454 



Mr DE morgan, ON THE SYLLOGISM, No. V. AND 



contained is the universe. When that universe is in any way divided into two parts, the 

 name by which the individuals in one part are distinguished from those in the other is a 

 term. All terms are names ; but some names are not terms. When animal is the universe, 

 hairy is a term, a divider of the universe: mineral is not a term, but a vacuous name; 

 sentient, sensu prceditus, is not a term, but an omnitenent name; mineral and sentient 

 equally fail to divide the universe, the first by non-continence, the second by non- exclusion. 

 These contraries, the vacuous and the omnitenent, must stand or fall together. When we 

 speak of terms only, we see as clearly that contrary terms have no term which is a common 

 whole as that they have no common part; for nothing less than the universe contains 

 both : no term contains both. To what I have said (in former papers) on the exclusion of 

 omnitenent' names, I add that, even in the prevailing system, the predicate of a negative 

 must not be of universal extent, for then some of the subject would be shut out of the 

 universe in which it is to be: and that if the predicate of an affirmative be a universal, the 

 proposition asserts no more than is held to be asserted of the subject by its mere presence. 



In order fairly to put the exemplar and cumular forms into connexion, it is necessary to 

 examine them with the fullest introduction of both sides of every correlation which makes 

 any appearance at all. Until lately I have never felt assured that they were not two 

 different systems, presenting points of agreement. But before making the investigation, 

 it may be shown that neither one system nor the other can claim to dictate the precise forms 

 of enunciation. That claim is made by another system, more fundamental than either ; and 

 is made demonstratively. 



The logicians have admitted only one idea of relation : the connexion between terms 

 as terms : I call the system thus produced by the name of onymatic. They make what ap- 

 pears to me a confusion between the term and the objects of thought which it represents : 

 they identify terms which are not identical as terms, whenever they can identify the objects 

 represented. Now two terms, as terms, whatever may be the case in etymology, cannot have 

 any relation to each other in logic except what they gain by their relations to things signified 

 or excluded. And the only relation of a term to a thing is that of applicable or not appli- 

 cable. And a term, as a term, has its contrary: a term^ without a contrary is no term. 



talks about a pure form of numbering from which matter of 

 number is excluded. With us numbers lie hid in sealed pack- 

 ets, marked outside with letters : but they are numbers, whether 

 before or after assignment or discovery of their values ; differ- 

 ences of value exist or may exist, though ignored as to amount 

 so long as only the consequences of difference as difference are 

 in question. L. It is, I dare say, not quite correct to affirm 

 that the form of the proposition is void of matter: we introduce 

 different matters, leaving the differences unsymbolised, except 

 as differences. But for this, the form should rather be " Every 

 is " than " Every X is Y ". M. Then what objec- 

 tion do you make, looking at the way in which man thinks his 

 thought and says his say, to the introduction of a sphere or 

 universe, say U, on the same terms as X or Y : as material as 

 they are, as unspecified with reference to this or that as they 

 are; allowing full right to consider, as one case, what I might 

 perhaps denote by U = co ? What Logicus answered I could 

 not even dream ; so I awoke. 



' This universe is sometimes all that exists objectively, and 

 sometimes all that can exist in thought. If there be any one 

 who demands yet more, and wants room for that which cannot 

 be in thought, whether as possible or impossible, he invades 

 the universe of a higher power, and will perhaps square the 

 circle; a problem which a speculator of the last century re- 

 duced to the following, — Construere mundum divina menti 

 analogum. 



' When Aristotle practically dismissed the privative term 

 under the name of aorist, he had previously denied it to be the 

 name of anything. My belief is that he was inclined to deny 

 that it is a term ; he thought that not-man, for instance, takes 

 in so much, and shuts out so little, that it is hardly distinctive 

 If such were his idea, he would have refused, o fortiori, the 

 title of name to a word which designates the whole universe, 

 both man and not-man; which shuts out nothing whatever. 



As to the aorist character, I should like to know, supposing 

 a name to include just half the universe, which is the aorist. 



