CHAPTER II - THE FIRST-ORDER PREDICATE LOGIC: I

Abstract

This chapter discusses first-order predicate logic or the functional calculus of first order. This logic contains the sentential logic within it as a proper part, in the sense that all reasoning that can be carried out within the sentential logic can also be carried out within the first-order predicate logic but not vice versa. Within the first-order predicate logic, the logical structure of formulas and of arguments can be presented considerably in detail than can be done within the sentential logic itself. Any system of logic that is satisfactory must enable to exhibit this difference. The first-order predicate logic as a formal system made its first appearance in Frege's Begriffsschrift. There is more than one way to set up the sentential logic, and there is more than one way to set up the first-order predicate logic also. A great variety of mathematical theories can be developed within the first-order predicate logic. Any formulation of the first-order predicate logic, which does not include predicate variables, such as the formulation F1, is often referred to as a simple applied first-order predicate logic. In addition, any mathematical theory stated within a simple applied first-order predicate logic is often referred to as an elementary theory or a theory with standard formalization.