ABSTRACT
We shall reformulate Grize’s axiomatization slightly to suit present purposes. The system will be described by relying on a set-theoretic predicate (see Stoll, 1963). In the ensuing discussion the traditional symbols of logic may be read as abbreviations for the usual English locutions. Thus, “if p then q” (for statements p and q) becomes “p → q”; “p if and only if q” becomes “p ↔ q”; “p and q” becomes “p & q”; “p or q or both” becomes “p ∨ q”; “not p” becomes “−p”; “x is identical to y” (for objects x and y) becomes “x = y” 1 ; “everything has property P” becomes “(∀x) (Px)”; “something has property P” becomes “(∃x)(Px).”
