On Jun 11, 2013, at 3:43 PM, omd wrote: > Arguments: ...but if the statement were true, it would also be true > that every judgement is appropriate and inappropriate, due to the > principle of explosion. There is no alternative to paraconsistent > logic. Any formal system that can be used to assign a truth value to > a statement like "TRUE is an appropriate judgement", but which does > not trivially derive it from the contradiction elsewhere, is > paraconsistent by definition. The answer to this CFJ merely depends > on how you want to make your logic paraconsistent. One method, which > you seem to support, is to simply blow away whatever axioms would make > the system inconsistent - or possibly only instantiations of axioms > with quantifiers that make the system inconsistent - which I suppose > could be called preservationism.
I wouldn't say I support blowing away whatever axioms would make the system inconsistent. I'd say that we just shouldn't consider a rule to be an axiom in the first place unless taking it as an axiom would result in a consistent system. I don't think this is a type of paraconsistent logic, since the principle of explosion remains a valid argument. —Machiavelli
