[FOM] Fwd: Did Goedel's result come as a surprise to Bertrand?
joeshipman at aol.com
Tue Apr 6 19:41:21 EDT 2010
There is a sense in which higher-order languages make Godel's
Incompleteness Theorem less philosophically troubling -- since pretty
much all mathematics can be interpreted in higher-order logic, the
import of the theorem becomes merely epistemological, that we can't
know all true mathematical facts, rather than ontological, that there
might exist sentences without a truth value.
From: Irving <ianellis at iupui.edu>
The best that we can do in this case is suppose that Russell,
while composing My Philosophical Development thought that his
discussion of higher-order languages in his introduction to the
Tractatus thought that introduction of higher-order languages
could have provided in advance a ready-made remedy to
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