II24 LIFE : OUTLINES OF GENERAL BIOLOGY 



science. Each contribution is useful, indeed indispensable, as an aid 

 to the understanding of the main science beyond it; yet is ever in 

 danger of mistaking its square of contribution for that of the science 

 itself. But with physical, biological and social sciences in order, we 

 see how each of the two latter is indispensably aided by the pre- 

 ceding ones. So far, then, this first outline view of the observational 

 sciences in their succession and unity. 



But all along we have been tacitly using a science of a different 

 order, not concrete but abstract; that of logic, indispensable to 

 make our interests in our observed world scientific at all. And with 

 this it soon becomes evident that we must also take that potent 

 logic of measure and quantity which we call mathematics; which 

 has almost from the first been indispensable to the astronomer and 

 the mechanician, and next also to physicists and chemists. So now 

 we need a fourth scientific range below our threefold concrete 

 world. Besides his primary services to the physical sciences, the 

 mathematician has long been making his contribution, and that of 

 arithmetic especially, to the social world; witness his statistics, as 

 notably of social relations in terms of money-notations; and this 

 indeed so clearly that economists long mistook such studies for 

 their whole science, without properly entering the social field at all. 

 Within recent times, too, indeed within living memory, the statistical 

 worker has successfully made contributions to the understanding of 

 biology as biometrics; so we are compelled to assign to mathe- 

 matics, at its longest range, not only a square of its own, but three 

 contributory ones, underlying each of the other sciences. His services 

 are thus great and even indispensable. Yet he is apt to go too far 

 when he claims that "all science is measurement": for though the 

 more quantitative measurement each science can get the better for 

 it, its own problem, quality, and character remain in every case 

 the main thing ; so that the function of mathematics is fundamental, 

 but not supreme. The mastery of the mathematician, as such, is 

 limited to considerations of space, movement, and time, and of 

 course number; and all observed phenomena have thus to be con- 

 sidered, as far as may be. The physicist has his own distinctive con- 

 cepts, of matter and energy: and these are fundamental to the 

 understanding of living beings. Yet never is the distinctive field of 

 the biologist superseded; for nutrition and reproduction, self -main- 

 taining and species-continuing f unctionings, are a long step beyond 

 the functioning of machines; since self-adjusting, self -adapting, 

 self -repairing, and self -co-ordinating, as no machines have ever been, 

 nor can be conceived fully to be. 



The biologist, in his turn, does great work underlying the dis- 

 tinctively social field, as, for instance, in elaborating his conditions 

 for public health; and again, as eugenist, by insisting on the signifi- 

 cance of heredity for the adequate continuance of the community. 



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