Deflationism, conservativeness and maximality

Abstract

Abstract We discuss two desirable properties of deflationary truth theories: conservativeness and maximality. Joining them together, we obtain a notion of a maximal conservative truth theory – a theory which is conservative over its base, but can’t be enlarged any further without losing its conservative character. There are indeed such theories; we show however that none of them is axiomatizable, and moreover, that there will be in fact continuum many theories of this sort. It turns out in effect that the deflationist still needs some additional principles, which would permit him to construct his preferred theory of truth.