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Single Idea 13255

[filed under theme 4. Formal Logic / E. Nonclassical Logics / 5. Relevant Logic ]

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.

The 8 ideas with the same theme [logic which requires some relevance of antecedent to consequent]:

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]