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  1. One Heresy and One Orthodoxy: On Dialetheism, Dimathematism, and the Non-normativity of Logic.Heinrich Wansing - 2024 - Erkenntnis 89 (1):181-205.
    In this paper, Graham Priest’s understanding of dialetheism, the view that there exist true contradictions, is discussed, and various kinds of metaphysical dialetheism are distinguished between. An alternative to dialetheism is presented, namely a thesis called ‘dimathematism’. It is pointed out that dimathematism enables one to escape a slippery slope argument for dialetheism that has been put forward by Priest. Moreover, dimathematism is presented as a thesis that is helpful in rejecting the claim that logic is a normative discipline.
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  • On the Provable Contradictions of the Connexive Logics C and C3.Satoru Niki & Heinrich Wansing - 2023 - Journal of Philosophical Logic 52 (5):1355-1383.
    Despite the tendency to be otherwise, some non-classical logics are known to validate formulas that are invalid in classical logic. A subclass of such systems even possesses pairs of a formula and its negation as theorems, without becoming trivial. How should these provable contradictions be understood? The present paper aims to shed light on aspects of this phenomenon by taking as samples the constructive connexive logic C, which is obtained by a simple modification of a system of constructible falsity, namely (...)
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  • Consistent Theories in Inconsistent Logics.Franci Mangraviti & Andrew Tedder - 2023 - Journal of Philosophical Logic 52 (04):1133-1148.
    The relationship between logics with sets of theorems including contradictions (“inconsistent logics”) and theories closed under such logics is investigated. It is noted that if we take “theories” to be defined in terms of deductive closure understood in a way somewhat different from the standard, Tarskian, one, inconsistent logics can have consistent theories. That is, we can find some sets of formulas the closure of which under some inconsistent logic need not contain any contradictions. We prove this in a general (...)
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  • Pecularities of Some Three- and Four-Valued Second Order Logics.Allen P. Hazen & Francis Jeffry Pelletier - 2018 - Logica Universalis 12 (3-4):493-509.
    Logics that have many truth values—more than just True and False—have been argued to be useful in the analysis of very many philosophical and linguistic puzzles. In this paper, which is a followup to, we will start with a particularly well-motivated four-valued logic that has been studied mainly in its propositional and first-order versions. And we will then investigate its second-order version. This four-valued logic has two natural three-valued extensions: what is called a “gap logic”, and what is called a (...)
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