Robert J. Kolker wrote: > Aatu Koskensilta wrote: > > > > > > > That's a question, and non-sense at that; sentences aren't true or false > > in theories. > > Not in the empirical sense. Sentences follow from the postulates > (axioms) of a theory or they don't, assuming the sentence is well formed > in the theory.
A whole new logic (NAFL) has been worked out based on the idea of truth with respect to axiomatic theories -- i.e., sentences of a theory are true or false or neither *with respect to that theory* and there is no need to postulate Platonic truth for the formal propositions of a theory. See, for example, <http://arxiv.org/abs/math.LO/0506475>. The research community is dong a great job of ignoring this work but it is not going to go away.