VII. On the Syllogism, No. IV, and on the Logic of Relations. By Augustus 

 De Morgan, F.R.A.S., qf Trinity College, Professor of Mathematics in 

 University College, London. 



fRead April 23, I860.] 



In my second and third papers on logic (Vol. ix. part 1, Vol. x. part 1,) I insisted on 

 the ordinary syllogism being one case, and one case only, of the composition qf relations. 

 In this fourth paper I enter further on the subject of relation, as a branch of logic. 



Much has been written on relation in all its psychological aspects except the logical 

 one, that is, the analysis of necessary laws of thought connected witii the notion of relation. 

 The logician has hitherto carefully excluded from his science the study of relation in general : 

 he places it among those heterogeneous categories which turn the porch of his temple into 

 a magazine of raw material mixed with refuse. Aristotle does not give this part of logic a 

 very hopeful look when (Categories, ch. v. or vii.) he puts forward no better phrase* than 

 irpos Ti to denote his abstract idea of relation. And such hope as there is becomes well- 

 nigh extinct when we learn that the rudder is not properly the rudder of the ship, because 

 people do not say (ov XiyeTai) that the ship is the ship of the rudder. Here, as occasionally 

 elsewhere, Aristotle is rather too much the expositor of common language, too little the 

 expositor of common thought. Surely the question, ' What sliip does this rudder belong to ?' 

 must sometimes have been heard in an Athenian dockyard: and if this question were not 

 equivalent to ' Which is the ship of this rudder ?' in the common idiom, the equivalence ought 

 to have been established by the logician so soon as wanted. Terms may be related, even 

 though they have more meaning than just goes to the relation. A ship is ' the steered' and 

 the rudder is ' the steerer :' that it happens to a ship to mean more than ' a thing steered,' 

 and to a rudder to mean no more than 'the thing which steers,' is a purely material 

 concomitant of the words. 



The logicians of our day seem to my mind to combine a want of memory by which 



* When a noun is thus formed, it is a sign that the mind 

 of the language has not possession of the idea. There is a 

 useful piece of furniture called a what-not, a holder of miscel- 

 laneous articles: the word is of the same type as w/jo's Ti. We 

 are an orderly people, and the notion of unarranged deposit is 

 not among those for which we find words of serious approval. 

 Dr Roget can produce no nouns which come close to the point 



except the contemptuous term medley, the corruption of a legal 

 term hodgepodge, also contemptuous out of law, and the best 

 word of all, the only one which perfectly applies, omnium 

 gatherum, contemptuous and not English. The applier of the 

 term what-not probably was not aware that he had the authority 

 of Aristotle for his mode of proceeding. 



