"Acosmist: at risk of being petty, I didn't say it because it was obvious."
I guess I'll fill in the correct words when you say incorrect things from now on. But I hate assuming; didn't that get me into trouble earlier in this thread? It happened somewhere, to be sure.
"I'm not a logical positivist."
Do you think science should deal with the physical universe, and nothing more?
"Rejecting all logic renders all logic unsound, and would be far simpler for you, but please, can you furnish me with an example where disjunctive syllogism is not valid?"
Paraconsistent logic doesn't reject all logic. Where did you get that idea? It's a logic, after all, and it has its logical rules.
Far simpler for me? I didn't invent this logic; I'm not even sure I buy the idea! But it certainly poses quite a challenge for LNC.
"can you furnish me with an example where disjunctive syllogism is not valid?"
Paraconsistent logic! I already did that, though. But let's take your attempt at explosion. If the logic at issue accepts some contradictions, then it is sometimes true that (p ^ ~p). So, p. Now you introduce a disjunction, like you did - p v q. But ~p is also true. So, from p v q and ~p we deduce, by disjunctive syllogism, that q. But hold on - the disjunction p v q is true even when ~p and ~q, because, after all, p ^ ~p is the assumption with which we started. Under paraconsistency, it's PERFECTLY valid to reject that this kind of explosion works.
You seem to think that I'm rejecting rules willy-nilly to make my own assumptions work. First of all, they aren't my assumptions - they're challenges to explosive logics introduced and refined by experts in the field of philosophical logic. I have no dog in this race, so to speak. Second, there is a consistency in the procedure by which these logicians work. They aren't revising their rules post hoc to make their assumptions work; they are adopting a set of principles that makes the "obvious" not seem as obvious anymore.
In fact, Graham Priest deals with the explosion objection FIRST in his article in The Law of Non-Contradiction. New Philosophical Essays. It's not as if these people overlook explosion, and they didn't do anything inconsistent with their assumptions in rejecting the rules of inference that would lead to successful explosion.
So, if you want an "example" I've provided it - it was the same one I linked to before, though...