496 OPERATIONS SUBSIDIARY TO INDUCTION. 



vestigation relates can be dismissed from the mind. Up to the establish- 

 ment of the equation, the language in which mathematicians carry on their 

 reasoning does not differ in character from that employed by close reason - 

 ers on any other kind of subject. 



I do not deny that every correct ratiocination, when thrown into the syl- 

 logistic shape, is conclusive from the mere form of the expression, provided 

 none of the terms used be ambiguous ; and this is one of the circumstances 

 which have led some writers to think that if all names were so judicious- 

 ly constructed and so carefully defined as not to admit of any ambiguity, 

 the improvement thus made in language would not only give to the con- 

 clusions of every deductive science the same certainty with those of mathe- 

 matics, but would reduce all reasonings to the application of a technical 

 form, and enable their conclusiveness to be rationally assented to after a 

 merely mechanical process, as is undoubtedly the case in algebra. But, if 

 we except geometry, the conclusions of which are already as certain and 

 exact as they can be made, there is no science but that of number, in which 

 the practical validity of a reasoning can be apparent to any person who has 

 looked only at the reasoning itself. Whoever has assented to what was 

 said in the last Book concerning the case of the Composition of Causes, 

 and the still stronger case of the entire supersession of one set of laws by 

 another, is aware that geometry and algebra are the only sciences of which 

 the propositions are categorically true ; the general propositions of all oth- 

 er sciences are true only hypothetically, supposing that no counteracting 

 cause happens to interfere. A conclusion, therefore, however correctly de- 

 duced, in point of form, from admitted laws of nature, will have no other 

 than an hypothetical certainty. At every step we must assure ourselves 

 that no other law of nature has superseded, or intermingled its operation 

 with, those which are the premises of the reasoning ; and how can this be 

 done by merely looking at the words ? We must not only be constantly 

 thinking of the phenomena themselves, but we must be constantly studying 

 them ; making ourselves acquainted with the peculiarities of every case to 

 which we attempt to apply our general principles. 



The algebraic notation, considered as a philosophical language, is per- 

 fect in its adaptation to the subjects for which it is commonly employ- 

 ed, namely those of which the investigations have already been reduced 

 to the ascertainment of a relation between numbers. But, admirable as 

 it is for its own purpose, the properties by which it is rendered such 

 are so far from constituting it the ideal model of philosophical language 

 in general, that the more nearly the language of any other branch of 

 science approaches to it, the less fit that language is for its own proper 

 functions. On all other subjects, instead of contrivances to prevent our at- 

 tention from being distracted by thinking of the meaning of our signs, we 

 ought to wish for contrivances to make it impossible that we should ever 

 lose sight of that meaning even for an instant. 



With this view, as much meaning as possible should be thrown into the 

 formation of the word itself; the aids of derivation and analogy being 

 made available to keep alive a consciousness of all that is signified by it. 

 In this respect those languages have an immense advantage which form their 

 compounds and derivatives from native roots, like the German, and not from 

 those of a foreign or dead language, as is so much the case with English, 

 French, and Italian ; and the best are those which form them according to 

 fixed analogies, corresponding to the relations between the ideas to be ex- 

 pressed. All languages do this more or less, but especially, among modern 



