SCIENCE AND DEMONSTRATION 229 



what are most remote are mainly universals, while what are nearest 

 are singulars : things mutually opposed to one another.&quot; This 

 distinction between the order of our experience and that of reality 

 is an important one. Acquaintance with &quot; particular &quot; facts of 

 sense experience is the beginning of all our knowledge ; while its 

 ultimate goal is an intellectual understanding of the &quot; universal &quot; or 

 common natures, the unifying specific types, or forms, or essences 

 (e So?), which are the source of their uniform activities, which 

 reveal to us the laws of their nature, and form the ground of all 

 our universal or scientific judgments concerning them, including, 

 of course, the consequent scientific (demonstrative or explanatory) 

 understanding of the (contingent) particulars as embodying these 

 (necessary) universals. When we have reached this understanding 

 of the &quot; kind &quot; or &quot; species,&quot; we have the key to all scientific 

 knowledge of the individuals in which the &quot; kind &quot; or &quot; species &quot; 

 is embodied. But how do we reach such knowledge of the uni 

 versal type ? 



Having in mind such an abstract science as geometry, Aris 

 totle answered, and rightly, that we get our definitions, which are 

 the mental expression of this knowledge, by abstracting concepts 

 from sense-data, comparing those concepts, and seeing intuitively 

 self-evident relations arise between the latter. 1 Sense experience 

 is necessary, no doubt, in order to furnish us with the concepts 

 of the common natures or essences, but these latter are not them 

 selves empirical facts ; they are not sensible, but intelligible ; they 

 are apprehended in the sense-data by intellectual abstraction and 

 intuition ; and what is true of those abstract objects of intellectual 

 thought is necessarily and universally true of the concrete par 

 ticulars which embody them ; while there is, besides, in each 

 particular, empirical fact, much that is contingent, and, therefore, 

 scientifically unknowable. 2 Thus, according to Aristotle, &quot;all 

 science is of the necessary and universal &quot; ; while, at the same time, 

 science gives us genuine knowledge about the particular pheno 

 mena of our sense experience, inasmuch as these latter are em 

 bodiments or realizations of universal natures or essences. 



253. RESTRICTED SCOPE OF ARISTOTELEAN &quot; SCIENCE &quot;.The explana 

 tion just outlined is quite satisfactory in its application to abstract metaphysics 

 and mathematics : the ultimate laws conceived by the mind in thinking about 

 real being laws of thought, as they are called and also the fundamental 



1 Cf. JOSEPH, op. cit., p. 355 ; WINDELBAND, History of Philosophy, pp. 136-43. 



2 WlNDELBAND, ibid., p. 143. 



