[FOM] Did G?del's result come as a surprise to Bertrand Russell?

joeshipman@aol.com joeshipman at aol.com
Tue Mar 30 23:08:50 EDT 2010


Henkin therefore actually found it
necessary to explain to Russell that Gödel's results did not say that
arithmetic is inconsistent, but that it is incomplete.

This is shocking; it is evidence of either a remarkable decline in 
Russell's mental powers, or an indifference so severe as to represent a 
complete repudiation of decades of his life's work.

Another interpretation of Russell’s reaction
to Henkin could arise from consideration of the fact that of course
Gödel’s results do not assert merely the impracticality of obtaining a
proof of the decidability of a theorem, but that it is theoretically
impossible to find such a proof, so that the effect of Gödel's work was
to deflate the sails of Russell's claims for logicism.

This may explain Russell's antipathy to Gödel's work. There are 
mathematical truths which are not logical truths. In my opinion, 
logicism can be taken very far, far enough to handle practically all 
mathematics as professionally practiced; but the existence of 
independent arithmetical statements for any axiomatization of 
mathematics cannot be gotten around. You have to accept that logic may 
establish the meaningfulness of a sentence without establishing its 
truth value, which may have contradicted Russell's notion of the 
meaning of the word "logic".

-- JS

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