Russell vs Hilbert

[Josef Urban]

This may be somewhat related. Russel says in "My Philosophical Development"
(p. 85):

"In my introduction to the Tractatus, I suggested that, although in any
given language there are things which that language cannot express, it is
yet always possible to construct a language of higher order in which these
things can be said. There will, in the new language, still be things which
it cannot say, but which can be said in the new language, and so on ad
infinitum. This suggestion, which was then new, has now become an accepted
commonplace of logic. It disposes of Wittgenstein's mysticism and, I think,
also of the newer puzzles presented by Godel."

When I was reading the book long ago, the last sentence (disposing of the
Godel puzzles) surprised me. But he may have meant various things and does
not elaborate (on Godel) further there.

Josef


On Wed, Dec 16, 2020 at 1:55 AM Joe Shipman <joeshipman at aol.com> 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
>
>
>
> Sent from my iPhone
>
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