160 JAMES A. WEISHEIPL 



Robert Kilwardby, on the other hand, represents a different 

 tradition in medieval thought.-" His is the Platonic tradition of 

 Robert Grosseteste, Pseudo-Grosseteste and Roger Bacon, 

 which considered natural science ordained to the mathematical, 

 and mathematics ordained to metaphysics. The Platonic hier- 

 archy of the sciences was seen to correspond to a real priority 

 of forms in nature, not, of course, existing apart from sensible 

 reality, but within physical bodies. Thus motion and sensible 

 qualities, the object of natural science, are radicated in the prior 

 forms of pure quantity, the object of mathematics; the forms 

 of quantity, in turn, are radicated in the prior form of nude 

 substance, the concern of metaphysics. Kilwardby, discussing 

 the four mathematical sciences, sees a perfect hierarchy of 

 priority and dignity among the mathematical forms. The 

 lowest of all the mathematical sciences is astronomy, for it con- 

 siders celestial motion through the principles of geometry; hence 

 astronomy is prior to and more abstract than natural science. ^^ 

 Since discrete quantity is simpler and prior to extension, all 

 the sciences which deal with number are prior to geometry. 

 Among these the lower is the ideal harmony of numerical 

 proportions; the science of numerical harmony, therefore, is 

 prior to geometry.-'' The highest and most abstract of all the 

 mathematical sciences is arithmetic, or algebra, quia ipsa ut 

 sic, nulla aliarum indiget.^° Thus arithmetic, the sciences of 

 pure number, is quasi mater aliarum [scientiarum].^^ But as 

 Kilwardby failed to distinguish the numerical " unity " dis- 

 cussed in mathematics from the entitative " unity " convertible 

 with being, he said that it belongs to the metaphysician to 

 explain the cause of plurality in mathematics.^" 



It may perhaps be a fair interpretation of Kilwardby 's mind 



"'' See my " Albertus Magnus and the Oxford Platonists," in Proceedings Am. 

 Cath. Phil. Assoc, XXXII (1958), 124-139. 



^** Kilwardby, De ortu scientiarum, cap. 16 ad 1. Meiton College, Oxford, MS 

 261, fol. 25v. 



^* Ibid., cap. 24 ad 4, fol. 32ra. 



*Ubid., cap. 19, fol. 27va. 



'^Ibid., cap. 22, fol. 28vb. 



^'^Ibid., cap. 24 ad 1, fol. 29rb; also cap. 14 ad 2, fol. 24vb. 



