562 



SCIENCE 



[N. S. Vol. XXXIX. No. 1007 



The nautical almanac (so you may say) is 

 the model of what applied science ought to 

 to be. The mortality table is the convenient 

 summary due to a necessary scientific evil. 

 It is a device for recording our ignorance 

 of the details of the world's mechanism 

 along with our imperfect knowledge of cer- 

 tain probable and approximate tendencies 

 to which the averages of many human lives 

 are subject. 



In other words, you may be disposed to 

 insist: "Mechanical theories are the canon- 

 ical forms towards which a growing scien- 

 tific knowledge guides our way. Compu- 

 tations of individual events in terms of in- 

 variant laws whose validity is independent 

 of time, are the models of what our scien- 

 tific ideals seek. The statistical view of 

 very complex mechanisms is an asylum in 

 which our ignorance, perforce, has to find 

 its refuge whenever, as in case of the swarms 

 of molecules and the labyrinthine com- 

 plications of organisms, the mechanical 

 view of nature, as applied by us, loses its 

 way. ' ' 



In answer to this very natural comment, 

 I am next led to say that, whether the nat- 

 ural world is a mechanism or not, the sta- 

 tistical view of nature would be, and so far 

 as we know the facts is, applicable to suffi- 

 ciently complicated systems of things and 

 events, not as a mere substitute for these 

 more exact computations which our igno- 

 rance of mechanical laws makes necessary, 

 but as an expression of a very positive, al- 

 though only probable and approximate, 

 knowledge whose type aU of the organic 

 and social sciences, as well as most aspects 

 of the inorganic sciences, illustrate. There 

 is therefore good reason to say that not the 

 mechanical but the statistical form is the 

 canonical form of scientific theory, and 

 that if we knew the natural world millions 

 of times more widely and minutely than we 

 do, the mortality tables and the computa- 



tions based upon a knowledge of averages 

 would express our scientific knowledge 

 about individual events much better than 

 the nautical almanac would do. For our 

 mechanical theories are in their essence too 

 exact for precise verification. They are 

 verifiable only approximately. Hence, 

 since they demand precise verification, we 

 never know them to be literally true. 



But statistical theories, just because they 

 are deliberate approximations, are often as 

 verifiable as their own logical structure per- 

 mits. They often can be known to be lit- 

 erally, although only approximately, true. 

 This assertion is, in its very nature, a 

 logical assertion. It is not any result of 

 any special science, or of any one group of 

 sciences. It solves no one problem about 

 vitalism. It is a general comment on the 

 value of the statistical point of view. 



But, if the assertion is true, it tends to 

 relieve us from a certain unnecessary rev- 

 erence for the mechanical form of scientific 

 theory — a reverence whose motives are 

 neither rationally nor empirically well 

 founded. It is the merit of Charles Peirce 

 to have emphasized these logical considera- 

 tions. Their importance for the study of 

 scientific methods has grown greater with 

 every year since 1891, when he began the 

 publication of his remarkable papers in the 

 Monist, entitled: "The Architecture of 

 Theories, " " The Doctrine of Necessity Ex- 

 amined ' ' and ' ' The Law of Mind. ' ' These 

 papers are fragmentary; and yet in their 

 way they are classical statements of the 

 limitations of the mechanical view of na- 

 ture, and of the significance of the statis- 

 tical view of nature. 



As I close, let me merely outline some as- 

 pects of Peirce 's extension of the statistical 

 view of nature beyond the range which 

 Maxwell's and Boltzmann's study of the 

 theory of gases directly exemplified. 



