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Aspects of the historical development of paraconsistent logic

In Graham Priest, Richard Routley & Jean Norman (eds.), Paraconsistent Logic: Essays on the Inconsistent. Philosophia Verlag. pp. 99--130 (1989)

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  1. Analytic Philosophy in Latin America (2nd edition).Diana I. Pérez & Santiago Echeverri - 2023 - Stanford Encyclopedia of Philosophy.
    Analytic philosophy was introduced in Latin America in the mid-twentieth century. Its development has been heterogeneous in different countries of the region but has today reached a considerable degree of maturity and originality, with a strong community working within the analytic tradition in Latin America. This entry describes the historical development of analytic philosophy in Latin America and offers some examples of original contributions by Latin American analytic philosophers.
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  • The Logical and Philosophical Foundations for the Possibility of True Contradictions.Ben Martin - 2014 - Dissertation, University College London
    The view that contradictions cannot be true has been part of accepted philosophical theory since at least the time of Aristotle. In this regard, it is almost unique in the history of philosophy. Only in the last forty years has the view been systematically challenged with the advent of dialetheism. Since Graham Priest introduced dialetheism as a solution to certain self-referential paradoxes, the possibility of true contradictions has been a live issue in the philosophy of logic. Yet, despite the arguments (...)
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  • History of logic in Latin America: the case of Ayda Ignez Arruda.Gisele Dalva Secco & Miguel Alvarez Lisboa - 2022 - British Journal for the History of Philosophy 30 (2):384-408.
    Ayda Ignez Arruda was a key figure in the development of the Brazilian school of Paraconsistent logic and the first person to write a historical survey of the field. Despite her importa...
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  • The Birth of Dialetheism.Elena Ficara - 2021 - History and Philosophy of Logic 42 (3):281-296.
    The aim of this paper is to lay bare the roots of dialetheism in discussions about dialectics and dialectical logic at the time of the first development of paraconsistent logics. In other words, th...
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  • Pavel Florensky’s Theory of Religious Antinomies.Paweł Rojek - 2019 - Logica Universalis 13 (4):515-540.
    Pavel Florensky (1882–1937), a Russian theologian, philosopher, and mathematician, argued that the religious discourse is essentially contradictory and put forward the idea of the logical theory of antinomies. Recently his views raised interesting discussions among logicians who consider him a forerunner of many non-classical logics. In this paper I discuss four interpretations of Florensky’s views: paraconsistent, L-contradictory, non-monotonic and rhetorical. In conclusion I argue for the integral interpretation which unites these four approaches.
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  • Enciclopédia de Termos Lógico-Filosóficos.João Miguel Biscaia Branquinho, Desidério Murcho & Nelson Gonçalves Gomes (eds.) - 2006 - São Paulo, SP, Brasil: Martins Fontes.
    Esta enciclopédia abrange, de uma forma introdutória mas desejavelmente rigorosa, uma diversidade de conceitos, temas, problemas, argumentos e teorias localizados numa área relativamente recente de estudos, os quais tem sido habitual qualificar como «estudos lógico-filosóficos». De uma forma apropriadamente genérica, e apesar de o território teórico abrangido ser extenso e de contornos por vezes difusos, podemos dizer que na área se investiga um conjunto de questões fundamentais acerca da natureza da linguagem, da mente, da cognição e do raciocínio humanos, bem (...)
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  • Paraconsistent Logic.David Ripley - 2015 - Journal of Philosophical Logic 44 (6):771-780.
    In some logics, anything whatsoever follows from a contradiction; call these logics explosive. Paraconsistent logics are logics that are not explosive. Paraconsistent logics have a long and fruitful history, and no doubt a long and fruitful future. To give some sense of the situation, I’ll spend Section 1 exploring exactly what it takes for a logic to be paraconsistent. It will emerge that there is considerable open texture to the idea. In Section 2, I’ll give some examples of techniques for (...)
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  • Tolerance and Mixed Consequence in the S'valuationist Setting.Pablo Cobreros, Paul Egré, David Ripley & Robert Rooij - 2012 - Studia Logica 100 (4):855-877.
    In a previous paper (see ‘Tolerant, Classical, Strict’, henceforth TCS) we investigated a semantic framework to deal with the idea that vague predicates are tolerant, namely that small changes do not affect the applicability of a vague predicate even if large changes do. Our approach there rests on two main ideas. First, given a classical extension of a predicate, we can define a strict and a tolerant extension depending on an indifference relation associated to that predicate. Second, we can use (...)
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  • Advice on Abductive Logic.Dov Gabbay & John Woods - 2006 - Logic Journal of the IGPL 14 (2):189-219.
    One of our purposes here is to expose something of the elementary logical structure of abductive reasoning, and to do so in a way that helps orient theorists to the various tasks that a logic of abduction should concern itself with. We are mindful of criticisms that have been levelled against the very idea of a logic of abduction; so we think it prudent to proceed with a certain diffidence. That our own account of abduction is itself abductive is methodological (...)
