Relevance - Logic

Logic

In formal reasoning, relevance has proved an important but elusive concept. It is important because the solution of any problem requires the prior identification of the relevant elements from which a solution can be constructed. It is elusive, because the meaning of relevance appears to be difficult or impossible to capture within conventional logical systems. The obvious suggestion that q is relevant to p if q is implied by p breaks down because under standard definitions of material implication, a false proposition implies all other propositions. However though 'iron is a metal' may be implied by 'cats lay eggs' it doesn't seem to be relevant to it the way in which 'cats are mammals' and 'mammals give birth to living young' are relevant to each other. If one states "I love ice cream," and another person responds "I have a friend named Brad Cook," then these statements are not relevant. However, if one states "I love ice cream," and another person responds "I have a friend named Brad Cook who also likes ice cream," this statement now becomes relevant because it relates to the first person's idea.

More recently a number of theorists have sought to account for relevance in terms of "possible world logics" in intensional logic. Roughly, the idea is that necessary truths are true in all possible worlds, contradictions (logical falsehoods) are true in no possible worlds, and contingent propositions can be ordered in terms of the number of possible worlds in which they are true. Relevance is argued to depend upon the "remoteness relationship" between an actual world in which relevance is being evaluated and the set of possible worlds within which it is true.