WHY THE ABSTRACT IS THE SCIENTIFIC. 143 



Outer Substances and Objects to which we subse- 

 quently apply them. So it is, also, that Points and 

 Lines which are really the Domain of the Science 

 of Geometry, the leading (relatively " Concrete ") 

 branch of Mathematics and Units or Thought-Points, 

 the Subject-Matter or Domain of Arithmetic (or the 

 Calculus), another (and the more Abstract) branch of 

 Mathematics; that the Mathematics, in fine, are or 

 belong to The Scientifically Positive or Governing 

 Domain of Being ivliich is "The Abstract ; " as against 

 the whole world of Sensibly Real Things, which are 

 The Concrete. This happens while, at the same time, 

 this whole Abstract Domain of Being is, from the Na- 

 tural, Real, or Materialistic Point of View, no Being 

 at all ; a mere congeries of Pure Nothings ; a Set of 

 Ideal Positings (Puttings of Points) and Cuts of mere 

 External Yacant Space, or still more subtly, of 

 Thought-Space ; or of still other Pure Nothings. 



171. But why is this Nothing-Realm, The Abstract, 

 assumed, as in the last preceding paragraph, to be 

 more cognate or closely allied with Science, than the 

 Real World of Objective or Concrete Things ? It is 

 because the outer Real World is Nature ; or has the 

 same alliance with Nature which the Abstract World 

 has with Science ; and because Nature is Spon- 

 taneous and utterly (or, at least, seemingly so) 

 Irregular. There are, for example, positively no 

 Straightnesses or Straight Lines in Nature. The near- 

 est approach to Straightness in her domain is, per- 

 haps, in the Edges of Crystals ; but even these suf- 

 ficiently magnified, or, at any rate, when tested by 



