Paraconsistent logics and paraconsistency. Notre Dame Journal of Formal Logic, Oct., vol. On the theory of inconsistent formal systems. Inconsistencias ¿Por qué no? Un estudio filosófico sobre la lógica paraconsistente. Princeton, NJ: Princeton University Press, 1985. Some Paraconsistent Positions in Medieval Logic.Ī Concise History of Contemporary Paraconsistency.ĪRISTOTLE.
We intend to present that such approach, supported in historical context of contemporary logic, is not only more accurate b On the basis of new historiographical foundation, we intend to show that a pure chronological way of thinking the history of the paraconsistent logic leads to equivocal conclusions. Third, we will outline contemporary history of paraconsistent logic in order to rescue the important role played by some forerunners and especially by the founders of this logical field of study. The medieval theory of consequences is the theoretical setting in which such disputations took place. Some of them work in a full-fledged logical perspective others work on behalf of preserving theological matters of falsity and trivialization. All these authors seem supporting paraconsistent positions. We will give special attention to claims of Peter Abelard, Adam of Balsham, William of Soissons, Petrus Hispanus and William of Ockham. Second, we will introduce textual evidence concerning mediaeval logic which can fix some misunderstandings still extant in some historical studies on paraconsistent logic. We also present that ex falso sequitur quodlibet, a classical thesis related to trivialization, as far as we know, although could not be deduced in Stoic logic, it seems coming from this tradition. Such classical approach contrast with paraconsistent positions found in Heraclitus and even in Aristotle. We will analyze some classical reductio ad absurdum inference schemata used by Zeno of Elea, Plato and Aristotle. The outline of this tutorial is as follows.įirst, we will study some passages from the Ancient Greek logic legacy in which we have found several theoretical positions, inference schemata and the logical rules usage, which can be interpreted today as being part of paraconsistent approach.
Such two issues are strictly connected and its analysis has offered a valid ground to a logical history of paraconsistent positions all along western thought tradition. In order to develop such discussion, we will focus on the history of the Principle of Non-Contradiction and also on that of the ex falso sequitur quodlibet rule. In this tutorial, we will present some research results concerning the history of paraconsistent logic. State University of Campinas, SP - Brazil A Concise History of Paraconsistent LogicĬentre for Logic, Epistemology and the History of Science
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