(I can’t get no) antisatisfaction

Synthese - Substructural approaches to paradoxes have attracted much attention from the philosophical community in the last decade. In this paper we focus on two substructural logics, named...     

Proof,Meaning and Paradox: Some Remarks

Topoi - In the present paper, the Fregean conception of proof-theoretic semantics that I developed elsewhere will be revised so as to better reflect the different roles played by open and closed...     

Natural Deduction for Dual-intuitionistic Logic

We present a natural deduction system for dual-intuitionistic logic. Its distinctive feature is that it is a single-premise multiple-conclusions system. Its relationships with the natural deduction systems for intuitionistic and classical logic are discussed.     

Truth from a Proof-Theoretic Perspective

Validity, the central concept of the so-called ‘proof-theoretic semantics’ is described as correctly applying to the arguments that denote proofs. In terms of validity, I propose an anti-realist characterization of the notions of truth and correct assertion, at the core of which is the idea that valid arguments may fail to be recognized as such. The proposed account is compared with Dummett’s and Prawitz’s views on the matter.     

The Naturality of Natural Deduction (II): On Atomic Polymorphism and Generalized Propositional Connectives

Studia Logica - In a previous paper (of which this is a prosecution) we investigated the extraction of proof-theoretic properties of natural deduction derivations from their impredicative...     

Stabilizing Quantum Disjunction

Since the appearance of Prior’s tonk, inferentialists tried to formulate conditions that a collection of inference rules for a logical constant has to satisfy in order to succeed in conferring an acceptable meaning to it. Dummett proposed a pair of conditions, dubbed ‘harmony’ and ‘stability’ that have been cashed out in terms of the existence of certain transformations on natural deduction derivations called reductions and expansions. A long standing open problem for this proposal is posed by quantum disjunction: although its rules are intuitively unstable, they pass the test of existence of expansions. Although most authors view instabilities of this kind as too subtle to be detected by the requirement of existence of expansions, we first discuss a case showing that this requirement can indeed detect instabilities of this kind, and then show how the expansions for disjunction-like connectives have to be reformulated to rule out quantum disjunction. We show how the alternative pattern for expansions can be formulated for connectives and quantifiers whose rules satisfy a scheme originally developed by Prawitz and Schroeder-Heister. Finally we compare our proposal with a recent one due to Jacinto and Read.