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? 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. -root
