FIGURES AND MOODS OF THE SYLLOGISM 333 



which cannot be aided by any logical rules. Besides, being 

 a material, rather than a formal process, it will find its proper 

 treatment in connexion with Demonstration (cf. 258), and not 

 in the present context which deals only with the more formal 

 aspect of the syllogism. The Scholastics felt the difficulty of 

 framing rules to direct us in the discovery of those &quot; middle 

 terms &quot; or &quot; means of proof,&quot; and practically confined their atten 

 tion to the first figure. To prove an affirmative conclusion in 

 this figure, they advise us to look for a middle term which is 

 intermediate in extension between the major and the minor extremes, 

 or, of which the major extreme can be predicated and which can 

 itself be predicated of the minor extreme. To prove a negative 

 conclusion, we are to look for a middle term about which the 

 major extreme can be denied while it can be affirmed itself of the 

 minor extreme. 



The work of &quot; discovering &quot; general truths, and the &quot; means &quot; 

 of proving them, is not such a simple process as rules like those 

 might lead one to believe. Whether in the abstract or in the 

 experimental sciences, new truths of importance are discovered 

 and explained or proved only by long and laborious research 

 (cf. 197, 198). 



The &quot; proofs &quot; that are often demanded from students, by 

 means of syllogisms to be constructed in some particular mood 

 and figure, are not to be confounded with the genuine proofs that 

 are forthcoming in each science for its own special conclusions. 

 The so-called syllogistic &quot;proofs,&quot; demanded in the study of 

 the formal -aspect of inference, are merely exercises in the con 

 struction of syllogisms, and are intended simply to familiarize the 

 student with the moods and figures. A few examples will 

 illustrate this. 



The student is, for instance, asked to disprove the statement 

 that &quot; Not all rebellions are justifiable &quot;. He does so by proving 

 its contradictory, viz. that &quot; All rebellions are justifiable&quot; . The 

 only mood to prove this is Barbara. He sets down the scheme 

 of Barbara, filling in all that is given, thus : 



M a P All are justifiable ; 



S a M All rebellions are 

 . . S a P . .All rebellions are justifiable. 



He has now to find a middle term which can be predicated 

 of &quot;all rebellions&quot; and of which &quot;justifiable&quot; can be predicated. 



