THOUGHTS ON BELIEF AND EVIDENCE, 245 



ness which is required in the sciences of number and magnitude, ratio- 

 cination or the deductive process is by no means the only or principal 

 means of attaining truth. It is necessary to man as an employer of lan- 

 guage with its generalisation and abstractions, and it is most important 

 both in excluding a large class of errors, limiting greatly the abuses to 

 which language is liable, and in presenting truths in various aspects, 

 leading to fresh applications of them, and exhibiting them in all possible 

 forms ; but other methods must be employed for a real exter.sion of 

 the bounds of human knowledge, and, admirable as logic may be as 

 one mode of exercise of the powers of the mind, under due discipline, 

 its merits must not be exaggerated, for, after all, the perceiving clearly 

 and certainly as a necessary truth, that what is meant by one set of 

 words arranged as a proposition is already implied in other proposi- 

 tions, the truth of which is admitted, is not to be accounted among 

 the greatest achievements of human intellect. The belief produced 

 is, that certain words express a real relation of the ideas conveyed by 

 them, which relation must first have become known by observation 

 or induction, and can only by reasoning be combined with other 

 admitted truths and set in various lights. Mathematics has the 

 advantage of its foundation in definitions, which secure its abstract 

 character, and of the wonderful variety of the relations which its 

 subjects, number, and the forms of magnitude admit. It is a wonder- 

 ful science equally admirable in its results, and in the high exercise 

 it affords to several most important faculties ; yet it is possible for it 

 to be too highly valued, and there is no inconsiderable danger of its 

 peculiar methods leading the mind astray in other inquiries. 



In all that I have said of the kinds and grounds of belief I have 

 not yet found it necessary to name intuition, and I am myself strongly 

 persuaded that the mind is incapable of reaching to any truth within 

 itself, and entirely independently of what comes from without, the 

 simplest and most universally admitted truths being believed from 

 early constant and universal experience. An axiom is only the verbal 

 expression of some relation which experience compels us all to know, 

 so that as soon as we understand the terms we admit the truth. If 

 any proof is required, the assertion cannot be called an axiom. It 

 was once thought by many philosophers that mathematical science 

 was built upon axioms — such an error now needs no refutation — the 

 axioms are laid down as a caution against assuming in our reasoning 



