Article

No Requirement of Relevance

John P. Burgess

in The Oxford Handbook of Philosophy of Mathematics and Logic

Published in print June 2007 | ISBN: 9780195325928
Published online September 2009 | | DOI: http://dx.doi.org/10.1093/oxfordhb/9780195325928.003.0024

Series: Oxford Handbooks

No Requirement of Relevance

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Classic logic defines entailment to hold between a premise (or set of premises) and a conclusion if and only if their logical form guarantees that either the premise (or at least one element of the set of premises) is false, or the conclusion is true. The definition obliges the logician to recognize certain degenerate entailments. A premise (or set of premises) that is contradictory in the sense that its logical form guarantees that it is false (or that at least one element of the set of is false) entails any conclusion: ex falso quodlibet. And a conclusion that is tautologous in the sense that its logical form guarantees that it is true is entailed by any premise (or set of premises): ex quolibet verum. The commitment of classical logic to these principles has frequently been attacked by indignant critics who denounce the degenerate cases of entailment as “paradoxes.”

Keywords: classic logic; set of premises; entailment; paradoxes; relevance; conclusion

Article.  9365 words. 

Subjects: Philosophy ; Philosophy of Mathematics and Logic

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