Chap. III. ANT IE NT METAPHYSICS, 393 



rent at firfl view, without inference or dedudion ; for, if A were equal 

 to C, and B equal to C, and yet A greater or leis than B, then it would 

 not occupy the fame fpace which B occupies, viz. the place of C, which 

 would be contrary to the hypothefis, laying it down, that A and B are 

 equal to C ; that is, occupy the fame fpace which C does. I therefore a- 

 gree with Proclus in the paflage above quoted, that this axiom is truly 

 an axiom, or feif-evident propofition, and that Apollonius was in the 

 wrong to feek for a demonftration of it. And accordingly Proclus 

 has fhown, that the propofition, by which he proves it, is plainly a 

 fuppofition of what is iaqueftion, or 2l petitio principiiy namely, that 

 two magnitudes, which poifefs the fame place with a third, poffefs 

 each the fame place that the other does. 



What I have faid of this firft: axiom concerning equality, will, I 

 hope, be fufficient to fliow that, not only the evidence of all the a- 

 xioms relating to equality, but of all the other axioms of Kuclid, a- 

 rifes from the inconfiftency and contradidlion to the hypothefis which 

 the mind immediately perceives there would be in luppofing the con- 

 trary; for it would be, to fuppofe the fame thing to be and not to be. If 

 a fceptic is not fatisfied with this, but inquires further, how the mind 

 perceives the connexion or contradidion betwixt the ideas in fuch pro- 

 pofuions? I anfwer that queftion by afking another, How does the 

 mind know that it perceives the two ideas ? The anfwer m.uft be, That 

 it is by confcioufncfs ; and I fay it is by the fame confcioufnefs that we 

 perceive the relation betwixt the two ideas, it being impoilible that we 

 fhould have the perception of the two ideas, and not, at the fame time, 

 perceive the relation betwixt them. 



It is by confcioufnefs, therefore, that we perceive truth ; for, with- 

 out confcioufnefs, we cannot know it to be truth. The brutes, 

 therefore, wanting confcioufnefs, have not, as Simplicius has obfer- 



D d d ved. 



