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Full Idea
Some relevant logics reject transitivity, but we defend the classical view.
Gist of Idea
Relevant logic may reject transitivity
Source
JC Beall / G Restall (Logical Pluralism [2006], 8)
Book Ref
Beall,J/Restall,G: 'Logical Pluralism' [OUP 2006], p.91
A Reaction
[they cite Neil Tennant for this view] To reject transitivity (A?B ? B?C ? A?C) certainly seems a long way from classical logic. But in everyday inference Tennant's idea seems good. The first premise may be irrelevant to the final conclusion.
15429 | Relevance logic's → is perhaps expressible by 'if A, then B, for that reason' [Burgess] |
8720 | A logic is 'relevant' if premise and conclusion are connected, and 'paraconsistent' allows contradictions [Priest,G, by Friend] |
13243 | Excluded middle must be true for some situation, not for all situations [Beall/Restall] |
13242 | It's 'relevantly' valid if all those situations make it true [Beall/Restall] |
13245 | Relevant consequence says invalidity is the conclusion not being 'in' the premises [Beall/Restall] |
13246 | Relevant logic does not abandon classical logic [Beall/Restall] |
13254 | A doesn't imply A - that would be circular [Beall/Restall] |
13255 | Relevant logic may reject transitivity [Beall/Restall] |