EXAMINATION OF THE PRINCIPLES 151 



is to be served. In a process of calculation the amount of in- 

 accuracy which we can tolerate in the premises depends on the 

 degree of accuracy which is required in the results. Thus the 

 captain of a disabled ship, whose sole object was to reach shore, 

 might be quite content with the accuracy of observations which 

 showed his position within a fraction of a degree, provided the 

 nearest land were a large island to the westward, extending over 

 several degrees of latitude. The Arctic explorer, who believed 

 himself to be near the pole, would find such rough calculations of 

 his position to be absolutely useless. The conclusion which the 

 captain would wish to draw would be merely the general direction 

 in which to sail; while the conclusion desired by the explorer 

 must be the exact direction in which, and the exact distance to 

 which he must change his position. 



But though error may be negligible is it not still error? Is not 

 the false judgment, which is near enough to truth for practical 

 purposes, still false? Granted. But suppose the judgment does 

 not pretend to exactness what then? We have an immense num- 

 ber of common-sense terms, which serve our purposes excellently, 

 but which are not to be rigidly defined. Is a child of two a baby? 

 Is a bachelor of thirty-five still young? How many grains make 

 a heap? And even mathematical terms may be toned down by a 

 cloudy modifier. Is it true or false that the earth is nearly spheri- 

 cal, or that San Francisco is about three thousand miles from New 

 York? The answer is indeterminate, unless the requirements of 

 the particular occasion determine it. How largely our judgments 

 are of this character is evidenced by the polemical success of 

 the ancient Megarian eristic, which was based upon the principle 

 that a 1 ! our judgments are similarly indefinite. Perhaps they 

 were not wholly wrong in their opinion. 



But scientific judgments evidently aim at a validity which is 

 higher than this, and that is why terms like heap and baby fail to 

 serve their turn and are replaced by a technical vocabulary. 

 The ideal is a truth that shall remain true for all possible purposes 

 and in all possible situations. But this ideal is assuredly not 



