S9^ A N T I E N T METAPHYSICS. ^ook V. 



out exception, of his tiine, and before his time, agreed in that prin- 

 ciple *. 



Thefe are axioms belonging to all the categories in general ; but 

 there are others which belong to fome of ihem in particular ; fuch as 

 concerning fubQance, that it muft neceffarily exiit by itfelf, and is the 

 ground-work or fubjecff, in which all the other categories are inherent ; 

 fo that it is an axiom relating to them, that they cannot exift by 

 themfclves. And, with refped to the category qf relation in particu- 

 lar, it is an axiom of which i have had occafion to make ufe t» ' That 



* it cannot fubfift without two things, at leaft, exifting at the fame 



* time.' And alfo, with refped to the category of fufFering, it is an 

 axiom, * That, where there is a patient, there mufl be alfo an agent.' 

 Many more axioms, relating to other things befides quantity, might 

 be enumerated ; but thefe are fufficient for the prefent purpofe. And 

 it is to be obferved, that the evidence of them is the fame as of the 

 geometrical axioms, namely, that the fuppofition of the contrary im- 

 plies a contradidion and impofhbility, which the mind immediately 

 perceives. 



Thus, I have endeavoured to give fome account of the truth of 

 axioms, without pretending that they are capable of demonftration ; 

 for, if they could be demonftrated, they would not be axioms ; and, if 

 there were no axioms, and every thing was to be demonftrated, there 

 could be no demonftration ; for the fame reafon, that, if there were 

 no categories, or general clafTes, to which things could be ultimately 

 referred, there could not, as 1 have obferved, be any definition J. And 

 the reafon is, that, in both cafes, the thing would go on in infinitum. 



Now, 



* Arlftotle, therefore, fays, that it was y.oivn h^ct ray (Pva-ix^y, which is pretty much 

 the fame name that I.uclid gives to his axioms, viz, Ktimt uftiK:, that is, notions cona^ 

 mou to all men that have any ufe of reafon. 



f Book 2. chap. 3. p 67. 



% Book 3. chap. I. p. 317. 



