Chap. III. ANTIENT METAPHYSICS. 395 



all fcience ; for, if it were not true, we could affirm and deny the 

 fame thing at the fame time, fo that nothing would be either true or 

 falfe. It is, as I have obferved, by difcovering this repugnancy and 

 contradidbion in the contrary of the geometrical axioms above men- 

 tioned, that we perceive' their evidence. And, if it was by inference 

 and deduction that we perceived this contradiction, I would fay, as 

 fome have faid, that they were demonftrable. But, as we perceive it 

 intuitively, and by one fmgle ad of the intellecSl *, I think they are 

 felf-evident propofitions of intuitive, not demonftrative truth. 



There is another logical axiom, which belongs alfo to the whole ca- 

 tegories, and which Ariftotle has made the foundation of his dodrine 

 of the fyllogifm, viz. ' What can be praedicated of any general, may 



* be praedicated of every particular comprehended under that general;* 

 or, as the fchoolmen have exprcfled it, ^lod verum eft de toto^ verum 

 eft de omni. 



There is alfo a third axiom, which applies to all the categories, and 

 is the foundation of all true phyfics and metaphyfics, viz. ' That no- 



* thing can be produced without a caufe ;' or, in other words, ' That 



* nothing can come out of nothing ;' an axiom, of which the truth 

 was admitted by all the philofophers of antiquity, by Epicurus as 

 well as Plato, who have both made it the foundation of their cof- 

 mogeny f. And Ariftotle tells us, that all the phyfiologifts, with- 



D d d 2 out 



• • M/« ivijioXvif as the Commentators upon Ariftotle exprefs it, whereas, in the pro- 

 ccfs of reafoning, there are TtXHom £7r<i3«A««, more afts or exertions of the intelledt up- 

 on the queftion propofed. 



f See Plato in the Timaetif, p'. 1046- fdit. Ficini. n«v ra y^yjawfye* vt* atnov nut 

 i\ Kvicyxftf y.iyvirxtf vxDTi itct^ (^vittrti x.o*i'i *tiriov yiHo-iv <r;^«v. And EpicurUS fayS, in Lu- 



cretius, 



Principium hinc cujus nobis exordia fumet, 



Nulhm rem e nihilo gigni divinitus unquam. Lik i. in initir 



