82 SCIENCE AND THE HUMAN MIND 



is, that at Oxford and Cambridge the governing power 

 has always rested with the teachers and not with the 

 students, as at Bologna and to some extent in Scotland, 

 where the election of the Rector is one of the last 

 traces of undergraduate control. 



As early as the Carolingian period, the academic 

 subjects of study had settled down into an elementary 

 trivium, comprising grammar, rhetoric and dialectic, 

 subjects which dealt with words, and a more advanced 

 quadrivium music, arithmetic, geometry and astro- 

 nomy, which were supposed, at all events, to deal with 

 things. Music contained a half-mystical doctrine of 

 numbers, geometry merely a series of Euclid's pro- 

 positions without the proofs, while arithmetic and 

 astronomy were esteemed chiefly because they taught 

 the means of fixing the date of Easter. All were 

 studied as a preparation for the study of the sacred 

 science theology. All through the Middle Ages, this 

 division of the subjects of study held good for the 

 elements of academic learning, and, with the growing 

 interest in philosophy, that study was merely super- 

 added to the simpler logical dialectic. 



The old controversy between Plato and Aristotle 

 on the nature of the idea of universals found its way 

 into the commentaries of Porphyry and Boetius, and 

 so reached the mediaeval mind. What is the meaning 

 of the power of classification ? Are the individuals 

 the only realities, the universals existing merely in 

 and with the objects of sense as their essence, as taught 

 by Aristotle, or even only as names or mental concepts 

 as the extreme Nominalists held ? Or had the ideas 

 or universals an existence apart from the phenomena 

 or the isolated beings, as in Plato's philosophy ? 



