Mb DE morgan, ON THE SYLLOGISM, No. Ill, 



The last verse may moan that Sanderson was then 

 forbidden, and sub poena. In 1680 was published at 

 Cambridge a neat edition (8vo) of the Logic of Bur- 

 gersdicius, with Heereboord's Synopsis. 



It would be rery desirable that such scraps should 

 be noti'd by those who casually pick them up. I will 

 undertake to arrange any that may be sent to me, and 

 to deposit them in Notes and Queries. 



§ VIII. It is hardly right to say that the distinc- 

 tion of extension and comprehension was wholly lost, \ 

 till revived by the Port-Royal authors. It always 

 existed as a metaphysical distinction, and, though not 

 fundamentally laid down in logic, made no infrequent 

 appearance. I think Occam, but I cannot now refer 

 to his work, expressly applies the whole predicate to 

 the whole subject; and whoever does so must think 

 of the comprehension of the predicate. In speaking 

 of the works which "carry on" the Port Royal dis- 

 tinction, I mean only to include those in which the 

 change of the quantity, so well laid down by Arnauld, 

 is distinctly stated, in some of its cases at least. Thus 

 though William Duncan of Aberdeen speaks of ex- 

 tension and comprehension, I cannot find that he lays 

 down anything on quantity. But Isaac Watts, in his 

 excellent and much underrated work, which I call the 

 English Port-Royal Logic, both lays down the distinc- 

 tion, and the universal comprehension of the predicate 

 of an affirmative ; this I have found only recently. 

 But Watts says nothing about the predicate of a nega- 

 tive, as to comprehension. Nor have I anywhere found 

 it laid down that in all terms of all propositions, the 

 quantities in extension and in comprehension are of 

 different names. 



§ X. 3. For animal-man and reason-man read 

 animal-in-man and reason-in-nian. 



§ XV. For 'X( or X(' read 'X( or )X.' 



§ XXV. The doctrine of modats may, I think, be 

 regarded as virtually incorporated into any system 

 which acknowledges the distinction of the mathema- 

 tical and metaphysical sides of logic. I never had the 

 curiosity to examine the old modal proposition closely 

 until long after the present paper was written : I now 

 add a brief account of the difficulty of this subject, 

 and of one reason of it. 



There are three ways in which one extent may be 

 related to another, definite expression of ratio being 

 forbidden : they are, complete inclusion, partial inclu- 

 sion with partial exclusion, and complete exclusion. 

 This trichotomy would have ruled the forms of logic, 

 if human knowledge had been more definite; if, for 

 instance, whenever complete inclusion is deniable, it 

 had been known which form of denial is the true one, 

 denial by affirmation of partial inclusion with partial 

 exclusion, or denial by affirmation of total exclusion. 

 As it is, we know well the grounds on which predica- 

 tion is not a trichotomy, but two separate dichotomies. 

 Nevertheless, when we come to speak metaphysically, 



when our propositions are made to convey our im- 

 pressions as to the nature of things, the trichotomy 

 demands establishment. How indeed could beings who 

 know why and how so soon as they know what imagine 

 themselves incapable of choosing between two forms 

 of denial ? Accordingly, must be, may or may not be, 

 cannot be, are the great distinctions of ontology : ne- 

 cessity, contingency, impossibility. This was clearly 

 seen by the logicians. But it was not so clearly seen 

 that this mode of predication tallies, not with the four 

 ordinary forms A, B, I, O, but with the three forms 

 A, (01), E. As in the following: — Every X is Y, 

 which is the consequence of necessity ; Some Xs are 

 Ys and some are not, which is the consequence of 

 contingency ; and No X is Y, which is the consequence 

 of impossibility. 



Accordingly, an attempt was made to pack up the 

 trichotomy with the dichotomies. It ought to have 

 been done in the following way, in which the proper 

 modal description follows the form of predication ; it 

 being assumed that the categorical form which exists 

 has its reason in the nature of things. 



A. Every X is Y. Necessity. 



0. Some Xs are not Ys. Non-necessity, i. e. 

 either contingency or impossibility. 



E. No X is Y. Impossibility. 



1. Some Xs are Ys. Non-impossibility, or pos- 

 sibility, i. e. either contingency or necessity. 



(O-I). Bo<A Some Xs are Ys and some not. Con- 

 tingency. 



(A, E). Either Every X is Y or No X is Y. 

 Non-contingency, i. e. either necessity or impossibility. 



Instead of this, \iov!ev(iv, possibility was pressed into 

 the list to make a fourth, but without any need ; for 

 the contingens was divided into the contingens esse, and 

 the contingens non esse, and applied to the forms I and 

 O ; while the possibile was similarly applied, under the 

 distinction of possibile esse and possibile non esse. But 

 some separated the possibile and the contingens, apply- 

 ing the possibile to the form I, and the contingens to the 

 form O. With them, contingens was equivalent to 

 possibile non esse, and possibile to contingens non esse. 



It must not be supposed that any of the objec- 

 tions I have hinted at were unseen or unnoticed. 

 What, indeed, did the schoolmen not discuss ? Two 

 contiguous paragraphs of the minute Cologne com- 

 mentary on Aristotle collected from Thomas Aquinas, 

 Gilbert Porretanus, and others, address themselves to 

 the questions why Aristotle did not introduce a single 

 mode contradictory of necessary, as he had done in the 

 case oi possibile and impossihile; and why, since possibility 

 and contingency are convertible, they are to be looked 

 upon as distinct modes. The answers are too deep for 

 mo at present: but I have in so many instances found 

 meaning in the schoolmen where I thought there was 

 none, and sense where I thought there was nonsense, 

 that I will not answer for the results of further con- 



