JO SI AH WILLARD GIBBS 471 



eint sclilagen. As science aims only to classify, predict and control 

 phenomena, it has no absolute philosophic certainty except as a logical 

 interpretation of the empirical facts of man's experience, and of the 

 relative limitations of mathematical deduction and physical induction 

 it has been well said that " the former breaks down on the subtlety 

 of nature, the latter on its imperceptibility."^ Galileo's telescope, 

 Leeuwenhoek's microscope, Lavoisier's balance, KirchhofPs spectroscope, 

 are doubtless of more practical value, but certainly not of more scien- 

 tific importance than formal and symbolic logic, the calculus, deter- 

 minants, quaternions, vector analysis or the improved formulation of 

 dynamics. Without induction, it is true, no new facts; but without 

 deductive methods there could be no interpretation of these facts, nor 

 would scientists have the means of predicting other facts which go 

 beyond experience, or of controlling phenomena. Yet an authority so 

 open-minded as Professor Huxley, who seems to have confused mathe- 

 matical methods with the scholastic reasoning and bigotry which 

 opposed the great cause he championed, seldom lost an opportunity to 

 say hard things about the science "which knows nothing of observa- 

 tion, nothing of experiment, nothing of induction, nothing of causa- 

 tion."* In Professor Sylvester's brilliant and memorable reply to some 

 of Huxley's after-dinner denunciations,^ " the most eloquent of mathe- 

 maticians " retorted upon his adversary that his chaflfing might have 

 been more guarded " had his speech been made before instead of after 

 dinner,'"' and went on to show that the maligned science employs not 

 only imagination and invention, but observation and experiment at 

 need. Even mathematicians, Sylvester pointed out, occasionally make 

 discoveries, as witness Eisenstein's discovery of invariants, which was 

 happened upon by purely physical observation " just as accidentally 

 and unexpectedly as M. du Chaillu might meet a gorilla in the country 

 of the Fantees."'^ The touchstone of the matter lies in the one really 

 telling remark that Huxley made about it, viz., that mathematics will 

 not yield correct results if applied to erroneous data.^ The advance 

 of modem science is largely bound up with the perfection of instru- 

 ments of precision, and we have learned from the teaching of Lord 

 Kelvin and the writings of Poincare to recognize that mathematical 



• " Lectures on the Method of Science," Oxford, 1905, 12. 



* Huxley, "Lay Sermons," New York, 1871, 168. 



" Hid., 66. 



'Nature, London, 1869-70, I., 237. 



'Ihid., 238. 



' " Mathematics may be compared to a mill of exquisite workmanship which 

 grinds you stuff to any degree of fineness; but, nevertheless, what you get out 

 depends upon what you put in; and as the grandest mill in the world will not 

 extract wheat flour from peascods, so pages of formulae will not get a definite 

 result out of loose data." Huxley, "Aphorisms and Reflections," London, 

 1907, 93. 



