Fwd: Russell vs Hilbert

[Deutsch, Harry]

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From: "Deutsch, Harry" <hdeutsch at ilstu.edu>
Date: December 17, 2020 at 8:26:11 AM CST
To: Patrik Eklund <peklund at cs.umu.se>
Subject: Re: Russell vs Hilbert


In a review of a book by Rebecca Goldstein on Gödel's incompleteness theorems, (London Review of Books, February 2006), Feferman attributes the following observation to Gödel :

(Meanwhile, mathematicians have happily gone on doing their thing; for as Gödel himself observed in his 1951 lecture on the foundations of mathematics, it is safe to say that 99.9 per cent of mathematics follows from a small, settled part of the axiomatic theory of sets.)

If so, Russell was 99.9 per cent correct!

Harry

On Dec 16, 2020, at 1:28 AM, Patrik Eklund <peklund at cs.umu.se<mailto:peklund at cs.umu.se>> wrote:

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A tweet shouldn't rewrite the history of the foundations of mathematics.

Reading Grundlagen der Mathematik I, II is still recommendable, but very few, unfortunately, know content in those volumes.

Hilbert is mostly ignored, even, funny as it is, Hilbert was the one speaking very strongly against "ignorabimus". That was in a certain sense at that time, and, little did he know that his and Bernays' GdM I, II would basically be ignored when decades after the rewriting of the history of logic began strongly influenced by Church and the way he controlled his journal.

Patrik


On 2020-12-15 23:47, Joe Shipman wrote:

One of my Twitter friends claims that the view that all mathematical propositions are decidable from a few axioms was held by Russell prior to Hilbert, and that Russell was claiming, in his books, not only to have reduced all mathematical reasoning to a few logical principles, but also to have claimed that those principles were sufficient to settle all questions.

This is based on his reading of the following 1903 passage:

"THE present work has two main objects. One of these, the proof that all pure mathematics deals exclusively with concepts definable in terms of a very small number of fundamental logical concepts, and that all its propositions are deducible from a very small number of fundamental logical principles"

In my opinion, by "propositions", Russell meant "theorems", not "true statements", and therefore one may not jump to the conclusion that Russell failed to achieve his object and did not prove what he claimed to be trying to prove.

Can any Russell experts shed light on this question?

— JS



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