Introduction

Abstract

A theory of deduction utilizes various ideas of logic that may appear strange, even foreign, to mathematics students with little background in logic. The main concern of this book is to develop the important theory of deduction known as the predicate calculus. In an effort to overcome the strangeness of the logical ideas and methods involved, we shall first present the theory of deduction based on the connectives ⇁ (not) and v (or). This theory, known as the propositional calculus, characterizes the conclusions, or consequences, of a given set of assumptions, and so provides us with the formal side of arguments. The question of the validity of a given argument of this sort is easy to solve by the truth-table method, and so is really trivial. Therefore, in studying the accompanying theory of deduction we are able to concentrate on the formal apparatus and methods of a theory of deduction, without the complications owing to the subject matter under investigation. In short, the propositional calculus is a convenient device for making clear the nature of a theory of deduction.