Notes on Logic: Difference between revisions

Cross-definability in the realm of general propositions leads to quite similar questions to those in the realm of ab-functions. There is the same objection in the case of apparent variables to the usual indefinables as in the case of molecular functions. The application of the ab notation to apparent variable propositions becomes clear if we consider that, for instance, the proposition "for all x, ϕx" is to be true when ϕx is true for all x's, and false when ϕx is false for some x's. We see that ''some'' and ''all'' occur simultaneously in the proper apparent variable notation. The notation is

Old definitions now become tautologous.