218 science progrp:ss 



say that term, proposition, and argument are all inconsistent 

 with Aristotle's teaching - , and therefore must be wrong. 



The fifth rule of the syllogism is that it is impossible to draw 

 any conclusion from two negative premisses. Unless one premiss 

 is affirmative, there can be no conclusion. Thus I achieve the 

 impossibility. 



XIII. If No one ever reasons by "logical" methods, 

 and No one always reasons erroneously ; 



then It is quite possible to reason correctly by non-logical methods. 



Of course, logicians will say that since the conclusion says 

 nothing about either All, Some, or None, the reasoning is not 

 reasoning and the conclusion is no conclusion ; but the non- 

 logical reasonerwill not much mind this fulmination, for he will 

 see, first, that the conclusion is in fact a good sound proposition, 

 and second, that it follows from the premisses. However, to 

 obviate the logical objection, I will put my conclusion into 

 another form, and say, Some non-logical reasonings are correct. 

 This, however, will not satisfy my logical friends. They will 

 say that since the premisses are not constructed with the verb 

 " is " or " are," the propositions are not propositions, etc. It is 

 as difficult to keep within the narrow boundaries of Logic as to 

 walk on a tight rope, but I will try again : 



XIV. If No argument from two negative premisses is valid, 

 and No argument from two particular premisses is valid ; 



then No argument from two particular negative premisses is valid, 

 and All arguments from particular premisses resemble all arguments 

 from negative premisses in being invalid. 



This specimen is extremely interesting in several ways. In 

 the first place, a single pair of premisses yields two conclusions, 

 and might easily be made to yield more, a fertility which is 

 unknown to the arguments of Logic. In the second place, the 

 conclusions are highly favourable to the pretensions of Logic ; 

 but in the third place, Logic is unfortunately forbidden by its 

 own rules to admit that the conclusions are valid. In the fourth 

 place, the argument is unique in the remarkable feature that the 

 attainment of a conclusion is a flat contradiction of the first 

 premiss ; and in the fifth place, in spite of this contradiction, the 

 argument is unquestionably valid. Such are the remarkable 

 consequences of " logical " rules. 



