146 LAY SERMONS, ESSAYS, AND REVIEWS. [vm. 



related to all; though the enormous practical difficulty of 

 applying mathematics to the more complex phaenomena of 

 nature removes them, for the present, out of its sphere. 



On this subject of mathematics, again, M. Comte indulges in 

 assertions which can only be accounted for by his total ignorance 

 of physical science practically. As for example : 



&quot;C est done par I e tude des mathe matiques, et settlement par elle, que Ton 

 pent se faire une ide juste et approfondie de ce que c est qu une science. 

 C est la uniquement qu on doit chercher a connaitre avec precision la methode 

 generate que Vesprit humain emploie constamment dans toutes ses recherches 

 2&amp;gt;ositives, parce que nulle part ailleurs les questions ne sont r^solues qu une 

 maniere aussi complete et les deductions prolongees aussi loin avec une 

 svrit rigoureuse. C est la egalement que notre entendement a donne les 

 plus grandes preuves de sa force, parce que les ide&quot;es qu il y considere sont 

 du plus haut degre&quot; d abstraction possible dans 1 ordre positif. Toute 

 education scientiftque qui ne commence point par une telle etude peche done 

 necessairement par sa base.&quot; l 



That is to say, the only study which can confer &quot; a just and 

 comprehensive idea of what is meant by science,&quot; and, at the 

 same time, furnish an exact conception of the general method of 

 scientific investigation, is that which knows nothing of obser 

 vation, nothing of experiment, nothing of induction, nothing of 

 causation ! And education, the whole secret of which consists 

 in proceeding from the easy to the difficult, the concrete to the 

 abstract, ought to be turned the other way, and pass from the 

 abstract to the concrete. 



M. Comte puts a second argument in favour of his hierarchy 

 of the sciences thus : 



&quot; CJn second caractere tres-essentiel de notre classification, c est d etre 

 necessairement conforme a 1 ordre effectif du deVeloppement de la 

 philosophic naturelle. C est ce que v^rifie tout ce qu on sait de 1 histoire 

 des sciences.&quot; &amp;gt;J 



But Mr. Spencer has so thoroughly and completely de 

 monstrated the absence of any correspondence between the 

 historical development of the sciences, and their position in the 

 Comtean hierarchy, in his essay on the &quot;Genesis of Science,&quot; 

 that I shall not waste time in repeating his refutation. 



1 &quot; Philosophic Positive,&quot; i. p. 99. 2 Ibid., i. p. 77. 



