464 



OPERATIONS SUBSIDIARY TO INDUCTION. 



after the question has been (to speak 

 technically) reduced to an equation, 

 that the unmeaning signs become 

 available, and that the nature of the 

 facts themselves to which the investi- 

 gation relates can be dismissed from 

 the mind. Up to the establishment 

 of the equation, the language in which 

 mathematicians carry on their reason- 

 ing does not differ in character from 

 that employed by close reasoners on 

 any other kind of subject. 



I do not deny that every correct 

 ratiocination, when thrown into the 

 syllogistic shape, is conclusive from 

 the mere form of the expression, pro- 

 vided none of the terms used be am- 

 biguous ; and this is one of the circum- 

 stances which have led some writers 

 to think that if all names were so 

 judiciously constructed and so care- 

 fully defined as not to admit of any 

 ambiguity, the improvement thus 

 made in language would not only give 

 to the conclusions of every deductive 

 science the same certainty with those 

 of mathematics, but would reduce all 

 reasonings to the application of a tech- 

 nical form, and enable their conclu- 

 siveness to be rationally assented to 

 after a merely mechanical process, as 

 is undoubtedly the case in algebra. 

 But, if we accept geometry the con- 

 clusions of which are already as cer- 

 tain 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 per- 

 son who has looked only at the reason- 

 ing itself. Whoever has assented to 

 what was said in the last book con- 

 cerning 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 propo- 

 sitions of all other sciences are true 

 only hypothetically, supposing that no 

 counteracting cause happens to inter- 

 fere. A conclusion therefore, however 

 correctly deduced, in point of form, 

 Uovfi 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 nature has superseded or intermingled 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 ac- 

 quainted with the peculiarities of every 

 case to which we attempt to apply our 

 general principles. 



The algebraicnotation, considered as 

 a philosophical language, is perfect in 

 its adaptation to the subjects for which 

 it is commonly employed, namely, 

 those of which the investigations have 

 already been reduced to the ascertain- 

 ment 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 consti- 

 tuting it the ideal model of philoso- 

 phical 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 sub- 

 jects, instead of contrivances to pre- 

 vent our attention from being dis- 

 tracted 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 con- 

 sciousness 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 ide^ to be expressed, All la«- 



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