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Category Archives: Logic
Santa’s singleton
Here’s a question which I’m sure bugs all my logical readers. Modern mathematics standardly recognises partial functions which can take something as input but deliver nothing as output (like the reciprocal function which isn’t defined for zero). Do we also … Continue reading
Posted in Logic
3 Comments
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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Thanks to Orlando May
I’m getting back down to work on the second edition of An Introduction to Gödel’s Theorems. One thing I plan to do is to put up some pages of exercises as I go along, which I’ve been meaning to do … Continue reading
Posted in Gödel's theorems
2 Comments
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
Log xy = Log x + Log y
In their (rich, original, ground-breaking) writings on plurals, Alex Oliver and Timothy Smiley more than once say that “mathematical practice” shows that addition is allowed to take plural terms as arguments. Thus, with a trivial change of variables, in their … Continue reading
Posted in Logic
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Good news on 2nd edn of IGT
Good news. I’ve a contract to do a 2nd edition of my Gödel book. Not quite under the terms I’d have ideally liked, like another 50 pages, a couple of years or more to do it, and of course a … Continue reading
Posted in Gödel's theorems
5 Comments
What’s so great about Kuratowski pairs?
I’m currently writing about countable order types — kinds of orderings of the naturals — and for various reasons want to do as much as I can without explicit talk about sets. But I obviously need to talk about ordered … Continue reading
Posted in Logic
7 Comments
Four lectures on the First Incompleteness Theorem
Better late than never — here’s what I said, more or less, in four lectures earlier this term on the First Incompleteness Theorem. The lectures were aimed for maths students, but only the last of the four requires a bit … Continue reading
Posted in Gödel's theorems
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IGT, 2nd edn again — and an unofficial bribe!
As I said in a post here a couple of weeks ago, I’m negotiating with CUP about a second edition for An Introduction to Gödel’s Theorems. (And if you have any suggestions/comments about what improvements you’d like to see, do … Continue reading
Posted in Gödel's theorems
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Thin Realism, Arealism, and other Big Ideas
Penelope Maddy’s recent Defending the Axioms is my sort of book. It is short (150 pages), beautifully clearly written (if there are obscurities, they are in the philosophy, not the prose), and I’m in fact rather sympathetic to her overall … Continue reading
Posted in Logic
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