Journal ArticleDOI
The logic of paradox
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A new way of handling the logical paradoxes is suggested, where instead of trying to dissolve them, or explain what has gone wrong, the authors should accept them and learn to come to live with them.Abstract:
The purpose of the present paper is to suggest a new way of handling the logical paradoxes. Instead of trying to dissolve them, or explain what has gone wrong, we should accept them and learn to come to live with them. This is argued in Sections I and II. For obvious reasons this will require the abandonment, or at least modification, of 'classical' logic. A way to do this is suggested in Section III. Sections IV and V discuss some implications of this approach to paradoxes.read more
Citations
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Correspondence analysis for strong three-valued logic
TL;DR: A new proof system for Lukasiewicz’s three-valued logic is obtained by characterizing each possible single entry in the truth-table of a unary or a binary truth-functional operator that could be added to K3 by a basic inference scheme.
Journal ArticleDOI
Accepting inconsistencies from the paradoxes
TL;DR: It is proved that a first-order language for number theory can be semantically closed by having its own global truth predicate under some non-standard interpretation and thus that it actually can contain the Liar sentence.
New Grounds for Naive Truth Theory
TL;DR: A theory is semantically closed if it contains, for each sentence A of the language in which it is framed, all biconditionals of the form T[A] ≡ A.
Book ChapterDOI
Two Genuine 3-Valued Paraconsistent Logics
TL;DR: This paper presents two genuine three-valued paraconsistent logics, i.e. logics obeying neither \(p, \l not p \vdash q\) nor \(\vdash \lnot (p \wedge p)\), and studies their basic properties and their relations with other paracons persistent logics.
Journal ArticleDOI
Measuring coherence using LP-models
TL;DR: A technique for measuring the degree of (in)coherence of inconsistent sets of propositional formulas is introduced, and Hunter's objections to many-valued paraconsistent logics as instruments for measuring (in]coherence are addressed.
References
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Book ChapterDOI
The Semantic Conception of Truth and the Foundations of Semantics
TL;DR: In this article, the notion of material adequacy of a definition of truth is defined as follows: if all these equivalences follow from it, then the definition is true if, and only if, p.X is true.
Journal ArticleDOI
The Semantic Conception of Truth: and the Foundations of Semantics
TL;DR: In this article, the notion of material adequacy of a definition of truth is defined as follows: if all these equivalences follow from it, then the definition is true if, and only if, p.X is true.
Book
Grundlagen der Mathematik
David Hilbert,Paul Bernays +1 more
TL;DR: In this article, a vorliegende Buch soll einer eingehenden Orientierung uber den gegenwartigen Stoff der HILBERTschen Beweistheorie dienen.
Journal ArticleDOI