> The difficulty in the Mx quantifier is actually a reflection on the > need of introducing to FOL new logical quantifiers: > > - Ix (There are infinitely many x's) > - Fx (There are finitely many x's)
So called "generalized quantifiers" have been studied. Mostowski comes to mind.
> And of one of the new "Anti-Inference" rules is: > > - From Fx one shall _not_ infer Ex.
And Lukasiewicz used rules of rejection.
So that'll be two more diversions to keep you from proving you claim about cGC and ~cGC being unknowable.