THE AIM AND ACHIEVEMENTS OF SCIENTIFIC METHOD. 107 



48. 



Whether, as Mach would have us believe,* Newton was well 

 aware that his concepts of quantitas motus, vis impressa, and 

 the like are merely of psychological value in connection with 

 the investigation and transformed statement of actual facts, or 

 whether he attributed to them objective validity, is a matter 

 upon which it would be neither easy nor profitable for us to- 

 come to a decision. There is no doubt whatever that the latter 

 is true of the majority of his contemporaries and successors, at 

 the very least until the time of D'Alembert, if not, indeed, 

 until the present day. Thus allusion has already been made to 

 the famous controversy between the followers of Descartes 

 and Leibniz, upon the subject of the " correct " method of 

 measuring that " force " of a body in motion which we have 

 noted as one of the vague notions in which the science of 

 mechanics has its birth. From the standpoint of the develop- 

 ment of the science, the great value of the controversy was that r 

 by concentrating attention upon the theoretical aspect of the 

 method by which individual problems in mechanics were 

 solved, it led to an elaboration of definite bodies of mechanical 

 doctrine with a definite nomenclature. From the critical point 

 of view, the controversy is most interesting as throwing light 

 upon the way in which the most pretentious and far-reaching 

 scientific doctrines are based upon a mass of vague experiences,, 

 of " instinctive perceptions," the precise nature of which it is 

 not always given to the founders of the science to recognise 

 for what it really is. Thus even Thomson and Taitf admit 

 that Newton's " axioms " " must be considered as resting on 

 convictions drawn from observation and experiment, not on 

 intuitive perception." But Newton, like Gauss, exhibited his 

 (edifice of thought to the world only "when the scaffolding had 

 been removed," and has left us no precise indication of the 



* Science of Mechanics, p. 193. 



t Thomson and Tait, A Treatise on Natural Philosophy, 1867, p. 178. 



