NATURE AND AXIOMS OF THE SYLLOGISM. 303 



...&quot; Quidquid ajfirmatur de subjecto abstractim considerate, affirm- 

 andum est de omnibus et singulis ejus inferioribus, uno verbo, universaliter. 



Quidquid negatur de subjecto abstractim considerato, negandum est de 



omnibus et singulis inferioribus ejus, uno verbo, universaliter . 1 



The significance of this modified presentation of the Aristotelean Dictum 

 will be better understood when we come to examine the objection so often 

 urged by philosophers, from Sextus Empiricus to John Stuart Mill, against 

 the syllogism as a process of reasoning : that, in so far as it purports to be 

 a process of genuine inference, it involves the fallacy of Petitio Principii(\^\ 



Some of those logicians who object to the Aristotelean Dictum as basing 

 the syllogism exclusively on what is a secondary aspect of the meaning of its 

 terms, viz. their extension, endeavour to base the syllogism themselves 

 exclusively on the comprehension or connotation of its terms. 



Thus, for example, Cardinal Mercier quotes from a French Scholastic 

 writer the following axiom analogous to the Dictum, but based on the compre 

 hension of the terms : Id quod includit continens includit etiam contentum ; 

 id quod excludit continens, excludit etiam contentum? 



Similarly J. S. Mill adopted an axiom analogous to the Dictum, but 

 based on connotation : Nota notae est nota rei ipsius ; repugnans notae 

 repugnat rei ipsi : Whatever characterizes (or is affirmed of) an attribute, 

 characterizes (or is affirmed of) the subject of that attribute ; Whatever is 

 incompatible with (or must be denied of) an attribute, is incompatible with (or 

 must be denied of) the subject of that attribute. Thus, the reasoning in the 

 syllogism &quot; Man is mortal ; Socrates is a man ; therefore Socrates is mortal &quot; 

 would be &quot; Mortality is a characteristic of humanity, which is a characteristic 

 of Socrates, therefore it characterizes Socrates &quot; ; and in the syllogism &quot; No 

 men are omnipotent ; all kings are men ; therefore no kings are omnipotent,&quot; 

 it would be &quot; Omnipotence is incompatible with humanity, which is an attri 

 bute or mark of kings ; therefore it is incompatible with kings.&quot; The 

 formula, according to Mr. Joseph (op. cit., p. 285, n. 2, and 274, n.) &quot; is really 

 an abridged equivalent of [a] passage in Ar. Cat., i b , 10-12 : 6 rai/ cWpoi/ K a0 

 CTepov KarTj-yopTJrai o&amp;gt;? KO.& vTroim/zez/ou, ocra Kara roG Kar^-yopou/^e i/ou Xeyerat 

 ndvra (cat Kara rov vTra/cfi/ieVov p^^^crerai, When one thing is predicated of 

 another as of a subject de quo, all that is asserted of the predicate will be 

 asserted of the subject as well. . . . &quot; This passage some have wrongly sup 

 posed to be the basis of the Dictum de omni. Mr. Joseph shows clearly s 

 that Aristotle was not contemplating syllogistic inference here at all. The 

 Nota notae, however, which is based upon it, gives a fairly good alternative 

 to the Dictum, or, rather, emphasizes the important aspect of intension 

 which the Dictum leaves in the background. 



Mill interprets the Nota notae in a different way from that given above. 



1 ibid., p. 185. Aristotle points to the necessity, and fundamental identity, of 

 both points of view, when he writes Tb Sf fv 6Xcp flvai erepoj/ erepy ical rb Kara iravrbs 

 KaT7j7oper&amp;lt;r0ai flarepou Qdrepov, Tavr6v ten. (In toto autem inesse alterum altero, et 

 alterum de altero omni praedicari, idem est.) Anal. Prior., i., i. 



2 RABiER, Logique, chap. v. , p. 52 ; apud MERCIER, op. cit., p. 184. [The second 

 portion of the axiom seems to be misstated. It should read: Id quod continet ex- 

 cludens, excludit etiam exclusum : M excludit P : S continet M; Ergo S excludit PJ. 



s p. 274, n. 



