The paper offers a critical examination of a prominent, “quasi-deflationist” argument advanced in the contemporary debate on the semantic paradoxes against non-naive and non-transparent theories of truth. The argument claims that truth unrestrictedly fulfils certain expressive functions, and that its so doing requires the unrestricted validity of naivety and transparency principles. The paper criticises the quasi-deflationist argument by considering some kinds of cases in which transparency and naivety arguably fail. In some such cases truth still fulfils the relevant expressive functions (...) without being transparent or naive; in some other such cases, truth does not fulfil the relevant expressive functions and other conceptual resources must be called upon. Thus, in different ways, all such cases belie the quasi-deflationist argument’s insistence that naivety and transparency should be unrestrictedly valid for truth unrestrictedly to fulfil the relevant expressive functions. There might however be other reasons for solving the semantic paradoxes by revising classical logic, and the paper in effect closes by offering versions of the liar paradox that rely on compelling but opacity-friendly truth-theoretic principles. (shrink)

This paper investigates how naive theories of truth fare with respect to a set of extremely plausible principles of restricted quantification. It is first shown that both nonsubstructural theories as well as certain substructural theories cannot validate all those principles. Then, pursuing further an approach to the semantic paradoxes that the author has defended elsewhere, the theory of restricted quantification available in a specific naive theory that rejects the structural property of contraction is explored. It is shown that the theory (...) validates all the principles in question, and it is argued that other prima facie plausible principles that the theory fails to validate are objectionable on independent grounds. (shrink)

A unified answer is offered to two distinct fundamental questions: whether a nonclassical solution to the semantic paradoxes should be extended to other apparently similar paradoxes and whether a nonclassical logic should be expressed in a nonclassical metalanguage. The paper starts by reviewing a budget of paradoxes involving the logical properties of validity, inconsistency, and compatibility. The author’s favored substructural approach to naive truth is then presented and it is explained how that approach can be extended in a very natural (...) way so as to solve a certain paradox of validity. However, three individually decisive reasons are later provided for thinking that no approach adopting a classical metalanguage can adequately account for all the features involved in the paradoxes of logical properties. Consequently, the paper undertakes the task to do better, and, building on the system already developed, introduces a theory in a nonclassical metalanguage that expresses an adequate logic of naive truth and of some naive logical properties. (shrink)

In other works, I’ve proposed a solution to the semantic paradoxes which, at the technical level, basically relies on failure of contraction. I’ve also suggested that, at the philosophical level, contraction fails because of the instability of certain states of affairs. In this paper, I try to make good on that suggestion.

Logical orthodoxy has it that classical first-order logic, or some extension thereof, provides the right extension of the logical consequence relation. However, together with naïve but intuitive principles about semantic notions such as truth, denotation, satisfaction, and possibly validity and other naïve logical properties, classical logic quickly leads to inconsistency, and indeed triviality. At least since the publication of Kripke’s Outline of a theory of truth , an increasingly popular diagnosis has been to restore consistency, or at least non-triviality, by (...) restricting some classical rules. Our modest aim in this note is to briefly introduce the main strands of the current debate on paradox and logical revision, and point to some of the potential challenges revisionary approaches might face, with reference to the nine contributions to the present volume.For a recent introduction to non-classical theories of truth and other semantic notions, see the excellent Beall a .. (shrink)

We present a revenge argument for non-reflexive theories of semantic notions – theories which restrict the rule of assumption, or initial sequents of the form φ ⊩ φ. Our strategy follows the general template articulated in Murzi and Rossi [21]: we proceed via the definition of a notion of paradoxicality for non-reflexive theories which in turn breeds paradoxes that standard non-reflexive theories are unable to block.