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.