[FOM] Godel on the true reason for incompleteness
Alasdair Urquhart
urquhart at cs.toronto.edu
Tue Oct 25 14:12:21 EDT 2005
As far as I know, Godel never wrote any of
the promised sequel to his 1931 incompleteness
paper. In a letter to Carnap of 28 November 1932
(Collected Works, Volume IV p. 355) he says that
"the second part of my paper exists only in the realm
of ideas." In the remainder of the letter he goes on
to give some explanations that throw some light
on the famous footnote 48a, in particular sketching
the way in which a truth definition for lower types
can be given in terms of higher type variables.
The headnote to the correspondence with Carnap,
written by Warren Goldfarb, gives a very illuminating
discussion of Godel's thinking at this time, and of his
relationship to Carnap.
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