On 4/14/2013 1:51 PM, Peter Percival wrote: > Nam Nguyen wrote: > >> 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. >
And, the "not infering Ex" from some other quantifier is clearly not the paradigm of first order logic.
Free logics are characterized by their difference with regard to existence assumptions and the denotations of terms. So, the fastest way to verify that this statement is not classical is found in the first paragraph of
The first-order presupposition binding denotations with existents comes from the description theories of Frege and Russell. In the first instance, the description theory arose from the insistence that logic be about truth, whence singular terms should not denote non-existent or self-contradictory objects. In the second instance, the description theory arose from the related problem of presupposition failure when denotations referred to non-existent objects.