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  • The philosophy of alternative logics.Andrew Aberdein & Stephen Read - 2009 - In Leila Haaparanta (ed.), The development of modern logic. New York: Oxford University Press. pp. 613-723.
    This chapter focuses on alternative logics. It discusses a hierarchy of logical reform. It presents case studies that illustrate particular aspects of the logical revisionism discussed in the chapter. The first case study is of intuitionistic logic. The second case study turns to quantum logic, a system proposed on empirical grounds as a resolution of the antinomies of quantum mechanics. The third case study is concerned with systems of relevance logic, which have been the subject of an especially detailed reform (...)
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  • Paraconsistent logic.Graham Priest - 2008 - Stanford Encyclopedia of Philosophy.
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  • (1 other version)Analytical tableaux for da Costa's hierarchy of paraconsistent logics Cn, 1≤n<ω.Itala M. Loffredo D'Ottaviano & Milton Augustinis De Castro - 2005 - Journal of Applied Non-Classical Logics 15 (1):69-103.
    In this paper we present a new hierarchy of analytical tableaux systems TNDC n, 1≤n<ω, for da Costa's hierarchy of propositional paraconsistent logics Cn, 1≤n<ω. In our tableaux formulation, we introduce da Costa's “ball” operator “o”, the generalized operators “k” and “(k)”, for 1≤k, and the negations “~k”, for k≥1, as primitive operators, differently to what has been done in the literature, where these operators are usually defined operators. We prove a version of Cut Rule for the TNDC n, 1≤n<ω, (...)
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  • Vagueness: Subvaluationism.Pablo Cobreros - 2013 - Philosophy Compass 8 (5):472-485.
    Supervaluationism is a well known theory of vagueness. Subvaluationism is a less well known theory of vagueness. But these theories cannot be taken apart, for they are in a relation of duality that can be made precise. This paper provides an introduction to the subvaluationist theory of vagueness in connection to its dual, supervaluationism. A survey on the supervaluationist theory can be found in the Compass paper of Keefe (2008); our presentation of the theory in this paper will be short (...)
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  • Review article.Kazem Sadegh-Zadeh - 1985 - Erkenntnis 23 (1):97-112.
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  • (1 other version)Analytical tableaux for da Costa's hierarchy of paraconsistent logics Cn, 1≤n<ω.Itala M. Loffredo D'Ottaviano & Milton Augustinis de Castro - 2005 - Journal of Applied Non-Classical Logics 15 (1):69-103.
    In this paper we present a new hierarchy of analytical tableaux systems TNDC n, 1≤n (...))
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  • On Jaśkowski's Discussive Logics.Newton C. A. da Costa & Francisco A. Doria - 1995 - Studia Logica 54 (1):33 - 60.
    We expose the main ideas, concepts and results about Jaśkowski's discussive logic, and apply that logic to the concept of pragmatic truth and to the Dalla Chiara-di Francia view of the foundations of physics.
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  • Remarks on the applications of paraconsistent logic to physics.Newton C. A. da Costa & Décio Krause - unknown
    In this paper we make some general remarks on the use of non-classical logics, in particular paraconsistent logic, in the foundational analysis of physical theories. As a case-study, we present a reconstruction of P.\ -D.\ F\'evrier's 'logic of complementarity' as a strict three-valued logic and also a paraconsistent version of it. At the end, we sketch our own approach to complementarity, which is based on a paraconsistent logic termed 'paraclassical logic'.
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  • Thinking About Contradictions: The Imaginary Logic of Nikolai Aleksandrovich Vasil’Ev.Venanzio Raspa - 2017 - Cham, Switzerland: Springer Verlag.
    This volume examines the entire logical and philosophical production of Nikolai A. Vasil’ev, studying his life and activities as a historian and man of letters. Readers will gain a comprehensive understanding of this influential Russian logician, philosopher, psychologist, and poet. The author frames Vasil’ev’s work within its historical and cultural context. He takes into consideration both the situation of logic in Russia and the state of logic in Western Europe, from the end of the 19th century to the beginning of (...)
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  • Is there a zande logic?Newton C. A. Da Costa, Otávio Bueno & Steven French - 1998 - History and Philosophy of Logic 19 (1):41-54.
    The issue of what consequences to draw from the existence of non-classical logical systems has been the subject of an interesting debate across a diversity of fields. In this paper the matter of alternative logics is considered with reference to a specific belief system and its propositions :the Azande are said to maintain beliefs about witchcraft which, when expressed propositionally, appear to be inconsistent. When the Azande have been presented with such inconsistencies, they either fail to see them as such (...)
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  • A Generalisation of a Refutation-related Method in Paraconsistent Logics.Adam Trybus - forthcoming - Logic and Logical Philosophy.
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  • Handbook of Logical Thought in India.Sundar Sarukkai & Mihir Chakraborty (eds.) - 2018 - New Delhi, India: Springer.
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