[FOM] Disproving Godel's explanation of incompleteness
ajoyk at cs.stanford.edu
Mon Oct 24 16:19:25 EDT 2005
Somewhat orthogonal to the main thrust of this thread, but, in Godel's
original paper, he
seems to have a slightly different take on the source of incompleteness:
"The true source of the incompleteness attaching to all formal
systems of mathematics, is to be found as will be shown in Part II of this
essay in the fact that the formation of ever higher types can be continued
into the transfinite ..., whereas in every formal system at most denumerably
many types occur. It can be shown, that is, that the undecidable
here presented always become decidable by the adjunction of suitable higher
types (e.g. of type 'omega' for the system P). A similar result also holds
the axiom system of set theory."
Part II doesn't seem to have been ever published. Not sure if some drafts
ever turned up.
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