Deflationary truth and pathologies

Journal of Philosophical Logic 39 (3):325 - 337 (2010)
Abstract
By a classical result of Kotlarski, Krajewski and Lachlan, pathological satisfaction classes can be constructed for countable, recursively saturated models of Peano arithmetic. In this paper we consider the question of whether the pathology can be eliminated; we ask in effect what generalities involving the notion of truth can be obtained in a deflationary truth theory (a theory of truth which is conservative over its base). It is shown that the answer depends on the notion of pathology we adopt. It turns out in particular that a certain natural closure condition imposed on a satisfaction class—namely, closure of truth under sentential proofs—generates a nonconservative extension of a syntactic base theory (Peano arithmetic).
Keywords Conservativeness  Deflationism  Truth  Satisfaction classes
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