[FOM] The liar and the semantics of set theory

[Roger Bishop Jones]

In response to Richard Heck's message, posted
Monday 23 September 2002  4:08 am:

I have already conceded that "The liar" proof of undefinability of truth
is likely to be generalisable to any language which is sufficiently
expressive (e.g. contains Robinson's Q) and whose truth
conditions are bivalent.

However, when there is more than one intended interpretation
of a first order language, even though the logic is classical,
it is reasonable to expect that the "truth predicate" is not bivalent.

In this circumstance, Tarski's schema T is not a satisfactory
account of how the truth conditions are to be defined,
(or of their "material adequacy") for it presumes that
the truth conditions are bivalent.

So I would be looking for a better reason than that to
persuade me that my counter-example is not a good one.

Your generalization seems only to generalize to the cases
which I had already conceded, and when it comes
to the cases which I am in doubt about you have nothing
(as yet) to say.
As you observe, and as I had already stated in the post
you were responding to, I am looking for a proof which
assumes something weaker and more plausible than
bivalence.

Roger Jones