264 REASONING. 



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) are conceived by 

 us not only as true, but as universally and necessarily true. 

 Now, experience cannot possibly give to any proposition this 



with the realities, since we know the realities only by our ideas." We know 

 the realities (I conceive) by our senses. Dr. Whewell surely does not hold the 

 " doctrine of perception by means of ideas," which Eeid gave himself so much 

 trouble to refute. 



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 sensations 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 the corresponding sensations, but they do so 

 with very different degrees of exactness and of reliability. No one, I presume, 

 can recal in imagination a colour or an odour with the same distinctness and 

 accuracy 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 colours or of odours 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 colour were peculiarly 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 

 colours ; that is, he might examine his mental pictures, and find there a pro- 

 perty of the outward objects. But in hardly any case except that 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 the 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 

 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 rec- 

 tangle. 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 perfectly, but in most other cases only 

 imperfectly, trust our recollections, 



