 20 (1):91–107 (2007)
Quine made it conventional to portray the contradiction that destroyed Frege’s logicism as some kind of act of God, a thunderbolt that descended from a clear blue sky. This portrayal suited the moral Quine was antecedently inclined to draw, that intuition is bankrupt, and that reliance on it must therefore be replaced by a pragmatic methodology. But the portrayal is grossly misleading, and Quine’s moral simply false. In the person of others – Cantor, Dedekind, and Zermelo – intuition was working pretty well. It was in Frege that it suffered a local and temporary blindness. The question to ask, then, is not how Frege was overtaken by the contradiction, but how it is that he didn’t see it coming. The paper offers one kind of answer to that question. Starting from the very close similarity between Frege’s proof of infinity and the reasoning that leads to the contradiction, it asks: given his understanding of the first, why did Frege did not notice the second? The reason is traced, first, to a faulty generalization Frege made from the case of directions and parallel lines; and, through that, to Frege’s having retained, and attempted incoherently to combine with his own, aspects of a pre-Fregean understanding of the generality of logical principles.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
Immanuel Kant (2007). Critique of Pure Reason. In Elizabeth Schmidt Radcliffe, Richard McCarty, Fritz Allhoff & Anand Vaidya (eds.), Philosophy and Phenomenological Research. Blackwell Pub. Ltd. 449-451.
Gottlob Frege (1991). Posthumous Writings. Wiley-Blackwell.
Michael A. E. Dummett (1993). The Seas of Language. Oxford University Press.
Michael A. E. Dummett (1991). Frege: Philosophy of Mathematics. Harvard University Press.
Michael Dummett (1991). Frege and Other Philosophers. Clarendon Press.
Citations of this work BETA
Philip A. Ebert (2016). Frege on Sense Identity, Basic Law V, and Analysis. Philosophia Mathematica 24 (1):9-29.
Similar books and articles
William Demopoulos (1994). Frege, Hilbert, and the Conceptual Structure of Model Theory. History and Philosophy of Logic 15 (2):211-225.
Gregory Currie (1983). I. Interpreting Frege: A Reply to Michael Dummett. Inquiry 26 (3):345 – 359.
Howard Wettstein (1990). Frege‐Russell Semantics? Dialectica 44 (1‐2):113-135.
Jamie Tappenden (1995). Geometry and Generality in Frege's Philosophy of Arithmetic. Synthese 102 (3):319 - 361.
Ivan Welty (2011). Frege on Indirect Proof. History and Philosophy of Logic 32 (3):283-290.
Jan Wolenński (1997). Hans Sluga (Ed.), The Philosophy of Frege. A Four-Volume Collection of Scholarly Articles on All Aspects of Frege's Philosophy, Vol.1: General Assessments and Historical Accounts of Frege's Philosophy, Vol.2: Logic and Foundations of Mathematics in Frege's Philosophy, Vol.3: Meaning and Ontology in Frege's Philosophy, Vol.4: Sense and Reference in Frege's Philosophy. [REVIEW] Erkenntnis 46 (3):407-410.
Mark Textor (2009). Unsaturatedness: Wittgenstein's Challenge, Frege's Answer. Proceedings of the Aristotelian Society 109 (1pt1):61-82.
Carlo Penco (2003). Frege: Two Theses, Two Senses. History and Philosophy of Logic 24 (2):87-109.
Sanford Shieh (2008). Frege on Definitions. Philosophy Compass 3 (5):992-1012.
Added to index2009-01-28
Total downloads35 ( #118,833 of 1,911,604 )
Recent downloads (6 months)3 ( #253,681 of 1,911,604 )
How can I increase my downloads?