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On the Formalization of the Law of Non-Contradiction

In Graham Priest, Jc Beall & Bradley P. Armour-Garb (eds.), The law of non-contradiction : new philosophical essays. New York: Oxford University Press (2004)

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The Logical and Philosophical Foundations for the Possibility of True Contradictions.Ben Martin - 2014 - Dissertation, University College Londondetails 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 (...) Download Export citation Bookmark 1 citation
A Rejection System for the First-Degree Formulae of some Relevant Logics.Ross T. Brady - 2008 - Australasian Journal of Logic 6:55-69.details The standard Hilbert-style of axiomatic system yields the assertion of axioms and, via the use of rules, the assertion of theorems. However, there has been little work done on the corresponding axiomatic rejection of non-theorems. Such Hilbert-style rejection would be achieved by the inclusion of certain rejection-axioms (r-axioms) and, by use of rejection-rules (r-rules), the establishment of rejection-theorems (r-theorems). We will call such a proof a rejection-proof (r-proof). The ideal to aim for would be for the theorems and r-theorems to (...) Download Export citation Bookmark 5 citations

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