FOM: CH and 2nd-order validity

John Steel steel at
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?

John Steel


More information about the FOM mailing list