282 



SCIENCE 



[Vol. LV, No. 1420 



"claims for its heritage the whole domain to 

 which the knowledge can be legitimately ap- 

 plied," and this is amplified by the remark 

 that "knowledge is essentially a description 

 and not an explanation," it being held at the 

 same time that the object of science is to 

 describe in conceptual shorthand the routine of 

 the past. Hence the importance of the 

 fact-gathering process being made as thor- 

 ough as it is required to be impartial. 

 Pearson properly points out the limitations of 

 Sir Francis Bacon's classification of the scien- 

 ces, failing in the supreme essential of a "clear 

 distinction between the material of knowledge 

 and knowledge itself, between the real and the 

 ideal, or between the phenomenal world and 

 the unreal products of metaphysical thought." 



This discussion of an adequate method of 

 classification is most illuminating, and the dif- 

 ferent attempts that have been made "show 

 how dangerous it is for any individual to at- 

 tempt to classify the sciences even if he pos- 

 sesses Spencer's ability." Pearson disavows 

 for his own system the pretense of "logical 

 exactness." For, he remarks, "science is not 

 a mere catalogue of facts, but is the concep- 

 tual model by which we briefly resume our 

 experience of those facts." But it would have 

 been to better advantage if these learned con- 

 clusions had been illustrated by a few con- 

 crete examples, for only in this wise can our 

 actual shortcomings be brought home to us. 



From Bacon and Compte to Jevons, Spencer 

 and Pearson, the classification of the sciences 

 has been confused with the organization of 

 knowledge as a prerequisite for an adequate 

 and satisfactory systematic outline of the or- 

 der of the universe. Pearson's own classifica- 

 tion into abstract, concrete, and biological 

 sciences may possibly answer the purpose, but 

 certainly not his amplification that these are 

 united pair and pair "by applied mathematics 

 and bioph^'sics." 



More has been claimed for mathematics than 

 for any other branch of science. Granted that 

 "It is the science of exact thought as applied 

 to natural phenomena," it does not at all fol- 

 low that it is essential or even advantageous 

 in matters in which the approximate truth 



guides human actions — ever has and ever will, 

 because of the variable conditions which gov- 

 ern our existence or the collective existence 

 of all mankind. No one has essayed upon this 

 question to better advantage than Sir Wil- 

 liam Hamilton in his discussion on "The Study 

 of Mathematics as an Exercise of Mind." 

 Thus, for illustration, the rather startling ob- 

 servation that "If we consult reason, experi- 

 ence, and the common testimony of ancient and 

 modern times none of our intellectual studies 

 tend to cultivate a smaller number of faculties 

 in a more partial or feeble manner than mathe- 

 matics." He quotes a German authoritj" 

 to the eifect that "We shall first of all 

 admit that mathematics only cultivate the 

 mind on a single phasis. Their object is mere- 

 ly form and quantity. They thus remain, as 

 it were, only on the surface of things without 

 reaching essential qualities or their internal or 

 far more important relations — namely, the 

 feelings and the will — and consequently without 

 determining the higher faculties of activity. 

 So likewise on the other hand the memory and 

 imagination remain in a great measure unem- 

 ployed." 



Sir William Hamilton was of the opinion 

 that mathematics "do not cultivate the power 

 of generalization" and what is even more im- 

 portant as a practical conclusion "the study 

 of mathematics educates to no sagacity in de- 

 tecting the fallacies which originate in the 

 thought itself of the reasoner." It is of 

 the utmost importance for the present pur- 

 pose that this conclusion should be clearly 

 grasped. It being held that the inductive pro- 

 cess of reasoning, or from the particular to the 

 general, is the only process Ijy which, in the 

 vast majority of cases, conclusions can be cor- 

 rectly arrived at, it must be self-evident that 

 a process of reasoning by pure deduction can 

 not likewise serve the same or a better purpose. 

 Sir William Hamilton makes this point more 

 clear in the statement that "The art of reason- 

 ing right is assuredly not taught by a process 

 in which there is no reasoning wrong," or to 

 use his own illustration, "we do not learn to 

 swim in water by previous practice in a pool 

 of quicksilver." The process of fact hunting, 



