Symbolic Logic: An Introductory Textbook for Non-Mathematicians

Symbolic Logic: An Introductory Textbook for Non-Mathematicians

Symbolic Logic: An Introductory Textbook for Non-Mathematicians

Symbolic Logic: An Introductory Textbook for Non-Mathematicians

Excerpt

The problem of teaching symbolic logic to persons who are not specially trained in mathematics is very different from that of teaching it to those who are; that is, to those who are proficient in handling the type of symbolism that mathematics uses in dealing with concepts at once highly abstract and precise. It is here that logical order and pedagogical order proceed in opposite directions. Logical order starts from the highly general and abstract and progresses toward the more specific and concrete. Pedagogical order, on the other hand, progresses from the familiar to the unfamiliar; and the familiar, to persons not mathematically trained, is the concrete. Concrete situations, although specific and at first imprecisely symbolized, can be so studied as to engender an understanding of logical abstractions and an ability to handle the abstractions by means of a precise and adequate symbolism. Easy familiarity with symbols and their use is a necessary condition of the grasp of the meanings and inter-relationships of logical concepts.

Introductory books in symbolic logic that begin with concepts of the greatest generality and proceed by rigid deduction often say that they require no specialized knowledge of mathematics; and this is true in the sense that they do not require knowledge of specific theorems or groups of theorems learned in some course in mathematics; but it is not true in the sense that they do not require ease and proficiency in dealing with mathematical symbolism. The purpose of the arrangement of topics in the first half of the present text is to develop proficiency in the use of symbols . . .

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