96 MCEWEN AND MICHAEL. 



possible a comparison with the results obtained by other observers. 

 Moreover, classification is the first step toward the important object 

 of determining the uniformities and other relationships exhibited by 

 the mass of facts in question. From definitions of the individual 

 facts, and their classification into groups we pass, by induction, to a 

 description of the observed system as a whole, i. e., to an empirical 

 law Though the observed system is only a fragmentary sample of 

 the "universe" it represents, the empirical laws are just as real, 

 insofar as they describe that sample, as are the individual facts. 

 The gain in simplicity and conciseness is made, of course, at the 

 expense of detail, as is true of any summary. Further, experience 

 shows that, as a rule, there is not in nature a one-to-one correspondence 

 between observations of one kind and those of another kind. A 

 plurality of causes, influences, factors, or w^hatever one may call 

 them, must, in general, be considered, and their mutual relations 

 taken into account. Considered quantitatively, this method of 

 acquiring knowledge is statistical mathematics,^ the ideal of which is 

 attained when the empirical laws and assignment of a- value to each 

 kind of quantity but one serves to determine the latter. 



In former times, when the fundamentals inherent in the deductive 

 method were largely the result of introspection, attention of scholars 

 was directed mainly to these fundamentals and their logical conse- 

 quences. Initial concepts and deductions from them were regarded 

 as the realities of nature, while direct evidence of the senses was dis- 

 credited. In spite of the downfall of scholasticism four centuries ago 

 there still is a strong tendency to regard observations as secondary 

 in importance, and even of no importance when they have no appar- 

 ent bearing upon some dominant theory or fail to fit in with a prevail- 

 ing practice. Such a tendency does not inhere in the empirical 

 method, which not only yields results as free as possible from personal 

 bias and preconceived opinion, but, when conscientiously applied, 

 affords the only basis for certain knowledge concerning any objective 

 phenomenon. 



After the objective phenomena constituting the subject-matter of 



1 The phrase "mathematical statistics" might have been better, since 

 it is in common use, were it not the prevailing pra;ctice, especially among 

 biologists, to base the mathematical reasoning, more or less unconsciously, 

 upon a preconception to which the statistical data treated do not necessarily, 

 or evenly usually, conform, e. g., the Gaussian law of error. Such a practice 

 is essentially an application of the deductive method to statistical problems; 

 statistical mathematics, on the other hand, is strictly empirical since the 

 mathematical logic is based solely upon the statistical data at hand. 



