On Fri, Oct 24, 2008 at 10:22 AM, Ed Murphy <[EMAIL PROTECTED]> wrote: > 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.
This would be clearer if both used the same phrasing. >> 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). I'm not clear on what you intend the distinction to be. -root
