164 



REASONING. 



tions with those facts of experience 

 on which, as evidence, they now con- 

 fessedly rest.* 



CHAPTER VI. 



THE SAME SUBJECT CONTINUED. 



§ I. In the examination which 

 formed the subject of the last chapter 



* The Quarterly Reviexo for June 1841 

 contained an article of great ability on Dr. 

 Whewell's two great ^rorks (since acknow- 

 ledged and reprinted in Sir John Herschel's 

 Essays) which maintains, on the subject 

 of axioms, the doctrine advanced in the 

 text, that they are generalisations from 

 experience, and supports that opinion by 

 a line of argument strikingly coinciding 

 with mine. When I state that the whole 

 of the present chapter (except the last four 

 pages, added in the fifth edition) was 

 written before I had seen the article, (rhe 

 greater part, indeed, before it was pub- 

 lished,) it is not my object to occupy the 

 readei's attention with a matter so unim- 

 portant as the degree of oiiginality which 

 may or may not belong to any portion of 

 my own speculations, but to obtain for an 

 opinion which is opposed to reigning doc- 

 trines the recommendation derived from 

 a striking concurrence of seiuiment be- 

 tween two inquirers entirely independent 

 of one another. I embrace the opportunity 

 of citing from a writer of the extensive 

 acquirements in physical and metaphysical 

 knowledge and the capacity of systematic 

 thought which the article evinces, passages 

 so remarkably in unison with my own 

 views as the following :— 



"The truths of geometry are summed 

 up and embodied in its definitions and 

 axioms. . . . Let us turn to the axioms, 

 and what do we find ? A string of proposi- 

 tions concerning magnitude in the abstract, 

 which are equally true of space, time, 

 force, number, and every other magnitude 

 suscepiible of aggregation and subdivision. 

 Such propositions, where they are not 

 mere definitions, as some of them are, carry 

 their inductive origin on the face of their 

 enunciation. . . . Those which declare that 

 two straight lines cannot enclose a space, 

 and that two straight lines which cut one 

 another cannot both be parallel to a third, 

 are in reality the only ones which express 

 characteristic properties of space, and these 

 it will be worth while to consider more 

 nearly. Now the only clear notion we can 

 form of straightuess is uniformity of direc- 

 tion, for space in its ultimate analysis is 

 nothing but an assemblage of distances and 

 directions. And (not to dwell on the 

 notion of continued contemplation, i.e., 

 wental experience, as included in the very 



into the nature of the evidence of those 

 deductive sciences which are commonly 

 represented to be systems of necessary 

 truth, we have been led to the follow- 

 ing conclusions. The results of those 

 sciences are indeed necessary, in the 

 sense of necessarily following from 

 certain first principles, commonly 

 called axioms and definitions ; that 

 is, of being certainly true if those 

 axioms and definitions are so ; for 



idea of uniformity : nor on that of transfer 

 of the contemplating being from point to 

 point, and of experience, during such 

 transfer, of the homogeneity of the mterval 

 passed over) we cannot even propose the 

 proposition in an intelligible form to any 

 one whose experience ever since he was 

 born has not assured him of the fact. The 

 unity of direction, or that we cannot march 

 from a given point by more tlian one path 

 direct to the same object, is matter of prac- 

 tical experience long before it can by pos- 

 sibility become matter of abstract thought. 

 We cannot attempt mentally to exemplify the 

 conditions of the assertion in an imaginary 

 case opposed to it, without violating our 

 habitual recollections of this experience, and 

 defacing our mental picture of space as 

 grounded on it. What but experience, we 

 may ask, can possibly assure us of tha 

 homogeneity of the parts of distance, time, 

 force, and measurable aggregates in gene- 

 ral, on which the truth of the other axioms 

 depends? As regards the latter axiom, 

 after what has been said it must be clear 

 that the very same course of remarks 

 equally applies to its case, and that its 

 truth is quite as much forced on the mind 

 as that of the former by daily and hourly 

 experience, . . . including always, be it 

 observed, in our notion of experience, that 

 which is gained by contemplation of the in- 

 ward picture which the mind forms to itself 

 in any proposed case, or which it arbitrarily 

 selects as an example — such picture, in virtue 

 of the extreme simplicity of these primary re- 

 lations, being called up by the imagination 

 with as much vividness and clearness as 

 could be done by any external impression, 

 which is the only meaning we can attach to 

 the word intuition, as applied to such rela- 

 tions." 



And again, of the axioms of mechanics : 

 --"As we admit no such propositions, 

 other than as truths inductively collected 

 from observation, even in geometry itself, 

 it can hardly be expected that, in a science 

 of obviously contingent relations, we should 

 acquiesce in a contrary view. Let us take 

 one of ttiese axioms and examine its evi- 

 dence : for instance, that equal forces per- 

 pendictxlarly applied at the opposite ends 

 of equal arms of a straight lever will balance 

 each other. What but experience, we may 

 sisk, in the first place, can possibly inform 



