eh. n.] THE SCOPE OF PHILOSOPHY. 37 



" the relation of one set of weights to their velocities equals 

 the relation of the other set of velocities to their weights." 

 So geometry in ancient times treated of questions relating to 

 particular figures ; but since the great discovery of Descartes, 

 it has dealt -with questions relating to any figure whatever. 

 So, in the progress of analytical mathematics, we have first 

 arithmetic which "can express in one formula the value of 

 a particular tangent to a particular curve;" and, at a later 

 date, algebra, which can express in one formula the values of 

 all possible tangents to a particular curve ; and, at a still 

 later date, the calculus, which can express in one formula 

 the values of all possible tangents to all possible curves. 1 



Fourthly, science is continually more and more clearly 

 differentiated from ordinary knowledge by the continually 

 increasing abstractness of the relations which it classifies. 

 This proposition is involved in the preceding one. For 

 clearly the progress towards higher and higher generality is 

 the progress towards a knowledge more and more inde- 

 pendent of special circumstances — towards a study of the 

 phenomena most completely disengaged from the incidents of 

 particular cases. 



And finally science differs from ordinary knowledge in ics 

 higher degree of organization — in the far greater extent to 

 which it carries the process of coordinating groups of like 

 orders of relations, and subordinating groups of higher and 

 lower orders of relations. This we habitually regard as such 

 a fundamental characteristic of scientific knowledge that we 

 grant the title of science to some departments of inquiry 

 which possess it, in spite of the fact that the only prevision 

 which is possible in them is neither certain nor quantitative. 

 Take, for instance, the case of biology. If quantitative pre- 

 vision were the only thing which distinguishes science, we 

 could hardly pretend to possess a science of life. Our power 

 of prevision in biology is for the most part strictly limited to 

 1 Spencer's Assays," 1st series, pp. 177 — 180. 



