DEMONSTRATION AND NECESSARY TRUTHS. 



t55 



pression, "a bent line," not by the 

 expression, " a straight line." * 



The preceding argument, which is, 

 to my mind, unanswerable, merges, 

 however, in a still more comprehen- 



• Dr. Whowell {Philosophy of Discovery, 

 p. 289) thinks it unreasonable to contend 

 that we know by experience that our idea 

 of a line exactly resembles a real line. "It 

 does not appear," he snys, *' how we can 

 compare our ideas with the realities, since 

 we know the realities only by our ideas." 

 We ki)Ow the realities by our sensations. 

 Dr. Whewell surely does not hold the "doc- 

 trine of perception by means of ideas," 

 which Reid gave himself ao much trouble 

 to refute. 



Jf Dr. Whewell doubts whether we com- 

 pare our ideas with the corresponding 

 ^ellsations, and assume that they resemble, 

 let me ask on what evidence do we judge 

 that a portrait of a person not present is 

 like the original. Surely because it is like 

 our idea, or mental image of the person, and 

 because our idea is like the man liimself . 



Dr. Whewell also says, that it does not 

 appear why this resemblance of ideas to 

 thu sensations of which they are copies, 

 should be spoken of as if it were a pecu- 

 liarity ot one class of Ideas, those of space. 

 My reply is, that I do not so speak of it. 

 The peculiarity I contend for is only one 

 of degree. All our ideas of sensation of 

 course resemble the corresponding sensa- 

 tion.s, but they do so with very different 

 d egrees of exactness a 1 ■ d of reliabili t y. No 

 one, I presume, can recall in imagination 

 H colour or an odour with the same dis- 

 tinctness and accuracy with which almost 

 every one can mentally reproduce an image 

 of a straight line or a triangle. To the ex- 

 tent, however, of their capabilities of ac- 

 curacy, our recollections of colouis or of 

 odours may serve as subjects of experi- 

 mentation, as well as those of lines and 

 spaces, and may yield conclusions which 

 will be true of their external prototypes. 

 A person in whom, either from natural 

 gift or from cultivation, the impressions 

 of colour were peculiarly vivid and distinct, 

 if asked which of two blue flowers was of 

 the darker tinge, though he might never 

 have compared the two, or even looked at 

 them together, might be able to give a 

 confident answer on the faith of his dis- 

 tinct recollection of tiie colours ; that is. 

 he miglit examine his mental pictures, and 

 find there a property of the outward ob- 

 jects. But in hardly any case except tiiat 

 of simple geometrical forms, could this be 

 done by mankind generally, with a degree 

 of assurance equal to that which is given 

 by a contemplation of tlie objects them- 

 selves. Persons differ most widely in the 

 precision of their recollection, even of 

 forms : one person, when he has looked 

 any one in the face for half a minute, can 



sive one, which is stated most clearly 

 and conclusively by Professor Bain. 

 The psychological reason why axioms, 

 and indeed many prof)Ositions not 

 ordinarily classed as such, may be 

 learnt from the idea only, without 

 referring to the fact, is that in the 

 process of acquiring the idea we have 

 learnt the fact. The proposition is 

 assented to as soon as the terms are 

 understood, because in learning to 

 understand the terms we have ac- 

 quired the experience which proves 

 the proposition to be true. " We re- 

 quired," says Mr. Bain,* "concrete 

 experience in the first instance to at- 

 tain to the notion of whole and part ; 

 but the notion, once arrived at, implies 

 that the whole is greater. In fact, 

 we could not have the notion without 

 an experience tantamount to this con- 

 clusion When we have mas- 

 tered the notion of straightness, we 

 have also mastered that aspect of it 

 expressed by the affirmation that two 

 straight lines cannot enclose a space. 

 No intuitive or innate powers or per- 

 ceptions are needed in such cases. 



We cannot have the full 



meaning of Straightness, without go- 

 ing through a comparison of straight 

 objects among themselves and with 

 their opposites, bent or crooked ob- 

 jects. The result of this comparison 

 is, inter alia, that straightness in two 

 lines is seen to be incompatible with 

 enclosing a space ; the enclosure of 

 space involves crookedness in at least 

 one of the lines." And similarly in 

 the case of every first principle,+ 

 •' the same knowledge that makes it 



draw an accurate likeness of him from 

 memory ; another may have seen him every 

 day for six months, and hardly know 

 whether his nose is long or short. But 

 everybody has a perfectly distinct mental 

 image of a straight line, a circle, or a rec- 

 tangle. And every one concludes confi- 

 dently from the.se mental images to the 

 corresponding outward things. The truth 

 is, that we may, and continually do, study 

 nature in our recollections, when the ob- 

 jects themselves are absent ; and in the 

 case of geometrical forms we can perfectly, 

 but in most other cases only imperfectly, 

 trust our recollectiona. 

 * Logic, i. 222. f Ibid. 226. 



