# Category Archives: Gödel’s theorems

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I’m sometimes asked for recommendations about what to read after IGT – or indeed, what to read instead of tackling IGT if you are looking for something less weighty, or for something more like a conventional mathematical text. So here … Continue reading

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## Gödel’s First Theorem, continuing the story

I’ve a book review to finish, reading for a seminar to get under my belt, and other time consuming stuff waiting. So I’m going to have put aside for a week or more the continuing self-imposed task of writing notes … Continue reading

## Gödel’s First Theorem, from Gödel 1931 to Kleene 1943

As ‘homework’, before writing more of the second edition of my Gödel book, I’m reading through the literature to see how others have handled the First Incompleteness Theorem, both in the early papers from Gödel on, and then in the … Continue reading

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## Carnap and the Diagonalization Lemma (Continued)

Let’s distinguish what I’ll call the Diagonalization Equivalence from the familiar Diagonalization Lemma. The former is a semantic claim: in the right conditions, for any one-place predicate of theory T there is a corresponding sentence such that is true if … Continue reading

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## Carnap and the Diagonalization Lemma

Carnap is often credited with proving the Diagonalization Lemma in Logische Syntax der Sprache. But where does he do it? Well, in §35 Carnap notes the general recipe for taking a one-place predicate and constructing a sentence such that is … Continue reading

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## Somewhat gappy Gödel

When planning and actually writing my Introduction to Gödel’s Theorems, I intentionally consulted other books as little as possible, trying to reconstruct strategies and proofs from memory as far as I could. I thought that would be a good discipline, … Continue reading

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## IGT2 A first instalment of the second edition of my Gödel book!

As I’ve said before, CUP have agreed to publish a second edition of An Introduction to Gödel’s Theorems. Camera-ready copy is due to be sent to them rather implausibly soon, by the end of July 2012, with publication six months … Continue reading

## 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

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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