![]() By the end of the twentieth century there were many paraconsistent logics with well-defined semantics and proof theories. The paraconsistent possibilities of the relevant logic of Alan Anderson and Nuel Belnap (1960s) was also soon recognized. Amongst the earliest paraconsistent logics were those proposed by Stanis ław Ja śkowski (1948) and Newton da Costa (1963). Modern formal paraconsistent logics started to appear in the second half of the twentieth century. But since the early twentieth century, the hegemony of Frege/Russell (classical) logic, according to which explosion is valid, has ensured the orthodoxy of the principle. All this was forgotten after the Middle Ages. A common move was to distinguish two notions of validity: one ( material ) for which they held and one ( formal ) for which they do not. Explosion and the disjunctive syllogism had variable fortunes in later Medieval logic. Then B follows by the disjunctive syllogism ( A, ¬ A v B ⊦ B ). The idea that explosion is a correct principle of inference seems to have arisen in the twelfth century, with the discovery of the following simple argument. ![]() 63 b31 –64 a16) points out, syllogistic is paraconsistent. A paraconsistent logic is one in which explosion is not valid. The principle of inference that contradictions entail everything is called explosion (or ex falso quodlibet sequitur ). This motivates the definition of a paraconsistent logic. Clearly, if one uses a logical consequence relation in which contradictions imply everything -that is, in which A, ¬ A ⊦ B, for all A and B -this is not possible: a person would have to conclude everything ( triviality ). ![]() The driving thought of paraconsistency is that there are situations in which information, or legal, scientific, or philosophical principles (and so on) are inconsistent, but in which people want to draw conclusions in a sensible fashion.
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