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

Alasdair Urquhart urquhart at cs.toronto.edu
Wed Mar 31 10:31:43 EDT 2010

Russell's reference to the incompleteness results are disappointingly
thin.  He was almost certainly aware of them in the 1930s.  I believe
that Goedel sent him an offprint of the incompleteness paper.  The Russell
Archives (McMaster University, Hamilton, Ontario) contain an offprint
of the 1931 paper, though it is not, I believe, a copy of the offprint
sent by Goedel.  It has no marginalia.

The second edition of the "Principles of Mathematics" has a reference
to the new "puzzles" presented by Goedel.  "An Inquiry into Meaning
and Truth" (1940) has an explicit reference to the concept of Goedel
numbering, so it is clear that Russell had understood this aspect
of the result.

This very sparse evidence perhaps suggests that Russell never entirely
understood the results, conceivably interpreting them as some kind of
new paradox, as Goedel himself thought.  The fact that Russell
never broke free from the conceptual world of Principia Mathematica
would make this reasonable -- in Principia Mathematica, the formalism
is indissolubly wedded to its informal interpretation.

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