Iviii PREFACE. 



has given us of it, in the fame Commentary upon Ariftotle's Cate- 

 gories. The work I mean is entitled, tts^i tuv dvTix.Bi{x,£vuv ; that is, 

 Cojicerning Oppofitcs ; upon which fubjed Ariftotle has added a Dif- 

 fertation to his Book of Categories, wherein he has followed Archy- 

 tas moft clofely, particularly his Fourfold Divifion of Oppofites is the 

 fame with that of Archytas, and exprefled in the fame words ; and 

 in explaining the members of this divifion, Simplicius has obferved 

 that Archytas is more full and accurate than Ariftotle : And all this 

 ■he has done, without fo much as ever mentioning the name of 

 Archytas. 



The dodrine of the Categories Ariftotle has very properly made 

 the foundation of his whole Logical Syftem ; for, as I have obferved 

 elfewhere, there could have been no Science of Logic without it, nor 

 indeed Science of any kind, as there could have been no definition. 

 Now, I think it is highly probable that thofe Pythagorean philofo^ 

 phers, having gone fo far in the Logical Syftem as to have explained 

 the nature of fimple terms, that they would cany their inveftigations 

 farther, to Propofitions and Syllogifms. 



4fc?,This might not appear fo probable, if we were not well afTured 

 that the Pythagoreans, in their School, had a complete fyftem of Phi- 

 lofophy, comprehending not only Phyfics, Metaphyfics, and Morals, 

 but alfo Logic, or Dialedic, as it was then called. This we are told 

 by Jamblichus, in his Life of Pythagoras, where he fays that Science 

 in general was treated of in that School, and the method of Demon- 

 ftration. Definition, and Divifion explained, as may be learned, 

 fays he, from Ptyhagorean books yet extant *. Now I think it i& 

 certain that the Pythagoreans could not have explained what De- 

 monftration was, without laying down the dodrine of Propofitions 

 and Syllogifms ; at leaft Ariftotle thought fo j for the intention of 



his 



• Sea."i6T. 



