S18 



Mr DE morgan, ON THE SYLLOGISM, No. Ill, 



is necessary. How completely the entrance of such syllogisms has defaced the Aristotelian 

 system, will easily appear : it has been well said that Aristotle commenced his synthesis before 

 he had completed his analysis; a thing which is almost always done by the first organiser of 

 any science or branch of science. 



If the relations A and B combine into C, it is clear that A without C following means that 

 there is not B ; and that B without C following means that there is not A. This important 

 principle, known only to the old logicians, in their practice, as a mode of reducing two obstinate 

 mal-contents into the first figure, might have led to such a classification* of syllogism as the 

 following. 



Throw out all needlessly strengthened or weakened forms, and there remain four syllo- 

 gisms in each of the first three figures. These divide into four cycles of three each, one out of 

 each figure : and in each cycle each syllogism is what I have called an opponent of each of the 

 others ; that is, has the form in which one premise admitted, and the conclusion denied, denies 

 the other premise. As follows : 



Figures. 



Cycles. 



Figure IV. Camenes Diraaris. Fresison. 



The fourth figure, always marked by the rest with some symptom of dislike, is here ab- 

 solutely excluded. It has three syllogisms which form a cycle by themselves. 



XXXVII. I shall not repeat the details of my former paper on the relations of the syl- 

 logistic forms. It will however be worth while to state the following arrangement of the forms, 

 which is, I think, the best I have given. 



VVP 



PVP 

 VPP 



VVV 



VPP 

 PVP 



VVP 



as that it should enter once universally. And it would have 

 been seen that if there be any rule at all on the subject, it must 

 be this one. For every syllogism may have the middle term 

 changed into its contrary : it cannot be the rule, then, that the 

 middle term should enter universally twice; for then there 

 would be a class of syllogisms in which it enters particularly 



twice ; and vice versd. Consequently the rule must be, if a 

 rule there be, that the middle term has one universal and one 

 particular entry. 



* This was communicated to me by my friend Sir William 

 Rowan Hamilton (Feb. 14, 1856), as a consequence of my 

 mode of expressing the connexion of premises and conclusion. 



