194 Mr De morgan, ON THE SYLLOGISM, No. III. 



from none to all, both ends included. But in logic, the exclusion of the terminus none is an 

 absolute necessity : its inclusion would bring under one word existence and non-existence, 

 would make falsehood the extreme case of truth. But it is otherwise at the second terminus. 

 Ambiguity here exists in thought and in usage. Accordingly, logic has always recognised two 

 kinds of some ; that of terminal ambiguity, some-it-may-be-all ; and that of terminal precision, 

 some-not-all, the some of common life. 



Some-not-all, separated by specific difference, and all, are in the relation of species and 

 genus ; a relation which is lost when some becomes all, in the old sense of the words species 

 and genus. But in ' All X is Y ' the force of Y is ' some or all Y, as it may happen.' It 

 is 'AH X is some-it-may-be-all Y.' The logicians frequently define some as not-all in the 

 outset, and then proceed to use it with an ambiguous terminus, by expressly laying down that 

 ' Some X is Y ' does not allow inference of ' some X is not Y.' This confusion still con- 

 tinues. We have been assured that ' All X is some Y ' is contradicted by ' All Y is some 

 X,' a proposition which cannot be made good except by some being declared not all. 



This distinction totally prevented the expression of any syllogism as a combination of 

 relations. No one could say that the process in Barbara is expressed by ' Species of species is 

 species.' This last expresses the act of mind in one of what I have called complex syllogisms, 

 each containing three simple syllogisms. The process in Barbara is as follows ; — That which 

 is either species or coextensive of that which is either species or coextensive of Z is itself either 

 species or coextensive of Z. Add to this that while the propositional forms were more of the 

 mathematical character, the predicables were more of the metaphysical. 



XII. I now come to the proposition, its form, quality, and quantity. For the distinc- 

 tion which I draw between the technical sense of affirmation and negation, and the general 

 words assertion and denial, I refer to the second part of this paper. 



A beginner in logic, on hearing the propositions ' Omnis homo est animal,"" ' Aliquis homo 

 est doctus,'' not only as first examples of predication, but as the ultimate instruments of syl- 

 logism, might be expected to say — I was told that logic was chiefly, if not wholly, conversant 

 with second intentions ; Pray what has become of them .'' The fact is that philosophy, in spite 

 of her proud tendency towards the universal and the necessary, and her contempt for what I 

 call the arithmetical whole, as vague, partial, and contingent, actually proceeded in this arith- 

 metical whole, not merely in the convenient expression, but in the scientific structure, of her 

 propositions. Her forms were all and some, as the fundamental discriminators of propositional 

 enunciations. Her good intentions as to second intentions — in adopting which she took a 

 course worthy of herself — were rendered of no effect, partly by the habit of the arithmetical 

 whole, partly by the want of the definite universe, partly by a preference for the aflfirmative 

 over the negative ; the first of a tendency towards the contingent, the second and third of 

 a tendency towards the necessary and universal. She saw, I suspect, that omniscience need 

 never use form of denial, because it is in possession of the counter-affirmation. All denial is 

 ignorance : no one need rest in ' No A is B ' if his knowledge will allow him to say ' Every 

 A is C ' where C and B are of essentially and visibly repugnant attributes. Or, to descend 

 to common life, no one replies by a simple negative to ' Does he live at No. 42 ."" if he know 

 that No. 43 is the true number. Vieta, an accomplished pupil of the schools, caught the 



