244 THOUGHTS ON BELIEF AND EVIDKNCE. 



different from what is done in some of the commonest proceedings of 

 language. The name of a colour implies a coloured object as much 

 as extension in one or more directions implies something extended, 

 hut we can think and speak of the colour without any reference to the 

 object, as we can of a line or surface without concerning ourselves with 

 extended substance. The abstraction and the absence of a real matter 

 of fact separation of the abstract ideas are the same in both instances, 

 but in the latter it relates to a class of ideas (those of number and 

 magnitude) specially fitteu for the exercise upon them of our powers, 

 and furnishing an endless variety of results. Having laid down our 

 definitions, we consider and logically develope the necessary relations 

 of the ideas submitted to us, so as to form a chain of inferences all 

 implicitly contained in those definitions. To believe one of these pro- 

 positions is to perceive its logical connection with those preceding it up 

 to the commencement, and its necessarily arising from the definitions. 

 If we are asked whether we really understand and believe the defini- 

 tions themselves we reply that although physically we cannot separate 

 position from magnitude or linear extension from the body extended, 

 yet the mind can consider the one without the other, and we under- 

 stand the definition as indicating that in the studies we are engaging 

 in, we have no concern with what is physical and material, but are 

 keeping in view one class of qualities or attributes so as from the re- 

 quired series of definitions to elicit a chain of absolute but abstract 

 truths, having a most important bearing on realities though founded 

 on assumptions impossible in fact. The very nature of mathematical 

 reasoning shows the mistake of supposing that any similar proof is 

 attainable in any case unless where we can begin by defining certain 

 ideas in the abstract, and then unfold their relations with uo other 

 assumptions, but such as must necessarily be admitted as soon as 

 understood by all human minds. Whether these conditions can be 

 found in any science besides logic and mathematics may be doubted, 

 certainly the method of demonstration is exceedingly limited in the 

 subjects to which it can be applied. "Want of attention to this truth 

 has been betrayed by a vain attempt to give the forms of demonstra- 

 tive proof to subjects which do not admit of the reality, and by a most 

 unreasonable demand for mathematical certainty in the case of ques- 

 tions involving matters of fact or relating to religion, morals and other 

 such subjects which have their own proper evidence, by the right appli- 

 cation of which alone they can be judged. Even setting aside the strict- 



