Jim Choate wrote: > Para-consistent logic is the study of logical schemas or > systems in which the fundamental paradigms are paradoxes. It's a way of > dealing with logical situations in which true/false can't be determined > even axiomatically.
Most paraconsistent logics deal with paradoxes, but I know of none whose "fundamental paradigms are paradoxes". That barely makes sense to me, and is certainly not true. Paraconsistent logics often* allow some but not all sentences within the logic to be both true and false. In paraconsistent logics that have simple notions of true and false** it is usually (at least sometimes) possible to axiomatically determine whether a sentence is true or/and false - they wouldn't be much use if you couldn't! (not that they are much use anyway). * Many logicians would say they all do, according to Vasiliev and Da Costa's original definition. Some would say only some do. And some logician somewhere will disagree with almost anything you say about paraconsistent logics... ** Not all do, eg some have multi-value truths. Some have conditional truths, or truths valid only in some worlds. Some have true, false, both and neither. And so on. As usual, some logicians will disagree with this. For those who might care, paraconsistent logics are usually defined as non-explosive* logics. Ha! There is some argument (lots!**) about that, but it's the generally accepted modern definition (or at least the one most often argued about). * logics in which ECQ does not hold. ECQ = Ex Contradictione Quodlibet, anything follows from a contradiction. In most "normal" logics, if any single sentence and it's negation can both be proved, then _every_ sentence can be proved both true and false. This property is known as explosiveness. ** For instance, it has recently been shown that some logics traditionally known as paraconsistent, eg Sette's atomic P1 logic, are explosive, contrary to that definition. There are arguments about the meaning of negation as well, all of which confuse the issue. BTW, the name doesn't have anything to do with paradoxes, at least according to the guy who invented it. The "para" bit is supposedly from an extinct word (I forget the language, Puppy-something, really) for "arising out of, coming from". Some say it's from the Greek para- "beyond"; but I've never heard the "paradox" story before. I hope this at least interested some, and was not just troll-food. -- Peter Fairbrother
