Yu asked:

Let me ask a question about Godel's Incompleteness Theorem.

Which is stronger, the claim that T is incomplete or the claim that T is undecidable?

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Strictly speaking, this is a mathematical and/ or logical issue. But philosophically it is undoubtedly the
second, undecidability, which is the stronger or more important outcome. You will recall that Hilbert's
programme (like that of Whitehead and Russell) was for a leak-proof set of axioms; that it failed was a
minor catastrophe for mathematics, for it showed by the paradoxical means of a rigorous proof that
certain logical problem are inherently insoluble (undecidable); and you probably also know that since
then Gregory Chaitin has shown with his elephantine 'Diophantine equation' that the whole notion of a
rigorous arithmetic can be dissolved in a game of pure chance. For philosophy this is a blessing
insofar as the core notion of human agency, which is always under threat when people start tinkering
with human substitutes, is thereby placed back in the driver's seat. As Kroneker used to say, "God
invented the whole numbers; everything else is the work of man."

Jürgen Lawrenz

Sydney