Page:Popular Science Monthly Volume 12.djvu/725

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ILLUSTRATIONS OF THE LOGIC OF SCIENCE.

To this two replies have been given by the maintainers of the theory: That the universe has either had a beginning in time; or that, if it be really eternal, there are revolutions in its laws unknowable to man—interpositions of Creative Will!

These men of science are plainly not afraid of carrying out their opinions rigorously to their logical conclusions, but is their information as to the nature and relations of the phases of energy wide and deep enough to warrant them in framing an hypothesis so lofty as to include the cosmos and eternity? Hardly.

At the present stage of science, a student pondering the subject so briefly presented here may be compared to a judge before whom a few witnesses in an important case have appeared. As he hears each one, he makes, for convenience sake, a provisional summing-up, and tacks the testimony together in one directive line. But it would be a most injudicial act to mistake a provisional opinion for a final judgment, and, with an indefinite number of witnesses unheard, to pronounce sentence of death.

 
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ILLUSTRATIONS OF THE LOGIC OF SCIENCE.
By C. S. PEIRCE,
ASSISTANT IN THE UNITED STATES COAST SURVEY.

FOURTH PAPER.—THE PROBABILITY OF INDUCTION.

I.

WE have found that every argument derives its force from the general truth of the class of inferences to which it belongs; and that probability is the proportion of arguments carrying truth with them among those of any genus. This is most conveniently expressed in the nomenclature of the mediæval logicians. They called the fact expressed by a premise an antecedent, and that which follows from it its consequent; while the leading principle, that every (or almost every) such antecedent is followed by such a consequent, they termed the consequence. Using this language, we may say that probability belongs exclusively to consequences, and the probability of any consequence is the number of times in which antecedent and consequent both occur divided by the number of all the times in which the antecedent occurs. From this definition are deduced the following rules for the addition and multiplication of probabilities:

Rule for the Addition of Probabilities.—Given the separate probabilities of two consequences having the same antecedent and incompatible consequents. Then the sum of these two numbers is the probability of the consequence, that from the same antecedent one or other of those consequents follows.