Russell vs Hilbert

[Joe Shipman]

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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