Synthese 196 (9):3789-3813 (2019)
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Abstract |
The purpose of this paper is to present a paraconsistent formal system and a corresponding intended interpretation according to which true contradictions are not tolerated. Contradictions are, instead, epistemically understood as conflicting evidence, where evidence for a proposition A is understood as reasons for believing that A is true. The paper defines a paraconsistent and paracomplete natural deduction system, called the Basic Logic of Evidence, and extends it to the Logic of Evidence and Truth. The latter is a logic of formal inconsistency and undeterminedness that is able to express not only preservation of evidence but also preservation of truth. LETj is anti-dialetheist in the sense that, according to the intuitive interpretation proposed here, its consequence relation is trivial in the presence of any true contradiction. Adequate semantics and a decision method are presented for both BLE and LETj, as well as some technical results that fit the intended interpretation.
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Reprint years | 2019 |
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DOI | 10.1007/s11229-017-1621-7 |
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References found in this work BETA
Natural Deduction: A Proof-Theoretical Study.Dag Prawitz - 1965 - Stockholm, Sweden: Dover Publications.
Logical Pluralism.Jc Beall & Greg Restall - 2000 - Australasian Journal of Philosophy 78 (4):475 – 493.
Science and Partial Truth: A Unitary Approach to Models and Scientific Reasoning.Newton C. A. da Costa & Steven French - 2003 - Oup Usa.
On the Theory of Inconsistent Formal Systems.Newton C. A. Costa - 1972 - Recife, Universidade Federal De Pernambuco, Instituto De Matemática.
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Citations of this work BETA
Measuring Evidence: A Probabilistic Approach to an Extension of Belnap–Dunn Logic.Abilio Rodrigues, Juliana Bueno-Soler & Walter Carnielli - 2020 - Synthese 198 (S22):5451-5480.
On Epistemic and Ontological Interpretations of Intuitionistic and Paraconsistent Paradigms.W. Carnielli & Abilio Rodrigues - forthcoming - Logic Journal of the IGPL.
Twist-Valued Models for Three-Valued Paraconsistent Set Theory.Walter Carnielli & Marcelo E. Coniglio - 2021 - Logic and Logical Philosophy 30 (2):187-226.
Models & Proofs: LFIs Without a Canonical Interpretations.Eduardo Alejandro Barrio - 2018 - Principia: An International Journal of Epistemology 22 (1):87-112.
Kripke-Style Models for Logics of Evidence and Truth.Henrique Antunes, Walter Carnielli, Andreas Kapsner & Abilio Rodrigues - 2020 - Axioms 9 (3).
View all 28 citations / Add more citations
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