GENERAL RULES OR CANONS OF THE SYLLOGISM 317 



If both are O premisses with M as predicate, the obversion of both will 

 show undistributed middle just as in the case of E E. If two O premisses have 

 M as subject the same result is reached by contraposition. Finally, if M be 

 subject of one O premiss and predicate of the other, the obversion of the 

 latter will show four terms. 



Two negatives, therefore, always lead either to undistributed middle or 

 to four terms : and the latter fallacy may be regarded as an extreme case 

 of the former ; for in quaternio terminorum neither extreme is compared 

 with even one single instance of the class with which the other extreme is 

 compared. 



(c) The first part of Rule (6) is deducible from Rule (5), and vice versa. 

 &quot;If two propositions P and Q together prove a third /?, it is plain that P and 

 the denial of 7? prove the denial of Q, for P and Q cannot be true together 

 without R. Now, if possible, let P (a negative) and Q (an affirmative) 

 prove R (an affirmative). Then P (a negative) and the denial of R (a nega 

 tive) prove the denial of Q. But by hypothesis two negatives can prove 

 nothing. 



&quot; It may be shown similarly that if we start by assuming the second of the 

 rules then the first is deducible from it.&quot; a 



158. ALTERNATIVE STATEMENT OF THE GENERAL RULES 

 OF SYLLOGISM. It was remarked above (156) that the first two 

 corollaries are sometimes given as general rules, increasing the 

 number of these to eight. 2 These eight canons are condensed 

 in the following mnemonic verses which are traditional in English 

 works on logic. 3 



&quot; Distribuas medium, nee quartus terminus adsit ; 

 Utraque nee praemissa negans, nee particularis ; 

 Sectetur partem conclusio deteriorem ; 

 Et non distribuat, nisi cum praemissa, negetve.&quot; 



&quot;You must distribute the middle term, and not have a 

 fourth ; both premisses must not be negative, nor both particular ; 

 the conclusion must follow the weaker part of the premisses, and 

 must not distribute a term, nor deny, unless one premiss does 

 the same.&quot; 



The pregnant phrase, that &quot;the conclusion must follow the 

 weaker part of the premisses,&quot; means (i) that it must be negative 

 if one premiss is negative, (2) that it must be particular if one 

 premiss is particular : the negative and the particular being 



I KBYNES, ibid., p. 293. 



2 See, for example, Palaestra Logica (by FORBES and HIRD, Oxford, 2nd ed. 

 1904), p. 46. 



3 ibid., p. 47; cf. JOYCE S Principles of Logic, p. 173, n. The lines are attri 

 buted to Petrus Hispanus, afterwards Pope John XXI. (KEYNES, op. cit. t p. 291). 



