Apsil 8, 1910] 



SCIENCE 



529 



over-individual purposes, -with those uni- 

 versal agreements, with that world-wide 

 consensus of opinion, in which all sane men 

 unite; in brief, mathematics and meta- 

 physics each belong in the group which 

 Miinsterberg calls the "normative sci- 

 ences. ' ' There is therefore a certain sense, 

 which in passing I merely mention, but do 

 not urge, in which all consideration of 

 number and quantity and limits which the 

 mathematical philosophers have handed 

 down, increases the debt of physics to 

 metaphysics. 



Sound method in drawing inferences is 

 a branch of science to which the physicist 

 owns no copyright, but one in which he 

 may claim to be fairly well versed. For 

 this method he is indebted in no small de- 

 gree to the development of logic in the 

 hands of the metaphysician. In brief, 

 modern physics, at its very inception 

 in the seventeenth century, found that 

 the schoolmen had already furnished it 

 with a set of beautiful tools in the shape 

 of fundamental logical ideas, including 

 "precise definition," "classification," and 

 "fallacies." Even Bacon when "preach- 

 ing the funeral sermon of scholasticism," 

 used the accurate methods of the school- 

 men. 



Space and time, as continuous quanti- 

 tities and as limiting conditions for all 

 phenomena, is another conception of no 

 small value which we have inherited from 

 the Greeks. The critical examination of 

 our conception of time, which was given 

 by Einstein^^ some five years ago, and per- 

 haps even earlier by Lorentz, had, among 

 other interesting and more valuable fea- 

 tures, the following: He showed clearly 

 — and, so far as I am aware, for the first 

 time— just what kind of "time" we have 

 been and are still using in ordinary New- 

 tonian mechanics, namely, time such as 



''Ann. der Physik (4), 17, 891-921 (1905). 



would result from having all our clocks 

 controlled by a single central time-keeper 

 ivhicJi would transmit its controlling sig- 

 nals with absolute instantaneity. 



The clear definitions of synchronous 

 clocks and simultaneity— in brief the idea 

 of local time— may be considered as be- 

 longing either to physics or to mathematics 

 — but surely the exposition in which Ein- 

 stein has taught us just what kind of time 

 we have been unconsciously using for more 

 than two centuries is a metaphysical con- 

 tribution of high order. 



The dangers of mere nominalism, or, if 

 you prefer, extrapolation, by which I 

 mean the danger of ascribing to any phys- 

 ical system a set of properties which we 

 have merely learned to associate with its 

 name, has been clearly pointed out in the 

 history of philosophy. Due regard for 

 this warning would, I believe, have saved 

 many pages that have been written con- 

 cerning the ether— especially those devoted 

 to a determination of its inertia, its weight, 

 and its place in the periodic table of Men- 

 delejeff. 



V. LIMITATIONS OF SCIENCE 



Fifthly and lastly the metaphysician has 

 rendered the inestimable service of point- 

 ing out to the experimental investigator 

 the paradox that his greatest strength lies 

 in his confessed limitations. Each of the 

 particular sciences views phenomena from 

 its own particular angle; but there is, I 

 fear, sometimes— often, indeed— a ten- 

 dency for the student of physics to think 

 that in measuring, say, the inertia of a 

 body, he is in some sense getting at the 

 ' ' quantity of matter " in it ; or to put it in 

 another way, there is often a tendency to 

 think that in determining the mass, on a 

 beam balance, he is perhaps doing some- 

 thing more fundamental than merely de- 

 termining inferentially the ratio of the 



