On the logic of quantification

Abstract

The notation that I shall use here for the logic of quantification is of the familiar kind wherein the letters ‘p’, ‘q’, etc. stand in place of unspecified statements and the letters ‘ƒ’, ‘g’, etc. stand in place of unspecified predicates. The present section will deal with the significance of this notation; the purpose and scope of the paper as a whole can better be indicated afterward, in §2.By “predicates” I mean, not properties (or classes) and relations, but merely certain notational expressions. As a first approach they may be thought of as expressions like ‘walks,’ ‘is red,’ ‘touches,’ ‘gives to.’ Where ‘ƒ’, ‘g’, ‘h’, and ‘k’ represent these four predicates, we may read ‘ƒx’ ‘gy’, ‘hxy’, and ‘κxyz’ as ‘x walks,’ ‘y is red,’ ‘x touches y,’ ‘x gives y to z.’