Citations of:
Conditionals in Theories of Truth
Journal of Philosophical Logic 46 (1):2763 (2017)
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We offer a defense of one aspect of Paul Horwich’s response to the Liar paradox—more specifically, of his move to preserve classical logic. Horwich’s response requires that the full intersubstitutivity of ‘ ‘A’ is true’ and A be abandoned. It is thus open to the objection, due to Hartry Field, that it undermines the generalization function of truth. We defend Horwich’s move by isolating the grade of intersubstitutivity required by the generalization function and by providing a new reading of the (...) 

This article introduces, studies, and applies a new system of logic which is called ‘HYPE’. In HYPE, formulas are evaluated at states that may exhibit truth value gaps and truth value gluts. Simple and natural semantic rules for negation and the conditional operator are formulated based on an incompatibility relation and a partial fusion operation on states. The semantics is worked out in formal and philosophical detail, and a sound and complete axiomatization is provided both for the propositional and the (...) 

In truth theory one aims at general formal laws governing the attribution of truth to statements. Gupta’s and Belnap’s revisiontheoretic approach provides various wellmotivated theories of truth, in particular T* and T#, which tame the Liar and related paradoxes without a Tarskian hierarchy of languages. In property theory, one similarly aims at general formal laws governing the predication of properties. To avoid Russell’s paradox in this area a recourse to type theory is still popular, as testified by recent work in (...) 



We present some prooftheoretic results for the normal modal logic whose characteristic axiom is \. We present a sequent system for this logic and a hypersequent system for its firstorder form and show that these are equivalent to Hilbertstyle axiomatizations. We show that the question of validity for these logics reduces to that of classical tautologyhood and firstorder logical truth, respectively. We close by proving equivalences with a Fitchstyle proof system for revision theory. 

We present an extension of the basic revision theory of circular definitions with a unary operator, □. We present a Fitchstyle proof system that is sound and complete with respect to the extended semantics. The logic of the box gives rise to a simple modal logic, and we relate provability in the extended proof system to this modal logic via a completeness theorem, using interpretations over circular definitions, analogous to Solovay’s completeness theorem forGLusing arithmetical interpretations. We adapt our proof to (...) 



