300 THE SCIENCE OF LOGIC 



152. THE ARISTOTELEAN SYLLOGISM AND THE &quot; DICTUM 

 DE OMNI ET NuLLO&quot;. Aristotle and the mediaeval Scholastic 

 logicians regarded as \heperfect sort of syllogism only that form 

 in which the middle term is sttbject in the major premiss which 

 should lay down a universal principle and predicate in the minor 

 premiss which should apply the general principle to some 

 particular case or class of cases. Syllogisms in this form &quot; All 

 (or No) M is P ; S is M \ therefore S is (or is not) P &quot; are said 

 to belong to fat first figure of syllogism (159). 



This is the form in which we most naturally argue from a 

 general principle to some narrower application of the latter, and 

 apply it to specific instances. Moreover, all other forms of 

 syllogistic inference must, as we shall see, agree with the present 

 form in this, that they are all inferences which involve among 

 their premisses a general principle : one of their premisses must 

 be universal (148). Furthermore, all the other forms may be 

 &quot; reduced &quot; by the application of processes of immediate infer 

 ence to their premisses (infra, Chap. IV.), though sometimes not 

 very naturally, to the present form. Hence it is not surprising 

 that this form should have been set up as the standard form of 

 the syllogism, that an axiom should have been formulated which 

 would express or typify it, so that the other forms could be tested 

 by this axiom only by , first &quot; reducing &quot; them to the present 

 form, and applying its axioms to them when so &quot;reduced&quot;. 



Such an axiom is the Aristotelean &quot; Dictum de omni&quot; : an 

 abbreviation of the expression &quot;Dictum de omni Dictum de 

 nullo &quot; : which is itself, in turn, an abbreviated expression of the 

 two axioms : (a) Dictum de omni dicitur de singulis, or, Quidquid 

 dicitur de omni did potest et de singulis ; and (U) Dictum de nullo 

 negatur de singulis, or, Quidquid negatur de omni negari potest et 

 de singulis} 



1 The Dictum is apparently founded on the following passage in Aristotle s 

 Prior Analytics (a. i. 245, 26-30) : rb Sf &/ 6\&amp;lt;f thai ilrepov erepy /col T& Kara iravrbs 

 Karr]yopf i(Tdai darepov 6drfpov ravr6v (&amp;lt;rriv. \(yo/j.fi/,8e rb Kara iravrbs Karrjyopf tffOai, 

 6rav fjLTjStv y Xafitlv r&amp;gt;v rov uiro/ctijuevou KO0 ov Qarepov ov \x^&quot;n arcTal Ka ^ r ^ Kara 

 jiTjScvbs wvavrcas. &quot; That one term should be contained in another as in a whole is 

 the same as for one to be predicated of all another. And it is said to be predicated 

 of all anything, when no part [i.e. logical part] of the subject can be found, of which 

 the other term [the predicate] will not be true ; and to be predicated of none similarly.&quot; 

 Cf. JOSEPH, op. cit., p. 274 n. The Dictum has been variously stated by the Schol 

 astic followers of Aristotle. The formula Quod valet de omnibus valet etiam de 

 singulis is misleading, inasmuch as it suggests the erroneous view that the middle 

 term is regarded as a collection of particular instances, and the major premiss as 

 a mere enumerative universal (cf. 153, 195, 198). 



