![]() ![]() The study of logic achieved mathematical articulation, that anĮxplosive logical theory became the standard. It was towards the end of the nineteenth century, when This contemporary view, however, should be put in a historical It is now standard to view ex contradictione quodlibet as 1.2 A Brief History of ex contradictione quodlibet ![]() Logic, the primary focus is not the obtainability of contradictionsīut the explosive nature of a consequence relation. A paraconsistent logician may feel some pull towards dialetheism, but most paraconsistent logics are (including every contradiction) is true if dialetheism is to be coherent, then it seems a dialethiest’s preferred logic must be paraconsistent (though even this has been challenged by Barrio and Da Ré, based on work by Ripley and others e.g. ‘trivialism’, the view that everything whatsoever For reasons that paraconsistency may lead to dialetheismĭialetheism is the view that some contradiction is true, which is a distinct thesis from Interpretation of paraconsistency is given by Carnielli and Rodrigues ![]() This has been argued recently byīarrio and Da Ré (2018), and an explicitly non-dialetheic Hence paraconsistency must beĭistinguished from dialetheism. Where this is the case at some world) does not mean that theĬontradiction is true per se. The fact that one can construct a model where aĬontradiction holds but not every sentence of the language holds (or Non-explosive consequence relation does not mean that some sentencesĪre true. Paraconsistency is a property of a consequence relation whereasĭialetheism is a view about truth. Not entail the view that there are true contradictions. The view that a consequence relation should be paraconsistent does Objections to paraconsistent logic, there has been some tendency toĬonfuse paraconsistency with dialetheism, the view that thereĪre true contradictions (see the entry on In the literature, especially in the part of it that contains Others do not (like, say, compactness, or multiple conclusions). ‘paraconsistency’ does not single out one particularĪpproach to logic, but is rather a property that some logics have and Twenty-first century, it seems fair to say that At this stage of development, well into the \wedge \neg A)\), even though they invalidate ECQ.īeyond the basic, definitional requirement that a paraconsistentĬonsequence relation be non-explosive, there is a huge divergence of Logics do validate the Law of Non-Contradiction (LNC), \(\vDash \neg(A As we will see below, many paraconsistent SimpleĬonsistency of a theory (no contradictions) is a special case ofĪbsolute consistency, or non-triviality (not every sentence Relaxed to the notion of coherence: no theory can includeĮvery sentence whatsoever if it is to be considered tenable. Namely, the most basic requirement that any theory must meet, is The role often played by the notion of consistency in orthodox logics, Paraconsistently invalid: in general, it is not the case that \(A\), The argument ex contradictione quodlibet (ECQ) is Paraconsistency is a property of a consequence relation. Relation \((\vDash\), either semantic or proof theoretic) is notĮxplosive. TheĪim is to describe some philosophically salient features of a diverseĪ logic is paraconsistent iff its logical consequence Such, this entry is not a complete survey of paraconsistent logic. Single set of open problems or programs in paraconsistent logic. Paraconsistent as long as it is not explosive. Paraconsistent logic is defined negatively: any logic is Paraconsistent logic as we will see below. The second, which provided different reasons for the development of Many paraconsistent logicians, however, have taken it to mean ![]() Mathematical Logic in 1976, he seems to have had the first meaning in When the term ‘paraconsistent’ wasĬoined by Miró Quesada at the Third Latin America Conference on ‘quasi’ (or ‘similar to, modelled on’) or The prefix ‘para’ in English has two meanings: That treats inconsistent information as potentially informative. Paraconsistent logic accommodates inconsistency in a controlled way Thus, if a consequence relation is paraconsistent, then even inĬircumstances where the available information is inconsistent, theĬonsequence relation does not explode into triviality. Relation is said to be paraconsistent if it is not explosive. Paraconsistent logic challenges this standard view. Inconsistency, according to received wisdom, Standard ‘non-classical’ logics too such as intuitionist Is entailed by any arbitrary contradiction \(A\), \(\neg A\) ( exĬontradictione quodlibet (ECQ)). A logical consequence relation isĮxplosive if according to it any arbitrary conclusion \(B\) A standard contemporary logical view has it that, from contradictory ![]()
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