REMAINING LAWS OF NATURE. 



397 



positions. When we cannot bring 

 two straight lines together to deter- 

 mine whether they are equal, we do 

 it by the physical aid of a foot-rule 

 applied first to one and then to the 

 other, and the logical aid of the gene- 

 ral proposition or formula, " Things 

 which are equal to the same thing are 

 equal to one another." The compari- 

 son of two things through the inter- 

 vention of a third thing, when their 

 direct comparison is impossible, is the 

 appropriate scientific process for as- 

 certaining resemblances and dissimi- 

 larities, and is the sum total of what 

 Logic has to teach on the subject. 



An undue extension of this remark 

 induced Locke to consider reasoning 

 itself as nothing but the comparison 

 of two ideas through the medium of a 

 third, and knowledge as the percep- 

 tion of the agreement or disagree- 

 ment of two ideas : doctrines which 

 the Condillac school blindly adopted, 

 without the qualifications and dis- 

 tinctions with which they were stu- 

 diously guarded by their illustrious 

 author. Where, indeed, the agree- 

 ment or disagreement (otherwise 

 called resemblance or dissimilarity) 

 of any two things is the very matter 

 to be determined, as is the case par- 

 ticularly in the sciences of quantity 

 and extension ; there, the process by 

 which a solution, if not attainable b}' 

 direct perception, must be indirectly 

 sought, consists in comparing these 

 two things through the medium of a 

 third. But this is far from being 

 true of all inquiries. The know- 

 ledge that bodies fall to the ground is 

 not a perception of agreement or dis- 

 agreement, but of a series of physi- 

 cal occurrences, a succession of sensa- 

 tions. Locke's definitions of know- 

 ledge and of reasoning required to be 

 limited to our knowledge of, and 

 reasoning about resemblances. Nor, 

 even when thus restricted, are the 

 propositions strictly correct, since the 

 comparison is not made, as he repre- 

 sents, between the ideas of the two 

 phenomena, but between the pheno- 

 mena themselves. This mistake has 



been pointed out in an earlier part of 

 our inquiry,* and we traced it to an 

 imperfect conception of what take* 

 place in mathematics, where very 

 often the comparison is really made 

 between the ideas, without any ap- 

 peal to the outward senses ; only, 

 however, because in mathematics a 

 comparison of the ideas is strictly 

 equivalent to a comparison of the 

 phenomena themselves. Where, as 

 in the case of numbers, lines, and 

 figures, our idea of an object is a 

 complete picture of the object so far 

 as respects the matter in hand, we 

 can, of course, learn from the picture 

 whatever could be learnt from the ob- 

 ject itself by mere contemplation of it 

 as it exists at the particular instant 

 when the picture is taken. No mere 

 contemplation of gunpowder would 

 ever teach us that a spark would 

 make it explode, nor, consequently, 

 would the contemplation of the idea 

 of gunpowder do so ; but the mere 

 contemplation of a straight line shows 

 that it cannot enclose a space : ac- 

 cordingly the contemplation of the 

 idea of it will show the same. What 

 takes place in mathematics is thus 

 no argument that the comparison is 

 between the ideas only. It is always, 

 either indirectly or directly, a com- 

 parison of the phenomena. 



In cases in which we cannot bring 

 the phenomena to the test of direct 

 inspection at all, or not in a manner 

 sufficiently precise, but must judge of 

 their resemblance by inference from 

 other resemblances or dissimilarities 

 more accessible to observation, we of 

 course require, as in all cases of ratio- 

 cination, generalisations or formulae 

 applicable to the subject. We must 

 reason from laws of nature ; from the 

 uniformities which are observable in 

 the fact of likeness or unlikeness.' 



§ 3. Of these laws or uniformities, 

 the most comprehensive are those 

 supplied by mathematics ; the axiom* 

 relating to equality, inequality, and 



* Supra, book i. ch. v. § 1, and book i; 

 ch. V. §5. 



