Monthly Archives: January 2012

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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Amethe von Zeppelin (continued)

A generous correspondent (much better at this Googling malarkey than I) writes: “Amethe Smeaton was the daughter of a colonial administrator (later a liberal MP) called Donald Smeaton. She was born in the late 1890s and was at Girton College … Continue reading

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Amethe von Zeppelin

I’ve had Carnap’s The Logical Syntax of Language on my shelves for over forty years. I can’t say it was ever much consulted; but I’ve been reading large chunks of it today, in connection with Gödel. Carnap’s book is often … 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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