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Full Idea
The argument from P to A is 'relevantly' valid if and only if, for every situation in which each premise in P is true, so is A.
Gist of Idea
It's 'relevantly' valid if all those situations make it true
Source
JC Beall / G Restall (Logical Pluralism [2006], 5.2)
Book Ref
Beall,J/Restall,G: 'Logical Pluralism' [OUP 2006], p.53
A Reaction
I like the idea that proper inference should have an element of relevance to it. A falsehood may allow all sorts of things, without actually implying them. 'Situations' sound promising here.
| 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] |