# Gödel Without Tears, slowly, 15

[I’ve retitled the previous post, to keep blog post numbers in sync with chapter numbers!]

We at last move on to the Second Theorem. In Chapter 15, we introduce the theorem, and explain its significance for Hilbert’s programme. This involves a  cartoon history trying to bring out the attractions of Hilbert’s programme (surely one of the great ideas in the philosophy of maths — if only it had worked!).

### 2 thoughts on “Gödel Without Tears, slowly, 15”

1. Yes, on the first point, will rephase to remove a suggestio falsi

Point taken on the over-cooked “battering”.

I didn’t know that it was moot what “moot” means …. :) On the other hand, probably best to avoid words that a non-native speaker will stumble over (as a significant proportion of readers are, as I have found).

2. Though I like this chapter, and it’s good to see Peirce mentioned, and to see a model-theoretic consistency point (p 111), I’m not entirely happy with some parts of the rational reconstruction of the history. It ends up sounding as if it was Cantor who ran afoul of Russell’s paradox rather than Frege, and even that Frege was trying to “reconstruct mathematics on a logical basis” (p 112) to avoid the paradoxes (which here seems to include Russell’s) that supposedly beset Cantor’s approach.

p 113, “battering” — I don’t think that’s fair as a characterisation of what Zermelo did, or of what he or formalists were keen on.

p 113, “Of course, it is a very moot point what exactly constitutes such ultra-‘safe’ finitary reasoning.” —

I think it would be better to rephrase to avoid using “moot point”. I’m thinking you mean “moot” in the sense of being subject to debate, dispute, or uncertainty; but people often use “moot point” to mean something irrelevant or insignificant. Whichever meaning you have in mind, though, some people might think it’s the other one.

However, I think your summary of Hilbert’s insight is good.

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