A Class Room Logic / Deductive and Inductive, with Special Application to the Science and Art of Teaching

by George Hastings McNair

1. INDUCTIVE AND DEDUCTIVE REASONING DISTINGUISHED.

It has been remarked that inference is the process of deriving a judgment from one or two antecedent judgments, and that mediate inference is inference by means of a middle term. But to reason by means of a middle term necessitates two judgments; hence mediate inference might be defined as the process of deriving a judgment from two antecedent judgments. In this treatment mediate inference and reasoning have been used interchangeably. This, then, becomes our definition for reasoning: Reasoning is the process of deriving a judgment from two antecedent judgments.

The syllogism results when the process of reasoning is formally clothed in words. Moreover, the conclusion of the syllogism may be more general than the premises or less general. This suggests the two important kinds of reasoning; namely, inductive and deductive. Inductive reasoning is reasoning from less general premises to a more general conclusion. Deductive reasoning is reasoning from more general premises to a less general conclusion.

ILLUSTRATION:

Inductive Syllogism.	Deductive Syllogism.
The robin, crow, sparrow, etc. have wings,  The robin, crow, sparrow, etc. are birds, ∴ All birds have wings.	All birds have wings,  The robin, crow, sparrow, etc. are birds, ∴ The robin, crow, sparrow, etc. have wings.
Iron, silver, gold, etc. are elements,  Iron, silver, gold, etc. are metals, ∴ All metals are elements.	All metals are elements,  Iron, silver, gold, etc. are metals, ∴ Iron, silver, gold, etc. are elements.
Boston, New York, Chicago, etc. have fine harbors,  Boston, New York, Chicago, etc. are large cities, ∴ All large cities have fine harbors.	All large cities have fine harbors,  Boston, New York, Chicago, etc. are large cities, ∴ Boston, New York, Chicago, etc. have fine harbors.

The student who is sufficiently familiar with the canons of the deductive syllogism will at once detect the fallacy of illicit minor in the foregoing inductive syllogisms; i. e., “birds” when used as the predicate of the minor premise of the first syllogism is undistributed, but as the subject of the conclusion “birds” is distributed. The same might be said concerning the terms “metals” and “large cities.” A portion of this chapter will be devoted to answering this criticism. At this point it may be stated that the inductive syllogism is not supposed to conform perfectly to the canons of the deductive syllogism.

2. THE INDUCTIVE HAZARD.

Referring to the first inductive syllogism of sectionone, it is assumed that the robin, crow and sparrow are representative birds, and that we are thus justified in concluding that if these type birds have wings, then all birds must have wings. Of course this is more or less of a conjecture or “a hazard”; since birds without wings may exist in some undiscovered corner of the globe. However, inasmuch as the generalization concerns a representative quality, we deem the assumption fairly well founded. The logical right to take this “leap into the unknown” will be discussed later. It will profit us at this time to realize more fully how essential the “inductive hazard” is to the progress of the world. When the Schoolmen of mediæval time refused to venture, they failed to progress, and thus came the dark days. Whenever man has ignored this God given instinct which leads to discovery, the world has stood still. This willingness to “take a leap into the dark” with the hope of finding, in the shadow, truth which would enhance man’s power and increase his serviceableness, has given to the world about all that is worth while. It was the spirit of the hazard which pushed Columbus to the discovery of a new world; which gave Newton the secrets of the motions of the universe; which enabled Edison to harness a multitude of lurking forces; and Morse and Bell to reduce distance to its lowest terms. In ordinary affairs with ordinary men those succeed best who manifest most a safe, steady, persistent spirit of discovery. Here, then, in the “inductive hazard” have we a most important phase of school life which, in this day of making the work easy, is being sadly neglected. On the other hand, anunregulated and insane spirit of venture may result in a great waste of energy, and in the development of low ideals of recklessness and inaccuracy. The “inductive hazard” must be cultivated; yet it must be regulated as well, and, as the reader already realizes, logic needs to concern itself mainly with this regulative aspect.

3. THE COMPLEXITY OF THE PROBLEM OF INDUCTION.

The problem of induction is much more complex than that of deduction because of these reasons: First. Deduction as a process of reasoning was the only kind discussed by the logicians for two thousand years. Aristotle is called the father of deductive logic and this Intellectual Giant, the greatest of ancient time and possibly of all time, so perfected the form of deductive reasoning that, up to the time of Francis Bacon, no scholar possessed the temerity to gainsay its supremacy in the field of logical reasoning. For twenty centuries Aristotle’s Deductive Logic was the Logicians’ Bible. On the other hand, inductive reasoning, though it was briefly discussed by Aristotle, received little attention till the versatile Francis Bacon placed it upon the stage of the thinking world. This makes deduction nearly two thousand years older than induction. Time, by eliminating the personal equation and exposing in various ways fallacious thinking, tends to unify and universalize truth. Hence, logicians are agreed so far as the fundamentals of deductive logic are concerned, but are still at odds over the true conception and use of inductive logic.