In the past few weeks I've been listening and speaking at a lot of different places around the northeastern United States and Scotland. And the question that keeps coming up -- about dialethism and paraconsistency -- is the following. It is simple to state and hard to answer:
How much inconsistency is too much?
Classically speaking, of course, the answer is easy. Any inconsistency at all is too much. But there are too many things we want to talk about, to know, to understand, for consistency to stand in the way: even to formulate sensible statements about all the truths, all the sets, all the properties, etc (not to mention vague predicates...) requires going over the line. Some inconsistency is needed, maybe even welcome.
But how much is too much?
Absurdly speaking, the answer is also easy. There is no limit; let us have all the inconsistency and more. But let's set such an extremum aside -- or, better, take it as an obvious limiting condition on our answer.
Some, but not all, inconsistency. That's what we're looking for in a good theory. Where to find the line, though? How much noise is too much noise? My best guess so far: It depends on what kind of music you like.
Perhaps next time someone asks me this question, a more precise answer will follow....