XXIX. On the Structure of the Syllogism, and on the Application of the Theory of 

 Prohahilities to Questions of Argument and Authority. By Augustus De Morgan. 

 Sec. R.A.S., of Trinity College, Cambridge, Professor of Mathematics in Uni- 

 versity College, London. 



[Read Nov. 9, 1846.] 



Since the time when the Aristotelian syllogism ceased to be regarded as an all-sufficient instru- 

 ment of inquiry, it has remained precisely in the state in which those who are called the schoo/iiien 

 left it. I have never heard* of any attempt to ascertain whether the forms which his followers 

 derived from the writings of the great master were the perfection of system and simplicity which 

 they were supposed to be. The uninquiring adherence of all writers on logic to the model 

 of the middle ages, proves one of two things: either that the model is human perfection, or that the 

 authority of the ancients has been followed as of course in the forms of logic long after it has been 

 abandoned in every other part. With such an alternative, it is not presumption to venture upon 

 the examination : and this is the more apparent when we consider that the general impression among 

 writers seems to be that there cannot exist any other theory of the syllogism except that derived 

 from Aristotle. If another can be produced, which is but self-consistent, true, and comprehensive, 

 the tacit assertion of all writers is overthrown, whether that system be or be not judged superior 

 to the one handed down. 



I here venture to propose a derivation and classification of the forms of the syllogism, differing 

 very widely from that in use. 



Section I. Ow the meaninc/ of the sijnple term. 



A TEKM, or name, is merely the word which it is lawful to apply to any one of a collection of 

 objects of thought : and, in the language of Aristotle, that name may be predicated of each of those 

 objects. He uses this word predicate only as "that which can be said of." When in later times 

 the negative proposition " A' is not 1'" was said to have }' for \\.s predicate, the word ought to have 

 been non- predicate, or some equivalent. The proper predicate is not-I', which I .shall call the 

 rnntrary of Y. 



When we use a term, such as " man," we predicate, in Aristotle's sense of the word, of every 

 Individual which the notirm can .suggest, of John, Thomas, William, &c. If we extend the word, 

 and allow 1' to be called the predicate of " X is not }'," we must then affirm that the word " man" 

 |)redicates of every object of thought, either affirmatively or negatively : affirmatively of John or 

 Thomas, negatively of a certain tree, or quadruped, or book. Every name then, in this .sense, 

 predicates of every thing: " X is either For not-F" is a proposition of universal identity. 



The cx])ress introduction and consideration of contraries ought, I think, to have followed the 

 extension of the word predicate. Aristotle rejects and then admits: not-man, he says, is not 

 a name ; and then he calls it an aorint name, which can be predicated both of existent and non- 

 existent things. I deny the justice of this distinction, for two reasons. 



Names in logic are used subjectively ; they are the representations of the notion in the mind. 

 Now man and not-man are equally the names of things which, objectively speaking, arc non- 

 existent. Not-man, Aristotle would say, is a name which can be ])redicated of the speaking bird 



* Sec the Addition at the end of thia Paper. 



3c2 



