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- scott on Gödel’s First Theorem, from Gödel 1931 to Kleene 1943
- Peter Smith on Gödel’s First Theorem, from Gödel 1931 to Kleene 1943
- scott on Gödel’s First Theorem, from Gödel 1931 to Kleene 1943
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Category Archives: Books
KGFM 7, 8: Computers and computation, Papadimitriou and Copeland
Looking at the postings on KGFM, I’ve been pretty negative so far. Sorry! OK, Macintyre’s paper is indeed a tour de force but is for a pretty specialized reader. Otherwise I can only really recommend Feferman’s paper. Am I being … Continue reading
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KGFM 4, 5, 6: More history, from Sigmund, Kennedy, and Feferman
I should have explained that Kurt Gödel and the Foundations of Mathematics is divided into three main parts, ‘Historical Context’, ‘A Wider Vision: the Interdisciplinary, Philosophical and Theological Implications of Gödel’s Work’, and ‘New Frontiers: Beyond Gödel’s Work in Mathematics … Continue reading
KGFM 2, 3: Kreisel and Grattan-Guinness
The second paper in the collection is a seven-page ramble by Georg Kreisel, followed by twenty pages of mostly opaque endnotes. This reads in many places like a cruel parody of the later Kreisel’s oracular/allusive style. I lost patience very … Continue reading
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KGFM 1: Macintyre on the impact of incompleteness on maths
I’m going to be reviewing the recently published collection Kurt Gödel and the Foundations of Mathematics edited by Baaz, Papadimitriou, Putnam, Scott and Harper, for Philosophia Mathematica. This looks to a really pretty mixed bag, as is usual with volumes … Continue reading
Posted in Gödel's theorems, KGFM
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TTP At long last, a short review
Very, very belatedly — and apologies for this in particular to Alan Weir — I’ve gathered together some of the thoughts from previous blog posts into a short review of Truth Through Proof. This is absurdly compressed, even though Mind … Continue reading
Posted in Truth Through Proof
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Just what we needed: more logic books
I’ve just finished writing a short paper with the title “Santa’s singleton” (think about it …), of which I’ll post a version here in due course, once I’ve tried it out in a talk or two. Try to contain your … Continue reading
TTP, 14. Worries about excluded middle
Weir’s formalist account of arithmetic in headline form comes to this: the arithmetical claim P is correct just in case that there is (or in practice could be) a concrete proof of P. (We’ll stick to considering the arithmetical case.) … Continue reading
Posted in Truth Through Proof
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TTP, 13. Formalism and “pluralism”
In TTP 11, I emphasized that Weir’s position interweaves two separable strands. One strand I called “formalism about arithmetical correctness”: at a first approximation, what makes an arithmetical claim correct is something about what can be done in some formal … Continue reading
Posted in Truth Through Proof
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Weir on colours, concepts, fiction, numbers, and more!
Alan has written a long reply to my reply to his comments on my last post. This should be of particular interest to anyone who is reading his book, so I thought I’d flag it up at the top level … Continue reading
Posted in Truth Through Proof
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TTP, 12. ‘The formal mode of assertion’
Weir himself distinguishes three model cases where a claim’s content is not transparently representational — to use my jargon for his idea — and I added a fourth case. (We are assuming, for the sake of argument, that the general … Continue reading
Posted in Truth Through Proof
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