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- scott on Gödel’s First Theorem, from Gödel 1931 to Kleene 1943
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Category Archives: Books
Just to keep you occupied over the holidays …
… and to dent your bank balances, here are three more rather sizeable logic books. First up, spotted in the CUP bookshop and snapped up, is the just-published Proofs and Computations by Helmut Schwichtenberg and Stanley S. Wainer. A mere … Continue reading
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Next up: Truth, Gödel, and other delights
OK: a review of Maddy’s very engaging recent book (written with Luca Incurvati, which was fun to do) has gone off to Mind. And in the next day or two, I must also put together a review for Phil. Math. … Continue reading
Posted in Books, Gödel's theorems
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KGFM 20, 21: Woodin on the transfinite, Wigderson on P vs NP
And so, finally, to the last two papers in KGFM. I can be brief, though the papers aren’t. The first is Hugh Woodin’s ‘The Transfinite Universe’. This inevitably mentions Gödel’s constructible universe L a few times, but otherwise the connection … Continue reading
Posted in KGFM
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KGFM 19: Cohen’s interactions with Gödel
The next paper in KGFM is a short talk by the late Paul Cohen, ‘My Interaction with Kurt Gödel: The Man and His Work’. The title is full of promise, but there seems relatively little new here. For Cohen had … Continue reading
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The Book Problem
Hello. My name is Peter and I am a bookaholic … Well, perhaps it isn’t quite as bad as that. But I’ve certainly bought far too many books over the years. Forty-five years as a grad student and a lecturer, … Continue reading
Posted in Books
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KGFM 17, 18: Kohlenbach and Friedman
Next up in Kurt Gödel and the Foundations of Mathematics is Ulrich Kohlenbach, writing on ‘Gödel’s Functional Interpretation and Its Use in Current Mathematics’. This rachets up the technical level radically, and will be pretty inaccessible to most readers (certainly, … Continue reading
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KGFM 16: Penrose on minds and computers
Stewart Shapiro has had two shots at exploring the troubles with Lucas/Penrose-style arguments, first in his well-known paper ‘Incompleteness, Mechanism and Optimism’ Bull. Symb. Logic (1998), and then — expanding his treatment of Penrose’s efforts in Shadows of the Mind … Continue reading
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KGFM 15: Putnam on minds and computers
In his 1967 paper, ‘God, the Devil, and Gödel’, Paul Benacerraf famously gives a nice argument, going via Gödel’s Second Theorem, that proves that either my mathematical knowledge can’t be simulated by some computing machine (there is no particular Turing … Continue reading
Heck’s Frege’s Theorem — and KGFM, 11–14
When I was in London for the Tennenbaum Workshop, I picked up a copy of Richard Heck’s very recent Frege’s Theorem, which collects together eleven of his papers — with some changes and some postscripts — together with a 39 … Continue reading
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KGFM 9, 10: Gödelian cosmology, Rindler and Svozil
The next piece is ‘Gödel, Einstein, Mach, Gamow, and Lanczos: Gödel’s Remarkable Excursion into Cosmology’ by Wolfgang Rindler. Rindler’s books on Relativity are real classics of exposition, so I was hoping for good things from this paper. I wasn’t disappointed. As Rindler says, Gödel … Continue reading