234 METAPHYSICS 



the other, for an equally salutary purgation of formal studies like 

 logic and arithmetic from the taint of corruption by the irrelevant 

 intrusion of considerations of empirical psychology. 



We cannot too persistently bear in mind that there is, correspond- 

 ing to the logical distinction between the analytic and the synthetic 

 proposition, a deep and broad general difference between the wants 

 of our nature ministered to by the formal and the applied sciences 

 respectively. The formal sciences, incapable of adding anything to 

 our detailed knowledge of the course of events, as we have seen, 

 enlighten us solely as to the general laws of interconnection by which 

 all conceivable systems of true assertions are permeated and bound 

 together. In a different connection it would be interesting to de- 

 velop further the reflection that the necessity of appealing to such 

 formal principles in all reasoning about empirical matters of fact 

 contains the explanation of the famous Platonic assertion that the 

 "Idea of Good" or supreme principle of organization and order in 

 the universe, is itself not an existent, but something m eVcKeu/a TT/S 

 ownas, "transcending even existence," and the very similar declara- 

 tion of Hegel that the question whether " God " in the sense of 

 such a supreme principle exists is frivolous, inasmuch as existence 

 (Daseiri) is a category entirely inadequate to express the Divine 

 nature. For my present purpose it is enough to remark that the 

 need to which the formal sciences minister is the demand for that 

 purely speculative satisfaction which arises from insight into the 

 order of interconnection between the various truths which compose 

 the totality of true knowledge. Hence it seems a mistake to say, as 

 some theorists have done, that were we born with a complete know- 

 ledge of the course of temporal sequences throughout the universe, 

 and a faultless memory, we should have no need of logic or meta- 

 physics, or in fact of inference. For even a mind already in possession 

 of all true propositions concerning the course of events, would still 

 lack one of the requisites for complete intellectual satisfaction 

 unless it were also aware, not only of the individual truths, but of 

 the order of their interdependence. What Aristotle said long ago 

 with reference to a particular instance may be equally said univers- 

 ally of all our empirical knowledge; "even if we stood on the 

 moon and saw the earth intercepting the light of the sun, we should 

 still have to ask for the reason why." The purposes ministered to 

 by the empirical sciences, on the other hand, always include some re- 

 ference to the actual manipulation in advance by human agency of 

 the stream of events. We study mechanics, for instance, not merely 

 that we may perceive the interdependence of truths, but that we 

 may learn how to maintain a system of bodies in equilibrium, or how 

 to move masses in a given direction with a given momentum. Hence 

 it is true of applied science, though untrue of science as a whole, that 



