ILLUSTRATIONS OF THE LOGIC OF SCIENCE. 705 



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 unknow- 

 able 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 informa- 

 tion 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 PAPEE. 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 ex- 

 pressed in the nomenclature of the mediaeval 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 al- 

 most every) such antecedent is followed by such a consequent, they 

 termed the consequence. Using this language, we may say that prob- 

 ability belongs exclusively to consequences, and the probability of any 

 consequence is the number of times in which antecedent and conse- 

 quent 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 : 



Mule for the Addition of Probabilities. Given the separate proba- 

 bilities of two consequences having the same antecedent and incom- 

 patible consequents. Then the sum of these two numbers is the prob- 

 ability of the consequence, that from the same antecedent one or 

 other of those consequents follows. 

 vol. xii. 45 



