root wrote: > On Thu, Oct 23, 2008 at 8:16 PM, Ed Murphy <[EMAIL PROTECTED]> wrote: >> * UNDECIDABLE, appropriate if the statement was logically >> undecidable or otherwise not capable of being accurately >> described as either true or false >> >> * FLOYD, appropriate if the statement logically could have been >> consistently described as either true or false > > But isn't a logically undecidable statement one that could be > consistently described as either true or false?
Arguably, on a FLOYD statement, one can come to either decision without incurring contradiction. > Actually, that's not quite true. Truth and falsehood of a statement > are relative to its interpretation, but decidability is relative to > the system in which one attempts to prove it, and isn't necessarily > related to truth at all. For example, in the trivial formal system > with no axioms and no rules of inference, nothing is a theorem, and so > everything is undecidable. Since we're interested in truth and not > decidability, we should probably just get rid of that clause > altogether. > > I don't see why FLOYD and UNDECIDABLE should be separate, though. > Most of the interesting game-winning paradoxes we've had have been > examples of FLOYD, and they shouldn't be disqualified from winning. > What about something like: > > * POSSIBLE, appropriate if the statement was neither uniquely true nor > uniquely false. FLOYD is specifically limited to logical interpretation, not legal interpretation. In particular, the paradox that led to my win in December 2006 depended on two equally-plausible legal interpretations, of which one was eventually discarded for entirely practical reasons (we needed to resolve the paradox somehow).
