EXAMINATION OF THE PRINCIPLES 155 



But what is thus true of science in those fundamentals which 

 mark its grand divisions is true throughout of the unsystematic 

 thinking of common sense. The exigencies of life force us con- 

 stantly to make assumptions, whose inconsistency becomes mani- 

 fest upon the most cursory examination, but which we have 

 neither occasion nor opportunity to harmonize. We must act 

 and act again, and the purposes of our conduct determine for us 

 what is essentially true of the surrounding world. The scientific 

 judgment, whatever may be its faults, is better than this. Its 

 ideal may be unattainable, but the advance in that direction is 

 none the less real and important. 



The highest level of universality yet reached is that of the 

 mathematical sciences; and, indeed, in common opinion they 

 are altogether removed from dependence upon the particular. 

 The mathematical stage is that to which every other science is 

 supposed to look forward as its ultimate perfection. The excep- 

 tional position of mathematics has usually led philosophers to 

 derive them as a separate sphere of knowledge, from a separate 

 faculty of the mind. Their axioms are intuitions of reason. 



Now in the case of mechanics, the patent historical fact that 

 its laws have been only gradually revealed by observation and 

 experiment, suggests very forcibly the opposite conclusion, that 

 the certainty and absolute exactness of these laws are illusory as 

 illusory as the primitive notion, which persists even in so astute 

 a thinker as Epicurus, that all things tend to fall downward in 

 parallel lines. Newton and the modern world have not been 

 more confident of the truth of his laws of motion, than Epicurus 

 and the greater part of the ancient world were of this other 

 principle or than Aristotle and his followers were of the division 

 of natural bodies into celestial and terrestrial, the former class 

 moving in circles, and the latter, under the influence of gravity 

 and levity, in straight lines. Logically, have not all these prin- 

 ciples stood upon the same basis? They have been universally 

 descriptive of the known facts of the matter, with an exactness 

 (within the limits of observation) surpassing the delicacy of any 



