How did Frege fall into the contradiction?

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)
DOI 10.1111/j.1467-9329.2007.00349.x
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 27,204
Through your library
References found in this work BETA
Critique of Pure Reason.Immanuel Kant - 1991 - In Elizabeth Schmidt Radcliffe, Richard McCarty, Fritz Allhoff & Anand Vaidya (eds.), Philosophy and Phenomenological Research. Blackwell. pp. 449-451.
Posthumous Writings.Gottlob Frege - 1991 - Wiley-Blackwell.
The Seas of Language.Michael A. E. Dummett - 1993 - Oxford University Press.

View all 6 references / Add more references

Citations of this work BETA
Frege on Sense Identity, Basic Law V, and Analysis.Philip A. Ebert - 2016 - Philosophia Mathematica 24 (1):9-29.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

37 ( #138,322 of 2,164,001 )

Recent downloads (6 months)

2 ( #188,660 of 2,164,001 )

How can I increase my downloads?

My notes
Sign in to use this feature

There  are no threads in this forum
Nothing in this forum yet.

Other forums