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Arguments enter the scene as the position is developed. The situation is no different with our pluralism. In response to various comments and questions on our position (many emails, some “live”), I figured I better make clear our starting point. We made this clear elsewhere; in fact, we made it clear all along. Still, if questions persist, then we need to either repeat or clarify. Here, I repeat; in the book, we clarify.
Our starting point is what we have previously called (V) pronounced Vee (and not to be confused with Frege relevant five). Perhaps we drop this name in the book, but for now I use it. (V) is simply an account of validity or consequence, or (as we see it) a schema for accounts of validity or consequence. Taking validity or consequence to be the follows from relation, (V) can be expressed thus:
(V) A conclusion, A, follows from premises, P, if and only if every situation in which (each element of) P is true is one in which A is true.
Our starting point, then, is (V). What to make of (V) is at the heart of our pluralism. One question to ask concerns (V) invocation of situations. Which situations (NB: Here, we are happy to use other common terms, including cases points worlds and more.) To this question we have an answer; however, our answer is likewise a part of our starting point; it is not something for which we provide arguments. (We are not sure whether reasonable arguments can be given for the answer; probably, only appeals to “intuition” are available, and intuitions are rarely the ingrediants for solid arguments.) Our answer to the question, “Which situations is part of our take on (V). Leaving out qualifications about entailment one way of putting our answer is voiced nicely by J. Michael Dunn (references to be posted soon) in what I (tentatively) call Dunn Doctrine:
In assessing the validity of an entailment every variety of situation must be considered.
With (V), combined with Dunn doctrine, pluralism begins. As above, arguments enter the scene from here on out. If, however, you reject the starting point (comprising both (V) and Dunn doctrine), the subsequent arguments will be of little use to you. Such is philosophy, at least as we know it.
For what it worth, we do take both (V) and Dunn doctrine to be fairly common, fairly uncontroversial. Where controversy arises concerns the variety of situations sanctioned. We think that there are various sorts of situation (case,
world, point, etc.), including some that may be represented by (negation ) complete and consistent sets of sentences. On this score, many philosophers and philosophical logicians agree. But we see no reason not to recognize natural variations on this (uncontroversial) sort of situation. For example, once we have complete situations, why not recognize a natural twist, namely incomplete situations We see no good reason against recognizing incomplete situations as a natural sort of situation. More controversially, however, we likewise see no good reason against recognizing inconsistent situations as a natural sort of situation. And, indeed, we recognize all these sorts of situation, each being variations on a commonly recognized sort of situation (again, the sort represented by complete and consistent sets of sentences). Defending the admission of these varieties requires argument, and this is (in part) what our book attempts to do. The point of this little entry, however, is not to do that. (Again, the point of this entry is simply to answer a fair few queries I received lately on our position and where its arguments rest, where its starting point lies, etc.)
There is, perhaps, one other “starting point” of our position, or at any rate a thesis we maintain without argument. The thesis in question is that all is a quantifier the range of which varies with context. (NB: Exactly how to cash this out is something we are working on. An earlier entry below, briefing noting comments from Daniel Nolan on a recent UQ talk by Greg, reflects some of the issues that need to be settled. For now, though, I just put the point in a simple, though currently tentative, fashion.) Combining this view about all with Dunn doctrine and (V) gives the heart of Pluralism: There are many different consequence relations governing English. Depending on the range of all in all situations one specifies different consequence relations underwriting the English language. (Interestingly, some philosophers have apparently taken us to be saying that there are different English languages, each corresponding to a different consequence relation so understood. This has never been our position, as far as I can remember, but apparently some have thought as much. In response to this sort of misinterpretation Greg has written a very nice comparison of our version of pluralism with that of Carnap where Carnap discusses a position closer to the misinterpretation mentioned above.)
Hope this helps. Thanks to all who asked questions. The book will fill this stuff out a lot more, and also answer numerous pressing questions that I haven even touched here. He talks more about the epistemic situation of the dog (who appears in many places in the literature on relevant/relevance logic). He also endorses our pluralism. (Actually, I not sure if Jay means to emphasise our pluralism, or some other kind of contextualism, but it not his fault if we not completely clear about it all.) Anyway,
it a great read.