On Thu, 18 Dec 2008, Alex Smith wrote: > On Mon, 2008-12-15 at 22:32 -0500, Warrigal wrote: >> Since apparently neither FALSE nor TRUE is appropriate, UNDECIDABLE is >> appropriate. >> >> The only reasonable way I can see to resolve this paradox is by >> repealing Rule 2110. > I believe it's a nice simple paradox, but not a game-winning one, as the > paradox arises as a result of the CFJ itself. > > Besides, arguably the chain of such CFJs described are false and true > alternately. The truth of the statement might change from moment to > moment, you know...
The first paradox that gave rise to this rule could also have been a moment- to-moment "true...false...true...false..." but that was similarly deemed to be just, well, a paradox. But overall this is trivial on two levels: one in that it arises through the CFJ, and secondly in that it should be obvious and trivial to any nomic player no self-contained system can decidably talk about all of its own paradoxes, and so any such rule is ultimately subject to its own paradoxes (perhaps it's unfair to say its trivial as it took until the 20th century to explain this formally, but any nomic player should know), and this was known when the rule was written. That doesn't stop a reasonable subset of paradoxes from being "interesting" paradoxes or wins. Maybe the rule should be more specifically written: "if a judgement of true would lead logically to a judgement of false, or vice versa, it is a win-quality paradox". -Goethe.
