On Tue, Jun 11, 2013 at 12:13 PM, Tanner Swett <swe...@mail.gvsu.edu> wrote: > it regulates the game > by instructing the players to interpret the rules as if the statement > "it is LEGAL to shout 'CREAMPUFF' if and only if it is ILLEGAL to > shout 'CREAMPUFF'" were true. If the statement were true, then TRUE > would be an appropriate judgement for a CFJ about it, and FALSE would > be an inappropriate judgement for a CFJ about it. Thus, because we're > instructed to act as if the statement as true, this means that TRUE > *is* an appropriate judgement for any CFJ about it, and FALSE *is* an > inappropriate judgement.
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. The method we seem to traditionally favor is to propagate indeterminacy, but only along explicitly defined lines, which is most like a three-valued logic. A benefit of preservationism is that it's consistent with how we deal with contradictions that occur between clauses rather than within a single clause (we disregard one of the clauses); drawbacks include that it's boring and precludes many forms of win by paradox (whether it precludes all depends on whether you lump a failure to define something in with inconsistencies). See: http://plato.stanford.edu/entries/logic-paraconsistent/
