Graph normal form, GNF, [1], was used in [2, 3] for analysing paradoxes in propositional discourses, with the semantics – equivalent to the classical one – defined by kernels of digraphs. The paper presents infinitary, resolution-based reasoning with GNF theories, which is refutationally complete for the classical semantics. Used for direct (not refutational) deduction it is not explosive and a...

Introducing The Liar Barwise and Etchemendy's The Liar presents two accounts of the semantics of the liar sentence \this sentence is not true", named for Russell and Austin, and informed by situation semantics and non-well-founded set theory. The accounts diier over how a speaker uses a sentence and the world to express a proposition. \By a statement we will understand certain sorts of datable ...

Abstract In this paper I argue that it’s impossible for there to be a single universal theory of meaning language. First, will consider some minimal expressiveness requirements language must meet able express semantic claims. Then in order have unified meaning, these satisfied by which the itself applies to. That is, we would need can its own meaning. It has been well-known since Tarski theorie...

The paradoxes of self-reference are genuinely paradoxical. The liar paradox, Russell's paradox and their cousins pose enormous diiculties to anyone who seeks to give a comprehensive theory of semantics, or of sets, or of any other domain which allows a modicum of self-reference and a modest number of logical principles. One approach to the paradoxes of self-reference takes these paradoxes as mo...

Self-reference is used to denote any situation in which someoneor something refers to itself. Self-reference is an important issuein philosophy, mathematics and computer science amongst oth-ers. In the philosophy of language the naive theory of truth hasbeen challenged by the Liar Paradox. The Liar Paradox is thecontradiction that emerges from trying to determine whether...

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 gra...

Many mathematicians have a dismissive attitude towards paradoxes. This is unfortunate , because many paradoxes are rich in content, having connections with serious mathematical ideas as well as having pedagogical value in teaching elementary logical reasoning. An excellent example is the so-called " surprise examination paradox " (described below), which is an argument that seems at first to be...

We show that self-referentiality can be formalized in Basic logic by means of a new connective: @, called "entanglement". In fact, the property of non-idempotence of the connective @ is a metatheorem, which states that a self-referential sentence loses its own identity. This prevents having self-referential paradoxes in the corresponding metalanguage.

parenthetical references are to the pages of this book. Kripke, “Outline of a theory of truth,” Journal of Philosophy 72 (1975), 690-716; reprinted in Robert L. Martin (ed.), Recent Essays on Truth and the Liar Paradox (Oxford: Clarendon Press,1984), pp. 53-81. A formal difference between Maudlin’s and Kripke’s constructions is that Maudlin’s language has both a truth and a falsity predicate, w...