404 CONSTITUTION OF THE INTELLECT. [CHAP. XXII. 



sion which affirms its possession by all the members of the class 

 in common. Now whether it is so or not, that principle of 

 order or analogy upon which the reasoning is conducted must 

 either be stated or apprehended as a general truth, to give vali- 

 dity to the final conclusion. In this form, at least, the necessity 

 of general propositions as the basis of inference is confirmed, a 

 necessity which, however, I conceive to be involved in the very 

 existence, and still more in the peculiar nature, of those faculties 

 whose laws have been investigated in this work. For if the pro- 

 cess of reasoning be carefully analyzed, it will appear that ab- 

 straction is made of all peculiarities of the individual to which 

 the conclusion refers, and the attention confined to those pro- 

 perties by which its membership of the class is defined. 



5. But besides the general propositions which are derived by 

 induction from the collated facts of experience, there exist others 

 belonging to the domain of what is termed necessary truth. Such 

 are the general propositions of Arithmetic, as well as the propo- 

 sitions expressing the laws of thought upon which the general 

 methods of this treatise are founded; and these propositions 

 are not only capable of being rigorously verified in particular 

 instances, but are made manifest in all their generality from the 

 study of particular instances. Again, there exist general pro- 

 positions expressive of necessary truths, but incapable, from the 

 imperfection of the senses, of being exactly verified. Some, if 

 not all, of the propositions of Geometry are of this nature ; but 

 it is not in the region of Geometry alone that such propositions 

 are found. The question concerning their nature and origin 

 is a very ancient one, and as it is more intimately connected 

 with the inquiry into the constitution of the intellect than any 

 other to which allusion has been made, it will not be irrelevant 

 to consider it here. Among the opinions which have most 

 widely prevailed upon the subject are the following. It has 

 been maintained, that propositions of the class referred to exist 

 in the mind independently of experience, and that those concep- 

 tions which are the subjects of them are the imprints of eternal 

 archetypes. With such archetypes, conceived, however, to pos- 

 sess a reality of which all the objects of sense are but a faint 

 shadow or dim suggestion, Plato furnished his ideal world. It 



