666 THE PRINCIPLES OF SCIENCE. [CHAP 



Limiting exceptions occur most frequently in the natural 

 sciences of Botany, Zoology, Geology, &c., the laws of which 

 are empirical. In innumerable instances the confident 

 belief of one generation has been falsified by the wider 

 observation of a succeeding one. Aristotle confidently 

 held that all swans are white, 1 and the proposition seemed 

 true until not a hundred years ago black swans were dis- 

 covered in Western Australia. In zoology and physiology 

 we may expect a fundamental identity to exist in the vital 

 processes, but continual discoveries show that there is no 

 limit to the apparently anomalous expedients by which 

 life is reproduced. Alternate generation, fertilisation for 

 several successive generations, hermaphroditism, are op- 

 posed to all we should expect from induction founded 

 upon the higher animals. But such phenomena are only 

 limiting exceptions showing that what is true of one 

 class is not true of another. In certain of the cephal- 

 opoda we meet the extraordinary fact that an arm of the 

 male is cast off and lives independently until it encounters 

 the female. 



Real Exceptions to Supposed Laws. 



The exceptions which we have lastly to consider are 

 the most important of all, since they lead to the entire 

 rejection of a law or theory before accepted. No law of 

 nature can fail ; there are no such things as real excep- 

 tions to real laws. Where contradiction exists it must be 

 in the mind of the experimentalist. Either the law is 

 imaginary or the phenomena which conflict with it ; if, 

 then, by our senses we satisfy ourselves of the actual 

 occurrence of the phenomena, the law must be rejected 

 as illusory. The followers of Aristotle held that nature 

 abhors a vacuum, and thus accounted for the rise of water 

 in a pump. When Torricelli pointed out the visible fact 

 that water would not rise more than 33 feet in a pump, 

 nor mercury more than about 30 inches in a glass tube, 

 they attempted to represent these facts as limiting excep- 

 tions, saying that nature abhorred a vacuum to a certain 

 extent and no further. But the Academicians del Gimento 



* Prim Anatytics, ii. 2, 8, and elsewhert 



