# Page:Popular Science Monthly Volume 13.djvu/486

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THE POPULAR SCIENCE MONTHLY.

 ILLUSTRATIONS OF THE LOGIC OF SCIENCE.

By C. S. PEIRCE,

ASSISTANT IN THE UNITED STATES COAST SURVEY.

SIXTH PAPER.—DEDUCTION, INDUCTION, AND HYPOTHESIS.

I.

THE chief business of the logician is to classify arguments; for all testing clearly depends on classification. The classes of the logicians are defined by certain typical forms called syllogisms. For example, the syllogism called Barbara is as follows:

S is M; M is P:
Hence, S is P.

Or, to put words for letters—

Enoch and Elijah were men; all men die:
Hence, Enoch and Elijah must have died.

The "is P" of the logicians stands for any verb, active or neuter. It is capable of strict proof (with which, however, I will not trouble the reader) that all arguments whatever can be put into this form; but only under the condition that the is shall mean "is for the purposes of the argument" or "is represented by." Thus, an induction will appear in this form something like this:

These beans are two-thirds white;
But, the beans in this bag are (represented by) these beans;
The beans in the bag are two-thirds white.

But, because all inference may be reduced in some way to Barbara, it does not follow that this is the most appropriate form in which to represent every kind of inference. On the contrary, to show the distinctive characters of different sorts of inference, they must clearly be exhibited in different forms peculiar to each. Barbara particularly typifies deductive reasoning; and so long as the is is taken literally, no inductive reasoning can be put into this form. Barbara is, in fact, nothing but the application of a rule. The so-called major premise lays down this rule; as, for example, All men are mortal. The other or minor premise states a case under the rule; as, Enoch was a man. The conclusion applies the rule to the case and states the result: Enoch is mortal. All deduction is of this character; it is merely the application of general rules to particular cases. Sometimes this is not very evident, as in the following:

All quadrangles are figures,
But no triangle is a quadrangle;
Therefore, some figures are not triangles.