William Elliot wrote: > On Sat, 22 Jun 2013, Peter Percival wrote: > >> Did you ever express the opinion that the continuum hypothesis was neither >> true nor false? I seem to recall that you did but I might be mistaken. If >> you did, why so? > > CH is undecidable, that is neither CH nor not-CH can be proved with ZFC. > As for being true or false, that's a philosophical problem of no concern.
May I ask you, what does the "not" in "not-CH" mean? CH is not especially relevant to what I'm asking, so what does "not" in "not-P" mean, where "P" is any statement? This seems at least a partial explanation to me:
not-P is false if P is true not-P is true if P is false
_If_ all statements are true or false, then that seems a pretty good explanation of the meaning of "not", *so long as* the notions of truth and falsity are clear.
If, on the other hand, truth and falsity are to be dismissed as of no concern, then it seems "not" (and thus "not-CH") must be dismissed as well. It may be that you don't wish to dismiss truth and falsity as of no concern in general, but just in the CH and similar cases. My worry: how extensive are the similar cases?
Another account might be:
not-P is just P with (say) "~" stuck in front of it; furthermore, if P is a statement the so is not-P; further furthermore that "~" may be manipulated according to certain, otherwise meaningless, rules
which leaves me unsatisfied.
[None of the above is well expressed, sorry.]
-- I think I am an Elephant, Behind another Elephant Behind /another/ Elephant who isn't really there.... A.A. Milne