FOM: CH and 2nd-order validity
steel at math.berkeley.edu
Tue Oct 17 17:42:26 EDT 2000
On Tue, 17 Oct 2000, Robert Black wrote:
> The point is that whatever your axioms are, for any sentence not decided by
> those axioms you can be (mis?)interpreted so that the sentence comes out as
> either true or false, and if the only constraint on correct interpretation
> is that the axioms should come out as true, the undecidable sentence will
> lack truth-value.
This (the position that the only constraint ....) sounds like a
pretty thoroughgoing formalist position. For any set of people, the axioms
explicitly stated and agreed to by those people are at worst a recursive
set, so their theory T is axiomatizable. Must the truth value of Con(T)
be undetermined by their usage of the language of T?
Is there any ambiguity in the language of Peano arithmetic?
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