In this paper we explain our pretense account of truth-talk and apply it in a diagnosis and treatment of the Liar Paradox. We begin by assuming that some form of deflationism is the correct approach to the topic of truth. We then briefly motivate the idea that all T-deflationists should endorse a fictionalist view of truth-talk, and, after distinguishing pretense-involving fictionalism (PIF) from error- theoretic fictionalism (ETF), explain the merits of the former over the latter. After presenting the basic framework (...) of our PIF account of truth-talk, we demonstrate a few advantages it offers over T-deflationist accounts that do not explicitly acknowledge pretense at work in the discourse. In turning to the Liar Paradox, we explain how the quasi-anaphoric functioning that our account attributes to truth-talk provides a diagnosis of the Liar Paradox (and other instances of semantic pathology) as having no content—in the sense of not specifying any of what we call M-conditions. At the same time, however, we vindicate the intuition that we can understand liar sentences, thereby avoiding one standard objection to “meaningless strategy” responses to the Liar Paradox. With this diagnosis in place, we then, by way of treatment, introduce a new predicate, ‘semantically defective’, and show how the explanation we give for its application allows for a consistent, yet revenge-immune, (dis)solution of the Liar Paradox, and semantic pathology generally. (shrink)

This paper deals with the proof theory of first-order applicative theories with non-constructive μ operator and a form of the bar rule, yielding systems of ordinal strength Γ0 and 20, respectively. Relevant use is made of fixed-point theories with ordinals plus bar rule.

This paper is a companion to work of Feferman, Jäger, Glaß, and Strahm on the proof theory of the type two functionals μ and E1 in the context of Feferman-style applicative theories. In contrast to the previous work, we analyze these two functionals in the context of Schlüter's weakened applicative basis PRON which allows for an interpretation in the primitive recursive indices. The proof-theoretic strength of PRON augmented by μ and E1 is measured in terms of the two subsystems of (...) second order arithmetic, Π10-CA and Π11-CA, respectively. (shrink)