604 THE POPULAR SCIENCE MONTHLY. 



of this masterly investigation, the words wherewith Pasteur himself 

 feelingly alludes to the difficulties and dangers of the experimenter's 

 art came home to me with especial force : " J'ai tant de fois 6prouve 

 que dans cet art difficile de l'experimentation les plus hahiles bron- 

 chent a chaque pas, et que l'interpretation des faits n'est pas moins 

 perilleuse." ' 







ILLUSTRATIONS OF THE LOGIC OF SCIENCE. 



By C. S. PEIRCE, 



ASSISTANT IN THE UNITED STATES COAST SURVEY. 



THIRD PAPER. THE DOCTRINE OF CHANCES. 



IT is a common observation that a science first begins to be exact 

 when it is quantitatively treated. What are called the exact sci- 

 ences are no others than the mathematical ones. Chemists reasoned 

 vaguely until Lavoisier showed them how to apply the balance to the 

 verification of their theories, when chemistry leaped suddenly into 

 the position of the most perfect of the classificatory sciences. It has 

 thus become so precise and certain that we usually think of it along 

 with optics, thermotics, and electrics. But these are studies of general 

 laws, while chemistry considers merely the relations and classification 

 of certain objects ; and belongs, in reality, in the same category as 

 systematic botany and zoology. Compare it with these last, however, 

 and the advantage that it derives from its quantitative treatment is 

 very evident. 



The rudest numerical scales, such as that by which the mineral- 

 ogists distinguish the different degrees of hardness, are found useful. 

 The mere counting of pistils and stamens sufficed to bring botany out 

 of total chaos into some hind of form. It is not, however, so much 

 from counting as from measuring, not so much from the conception 

 of number as from that of continuous quantity, that the advantage 

 of mathematical treatment comes. Number, after all, only serves to 

 pin us down to a precision in our thoughts which, however beneficial, 

 can seldom lead to lofty conceptions, and frequently descends to pet- 

 tiness. Of those two faculties of which Bacon speaks, that which 

 marks differences and that which notes resemblances, the employment 

 of number can only aid the lesser one; and the excessive use of it 

 must tend to narrow the powers of the mind. But the conception of 

 continuous quantity has a great office to fulfill, independently of any 

 attempt at precision. Far from tending to the exaggeration of differ- 

 ences, it is the direct instrument of the finest generalizations. When 



1 Comptes Rendus, lxxxiii., p. 177. 



