218 SCIENCE IN GRECO-ROMAN ANTIQUITY 



in a necessary manner in the same way as a particular 

 fact to its cause. The obj ects of science can be classified, 

 as regards their matter, in two groups, according as they 

 arise directly or not from sensible observation. 



When the object is not directly related to sensation, 

 as is the case with mathematical facts, the science can 

 be rigorously constituted, because there are a number 

 of primary conceptions from which consequences can be 

 inferred by means of reasoned deduction. For this it 

 is necessary that these primary conceptions should be 

 as logical and as few as possible. The mind is then 

 master both of the form and of the matter of the 

 science, since the latter contains no element foreign to 

 reason. 



The sciences which are based upon sensible observa- 

 tion show, like mathematics, a disagreement between 

 form and matter, between a collection of data and a 

 chain of reasoning based on these data. In this case, 

 however, the matter is composed of the individual 

 elements revealed to us by sensation, which can be 

 classified according to the genus, species, etc., to which 

 they belong. In order to make this classification it is 

 necessary in the first place to have recourse to analogical 

 reasoning founded on observation, but, when the classi- 

 fication has once been effected, a deductive syllogism 

 enables each thing to be assigned its place in the 

 universe. 



To the Greeks, there was no radical opposition 

 between the inductive and the deductive syllogism. 

 When, having a knowledge of the science, we reason by 

 deduction, we are reproducing the order of nature which 

 creates individuals as a function of the genus and species 

 to which they belong. On the other hand, in order to 

 acquire a knowledge of the science we must start from 

 individual observations and have recourse to inductive 

 syllogism. " Men, horses and mules are long-lived. 

 Now men, horses and mules are animals which have no 



