448 INTRODUCTION TO PHILOSOPHY OF SCIENCE 



MATHEMATICAL IDEALISM 



Jeans begins, as does Eddington, with the general fact of 

 science as a system of symbols attempting to portray the 

 character of a world which is directly revealed. But the given 

 world proves to be one of shadows, not realities. In terms 

 of Plato's famous figure, man is imprisoned in a cave with 

 his back to the light, and he cannot observe reality but must 

 rest content with watching the shadows as they play on the 

 wall. The task of science is the task of the man in the cave, 

 viz., to classify and explain the shadows in the simplest pos- 

 sible way. 1 Many historical attempts to explain the shad- 

 ows have failed. Primitive man tried anthropomorphic 

 concepts, and the science of the last century employed me- 

 chanical concepts. Both of these attempts proved unsuc- 

 cessful. But we have at last discovered an interpretation 

 which seems to be adequate. We find that every successful 

 picture of nature which we now draw is mathematical. 2 This, 

 then, must be the magic key which unlocks reality, and our 

 only conclusion must be that nature itself is somehow more 

 congenial to the concepts of pure mathematics than to those 

 of biology or of engineering. This is not to deny that mathe- 

 matics may, in turn, be a man-made mold. But this sym- 

 bolic scheme "fits" nature in a way which surpasses those 

 already tried. 3 



It appears, then, that the shadow world is the world of 

 familiar objects. But science is not content with merely 

 accepting this realm as given; it attempts to explain. The 

 result of this attempt is the disclosure of a new realm which 

 might be called the realm of scientific objects, or symbols. 

 Here we find such things as differentials and integrals, space 

 which is curved and expanding, waves of probability and 

 entropy. An examination of these entities reveals their 

 mathematical character; in fact, it shows them to be 

 not merely mathematical but objects of pure mathematics. 

 As such they could not have been derived from our experience 



1 The Mysterious Universe (New York: Macmillan, 1932), p. 151. 



2 Ibid., p. 150. 3 Ibid., p. 158. 



