METHODS OF SCIENTIFIC PROOF. 353 



methods of proof. The method of proving by its equal is 

 based upon the principle that we may substitute like for 

 like in our experiments without altering the result, and 

 like for like in our thoughts and evidence without weak- 

 ening the argument. That of proving it by disproving 

 its negative is based upon the principle that a thing can- 

 not both be and not be. And the method of indirect 

 inference is based upon the axiom that a thing must 

 either be or not be, and agrees with the proposition that 

 every positive statement may have a corresponding nega- 

 tive one. By the indirect method we prove a conclusion 

 by showing that it can be nothing else, or by showing that 

 every other supposition possible in the case leads to con- 

 tradictions of what we know to be true. And in each of 

 these cases the real test is agreement with the truths of 

 nature. 



In nature there exist multitudes of things which 

 cannot be separated. For instance, none of the qualities, 

 properties', or forces of bodies can be isolated, or perceived 

 in a separate state. But that which is inseparable in 

 nature is not necessarily inseparable in thought ; nor is 

 that which is necessarily separate in nature incapable of 

 being combined in thought. We can mentally analyse 

 the most complex un decomposable existences. 



There are multitudes of ideas which can only be 

 acquired by a process of mental analysis, because their 

 corresponding objects in nature cannot be isolated; and 

 the existence and relations of such objects can often only be 

 proved by indirect inference, by showing that they cannot 

 be anything else. It is a logical axiom that every term 

 and idea has its negative in thought ; such negative- con- 

 sists of the collection of all other terms and ideas (except 

 itself) belonging to the entire sphere of thought, dis- 

 course, or research in contemplation at the time ; and as 



A A 



