CELESTIAL ]\IOVERS IN MEDIEVAL PHYSICS 155 



causal dependencies between principle and conclusion, this 

 knowledge would not deserve the name of science. The mathe- 

 matical principles of astronomy are themselves demonstrated in 

 one of the purely mathematical sciences. Moreover, in theory 

 " mathematical principles can be applied to motion," ^~ and 

 sometimes the application is clear. But very often geometrical 

 figures and principles must be assumed as applicable to the 

 celestial phenomenon under consideration, as in the case of 

 Eudoxus' four spheres to explain the motions of Jupiter, Cal- 

 lippus' seven spheres and Ptolemy's epicycle. Nevertheless, the 

 relationship between the principles assumed, even assumed as 

 applicable, and the celestial phenomenon to be saved can be 

 one of necessity. This connection of necessary dependency of 

 the conclusion on the assumed principles is sufficient to estab- 

 lish astronomy as a demonstrative science. It was in this sense 

 that St. Thomas and St. Albert interpreted Aristotle's state- 

 ment that, " It is the business of the empirical observers to 

 know the fact, of the mathematicians to know the reasoned 

 fact." ^^ Between the mathematical principle and the quantified 

 aspect of the fact, there may well be a propter quid relationship, 

 that is, the immediate, proper and convertible middle term of 

 the measured facts of the conclusion may be the mathematical 

 principle invoked. To this extent astronomy should be called, 

 and was called a true science subalternated to mathematics. 

 To be sure, astronomical science fell far short of the ideal of 

 scientific knowledge described by Aristotle in the Posterior 

 Analytics. It did not demonstrate through the immediate, 

 physical cause of celestial phenomena; at best, it demonstrated 

 through a kind of extrinsic formal cause (secundum causam 

 formalem remotam) of the natural phenomena." Even this, as 

 has already been suggested, is most often in a tentative, dia- 

 lectical and hypothetical manner. 



Considered in relation to the physically real celestial bodies 



^^ St. Thomas, In Boeth. de Trin., q. 5, a. 3 ad 5. 



"^^Post. Anal., 1, c. 13, 79a2-3. St. Thomas, In I Post. And., lect. 25, n. 4; St. 

 Albert, Lib. I Post. Anal, tr. Ill, c. 7. 



" St. Thomas, In I Post. Anal., lect. 25, nn. 4 & 6. 



