176 REASONING. 



The pi'oceding argument, which is, to my mind unanswerable, merges, 

 however, in a still more comprehensive one, which is stated most clearly 

 and conclusively by Professor Bain. The psychological reason why ax- 

 ioms, and indeed many pi-opositions not ordinarily classed as such, may be 

 learned from the idea only without referring to the fact, is that in the proc- 

 ess of acquiring the idea we have learned the fact. The proposition is 

 assented to as soon as the terms are understood, because in learning to un- 

 derstand the terms we have acquired the experience which proves the propo- 

 sition to be true. " We required," says Mr. Bain,* " concrete experience in 

 the first instance, to attain 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 conclusion 



When we have mastered the notion of straightness, we have also mastered 

 that aspect of it expressed by the affirmation that two straight lines can 

 not inclose a space. No intuitive or innate powers or perceptions are 

 needed in such cases We can not have the full meaning of Straight- 

 ness, without going through a comparison of straight objects among them- 

 selves, and with their opposites, bent or crooked objects. The result of 

 this comparison is, inter alia, that straightness in two lines is seen to be 

 incompatible with inclosing a space ; the inclosure of space involves crook- 

 edness in at least one of the lines." And similarly, in the case of every 

 first principle,f " the same knowledge that makes it understood, suffices to 

 verify it." The more this observation is considered the more (I am con- 

 vinced) it will be felt to go to the very root of the controversy. 



§ 6. The first of the two arguments in support of the theory that axioms 

 are a priori truths, having, I think, been sufficiently answered; I proceed 

 to the second, which is usually the most relied on. Axioms (it is asserted) 



If Dr. Whewell doubts whether we compare our ideas with the corresponding sensations, 

 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 himself. 



Dr. Whewell also says, that it does not appear why this resemblance of ideas to the sensa- 

 tions of which they are copies, should be spoken of as if it were a peculiarity of 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 tlie corresponding 

 sensations, but they do so with very different degrees of exactness and of reliability. No one, 

 I presume, can recall in imagination a color or an odor with the same distinctness and ac- 

 curacy with which almost every one can mentally reproduce an image of a straight line or a 

 triangle. To the extent, however, of their capabilities of accuracy, our recollections of colors 

 or of odors may serve as subjects of experimentation, 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 color were peculiarl}' vivid and 

 distinct, if asked which of two blue flowers was of the darkest 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 distinct recollection of the colors ; that is, he might examine his 

 mental pictures, and find there a property of the outward objects. Bnt in hardly any case 

 except that of simple geometrical forms, could this be done by mankind generally, with a de- 

 gree of assurance equal to that which is given by a contemplation of the objects themselves. 

 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 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 every body has a perfectly distinct mental image of a 

 straight line, a circle, or a rectangle. And every one concludes confidently from these mental 

 images to the corresponding outward things. The truth is, that we may, and continually do, 

 study nature in our recollections, when the objects themselves are absent ; and in the case of 

 geometrical forms we can perfectlv, but in most other cases only imperfectly, trust our recol- 

 lections. ' * Logic, i., 222. t Jbid., 226. 



