On the Ternary Relation and Conditionality

Here is a familiar history: modal logics (see [13]) were around for some time before a semantic framework was found for them (by Kripke and others).1 This framework did at least two Very Good Things for modal logics: 1) it connected the powerful mathematical tools of model theory to these logics, allowing a variety of technical results to be proven, and 2) it connected modal logics (more) firmly to philosophy, allowing their application to the understanding of metaphysics, tense, scientific laws, modal verbs, and so on. This application crucially depends not only on simply having Kripke-style semantic frameworks, but on interpreting the frameworks in various ways. The points of evaluation of the framework, in various interpretations, might be metaphysically possible worlds, say, or times, or morally allowable outcomes, or fictions of some sort, or . . . whathaveyou; these interpretations give modal logics an ‘applied semantics’ as opposed to merely ‘pure semantics’. Relevant logics have a similar history. The logics themselves were articulated and explored (see [1]) before semantic frameworks were found for them [11, 24, 25, 26, 28, 31]. Of these frameworks, the one that’s had the most mileage put on it is the Routley-Meyer one, and that’s the one we’re most concerned to