336 THE SCIENCE OF LOGIC 



applying to them either the general rules of syllogism or the 

 special canons of the figure in question. 



Hence, reduction of the other figures to the first is not a 

 necessary portion of the theory of syllogistic inference. And 

 wherever arguments fall more naturally into other figures than 

 the first, reduction to the latter figure is neither the most obvious 

 way of testing the validity of such arguments, nor does it really 

 establish the equivalence or unity of the different figures. We 

 shall see that the first, second, and third figures are specifically 

 distinct types or modes of what is generically one and the same 

 sort of inference. Were there not a generic unity in the syllo 

 gistic process, as illustrated in all the figures and moods, these 

 could not be shown to be &quot; reducible &quot; to one another. Reduc 

 tion brings out this fundamental unity. It is, moreover, a useful 

 logical exercise. We shall first explain the process, and then 

 investigate more closely the relations between the various figures. 



It was partly as an aid to the process of reduction that the 

 mnemonic lines were constructed (162). We have seen already 

 that the first three vowels in each word denote the quality and 

 quantity of the propositions they respectively stand for major, 

 minor, and conclusion. Now as regards the consonants : 



(1) B, C, D, and F, the first four capital consonants of the 

 alphabet, have been naturally chosen as the initial consonants of 

 the words representing the moods of the first figure. Which 

 ever of these four consonants is the initial consonant of the name of 

 a mood of any other figure, indicates that this mood is to be reduced 

 to the mood whose name commences with the same consonant in the 

 first figure. Thus, Darapti is to be reduced to Darii, Camestres 

 to Celarent, Bramantip to Barbara, Felapton to Ferio, etc. 



(2) Of the consonants contained in the body of the words : 

 s denotes that the preceding proposition of the original syllo 

 gism is to be converted simply in the process of reduction. 



p similarly indicates conversio per accidens of the preceding 

 proposition of the original syllogism. 



m signifies metathesis, or mutatio praemissarum, i.e. transposition 

 of the premisses so that the major of the original becomes the 

 minor of the new syllogism, and the minor of the original the 

 major of the new one. 



(3) Of the consonants occurring at the end of the words : 

 It will be noted that wherever m occurs in the body of a word, 

 either s or p occurs at the end of it ; and this signifies that the 



