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Monday, April 11, 2011

The Recurring Question

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....


  1. I wonder if it is like asking how many universal statements, conjunctions or negations we should believe. Since contradictions are just, from a dialetheist point of view, certain kinds of statements like the others (no logical barrier to conjunctions, etc. ... no logical barriers to contradictions) the grounds for acceptance are just those for any such contingency. Barriers to acceptance no longer include purely logical grounds so the usual more messy case by case considerations dominate (lack of simplicity, parsimony, explanatory value, coherence with other commitments, etc.).

    Another angle on the question is to rephrase it as a request for the bounds of consistency per se. (This interprets the question as a request for a *general* answer. Where can we reasonably expect consistency as an extra-logical assumption? There is a bit written about this by Graham that suggests we can expect it in the observable realm but your paraconsistent analysis of vagueness rather undermines that claim.

  2. There is no consistancy and there is no recurrance. Every imaginable variables are constant and singular. None of the wave line created on the sea shore are the same and they will never be. Very interestingly, if every infinitasimle events are singular or not recurring then the set of all events is growing. Recursive events can cause no acceleration. May be then things stops happening and start to crunch

  3. what is scientific notation
    Scientific Notation include in the mathematics course. In the world of science some time we deal with numbers which are very small and those which are very large. In some branches of science large numbers while in others very small numbers are used.