Title:
An impossibility result for theories of determinateness
Abstract:
In response to semantic paradoxes, several proposals have been made to distinguish
paradoxical from non-paradoxical sentences by appealing to notions such as
groundedness, meaningfulness, determinateness. In their recent paper "Classical
Determinate Truth I", Fujimoto and Halbach introduce a theory of truth and
determinateness and ask whether it can be consistently extended with an axiom stating
that, for every sentence, it is determinate whether it is determinate. In this talk, I show
that a negative answer to this question follows as a corollary of a general impossibility
result for a broad class of theories of determinateness-like predicates.
This is joint work with Maciej Głowacki and Bartosz Wcisło.