354 Mr DE morgan, ON THE SYLLOGISM, No. IV, 



then Y, a descendant of X, would also be a descendant of Z, which he is not. But this is 

 not all the conclusion. The full conclusion is that X is not an ancestor of none but descendants 

 of Z : not Z himself nor herself, not his wife nor her husband, not any descendant of Z, and 

 not the wife nor the husband of any descendant ; unless, in the cases where wife or husband 

 is mentioned, there be another marriage and a fruitful one with a non-descendant. 



Looking through the phases of the figures, and making L the minor relation in all cases, 

 the major relation being L or L~', we have the following Table of cases in which L or L~' 

 is a legitimate conclusion. 



II 



III 



IV 



Y.LX Y. LX Y..LX 



Z. L-'Y Z..L-'Y Z..LY 



X. LZ X . L-'Z X. L-'Z 



In rejecting all conclusions which do not contain L or L"', we must not forget that these 

 conclusions exist : I was only, by such rejection, preparing the way for the complete analogues 

 of the common syllogism. For instance X..LY, Y..L~*Z, give X..LL"^Z, not neces- 

 sarily either LZ or L""'Z, though possibly either. But still it is a conclusion, and to some 

 persons an important one: for if L mean descendant, and therefore L~' ancestor, then, Z 

 being the Queen, X is entitled to an honorary degree. 



In my second paper I pointed out the law according to which L and L"' are distributed. 



The radical forms of the four figures are here ++,-+, H — , ; in my former paper, 



in which, according to usual practice, the major premise was written first, the radical forms 

 were + +, +-, — h, . The rule is, that the radical form does not admit the con- 

 verse relation : but that when one premise differs in quality from the radical form, the con- 

 verse relation is thrown upon the other ; when both, upon the conclusion. 



Agreeing with the logicians that all judgment either identifies or separates two objects of 

 thought, I maintain against them that this great alternative, though a real form inherent in 

 all judgment, does not give the whole basis of the fundamental act of reasoning, or compa- 

 rison of judgments. The old logicians carried their system all the length which its pre- 

 tensions justified : the modern logicians, without abating a jot of the pretension, have tacitly 

 dropped greatly short of the length. The restorer of logical study in England, Archbishop 

 Whately, directs against many of his predecessors the reproach that, strongly as they con- 

 tend for the syllogism containing the whole form of inferential thought, they seem never to 

 use it nor to care about it when they come to their so-called applications of logic. I sup- 



