A Concise History of Paraconsistent Logic
Department of Philosophy
Centre for Logic, Epistemology and the History of Science
In this tutorial, we will present some research results concerning the history of paraconsistent logic. 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. 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. The outline of this tutorial is as follows. First, 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. We will analyze some classical reductio ad absurdum inference schemata used by Zeno of Elea, Plato and Aristotle. Such classical approach contrast with paraconsistent positions found in Heraclitus and even in Aristotle. 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. Second, we will introduce textual evidence concerning mediaeval logic which can fix some misunderstandings still extant in some historical studies on paraconsistent logic. We will give special attention to claims of Peter Abelard, Adam of Balsham, William of Soissons, Petrus Hispanus and William of Ockham. All these authors seem supporting paraconsistent positions. Some of them work in a full-fledged logical perspective; others work on behalf of preserving theological matters of falsity and trivialization. The medieval theory of consequences is the theoretical setting in which such disputations took place. 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. 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. We intend to present that such approach, supported in historical context of contemporary logic, is not only more accurate b ut also more full and reasonable. Section 1 Section 2 Section 3
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Bibliography ARISTOTLE. The complete works of Aristotle. Edited by J. Barnes. Princeton, NJ: Princeton University Press, 1985. 2 vols. (Bollingen series, LXXI).
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