3&8 ON HUMAN UNDERSTANDING. 



there can be no intermediate idea capable of possessing- a closer connexion 

 with either proposition, and consequently fitted to enter between them. " Here, 

 then," to adopt the language of Bishop Butler, whose reasoning upon this sub- 

 ject bears a (rlose resemblance to the present, " we can go no farther. For it is 

 ridiculous to attempt to prove the truth of those perceptions whose truth we 

 can no otherwise prove than by other perceptions of exactly the same kind with 

 them, and which there is just the same ground to suspect; or to attempt to prove 

 the truth of our faculties, which can no otherwise be proved than by the use 

 or means of those very suspected faculties themselves."* 



1 may now advance a step farther, and observe that in all cases in which 

 the agreement or disagreement of two or more ideas can be immediately 

 perceived and compared together, our knowledge is of a like kind, and con- 

 sequently approaches to intuitive ; although to other persons such ideas may 

 be very remote, and require a long chain of intermediate ideas to connect or 

 separate them, or prove their agreement or repugnancy. Thus I know intui- 

 tively, or without going through the process, that the arc of a circle is less 

 than the entire circle ; that a circle itself is a line equidistant in every part 

 of it from its centre ; that the three angles of a triangle are equal to two right 

 angles ; that the square of four is sixteen. No man, however, can, perhaps, 

 have any kind of knowledge at first sight upon any of these subjects ; he 

 cannot put the extreme ideas together in such a manner as to perceive their 

 agreement or disagreement, and he is not acquainted with the intermediate 

 ideas which are to compare them, and prove their relation. If he could per- 

 ceive that relation at first sight, he would at first sight have intuitive know- 

 ledge upon the subject; and some persons have a much more comprehensive 

 power of this kind than others ; for they can perceive and compare the rela- 

 tions of ideas both more readily and more extensively. Euler was a striking" 

 example of this endowment, in regard to the science of abstract quantities : 

 Jedediah Buxton appears to have obtained a similar degree of intuitive 

 knowledge in regard to the science of numbers ; and we seem in our own 

 day to have another instance of the same kind in the very extraordinary young 

 calculator from America, not more than eight years old.f 



I have already stated, that when we cannot immediately perceive the agree- 

 ment or disagreement of two or more ideas, which we are desirous of bring- 

 ing into comparison, we are obliged to seek out for some intervening idea 

 whose agreement or disagreement with them is obvious to us ; and I have 

 also stated, that as this general search is the immediate office of the faculty 

 of reason, the knowledge thus obtained is called rational knowledge. In 

 many cases we are so fortunate as to hit upon intervening ideas whose con- 

 nexion with the one, the other, or both, as in a chain of perfect evidence, is 

 clear and distinct; and in such case, whether the reasoning consist of a 

 single step or of many, as soon as the mind is able to per(;eive the connexion 

 or repugnancy, the agreement or disagreement, of the ideas in question, the 

 degree of rational knowledge hereby obtained becomes equal, or nearly so to 

 INTUITION, and is called demonstration. If the proofs, or intervening ideas, 

 do not quite amount to this, we have necessarily an inferior degree of 

 rational knowledge, and we distinguish it by the name of belief, assent, or 

 opinion; and according to the nature of the proofs or intermediate ideas, as 

 decided by the faculty of the judgment, the opinion is rendered indubitable, 

 probable, conjectural, or suspicious. 



It is upon this comparison of two ideas, by means of a mediate idea expressed 

 or understood, that most of our moral information or common knowledge 

 would be found to depend, if we were to analyze it. Thus, on going into the 

 street, and hearing- a man whom 1 am acquainted with asking which is the 

 way to London Bridge, I may, perhaps^ observe to a by-stander, *' That man 

 ought to know the way." The by-stander immediately compares the two 



* Analogy of Religion, Natural and Revealed. Of Personal Identity, forming Diss. I. 



t See "Some account of Zerali Colburn, an American child, who possesses some very remarkable po\y- 

 ers of solving queslions in arithmetic, by computation without writing, or any visible contrivance. "-r- 

 Nicholspn's Journal of Nat. Phil. vol. xxxiv. p. 5. 



