REMAINING LAWS OF NATURE. 427 



comparison is impossible, is the appropriate scientific process for ascertain- 

 ing resemblances and dissimilarities, and is the sum total of what Logic 

 has to teach on the snbject. 



An undue extension of this remark induced Locke to consider reasoning 

 itself as nothing but the comparison of two ideas through the medium pf 

 u third, and knowledge as the perception of the agreement or disagreement 

 of two ideas ; doctrines which the Condillac school blindly adopted, with- 

 out the qualifications and distinctions with which they were studiously 

 guarded by their illustrious author. Where, indeed, the agreement or dis- 

 agreement (otherwise called resemblance or dissimilarity) of any two things 

 is the very matter to be determined, as is the case particularly in the sci- 

 ences of quantity and extension ; there, the process by which a solution, if 

 not attainable by 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 knowledge that bodies fall to the 

 ground is not a perception of agreement or disagreement, but of a series 

 of physical occurrences, a succession of sensations. Locke's definitions of 

 knowledge 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 rep- 

 resents, between the ideas of the two phenomena, but between the phenome- 

 na themselves. This mistake has been pointed out in an earlier part of our 

 inquiry,* and we traced it to an imperfect conception of what takes place in 

 mathematics, where very often the comparison is really made between the 

 ideas, without any appeal to the outward senses; only, however, because 

 in matheinatics a comparison of the ideas is strictly equivalent to a com- 

 parison 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 learned from the object itself by mere contem- 

 plation 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 can not inclose a space ; accordingly 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 comparison of the phenomena. 



In cases in which we can not 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 ra- 

 tiocination, generalizations or formul£e 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 sup- 

 plied by mathematics ; the axioms relating to equality, inequality, and pi'o- 

 portionality, and the various theorems thereon founded. And these are the 

 only Laws of Resemblance Avhich require to be, or which can be, treated apart. 

 It is true there are innumerable other theorems which affirm resemblances 



* Supra, book i., chap, v., § 1, and book ii., chap, v., §5. 



