CHAPTER IV. 



THE DOCTRINE OF REDUCTION ; ANALYSIS OF THE 

 FIGURES. 



1 68. THE NATURE AND AIM OF &quot;REDUCTION &quot; : EXPLAN 

 ATION OF THE MNEMONIC LINES. We have now to examine 

 the characteristics of each of the figures, their mutual relations, 

 and the logical significance of the traditional doctrine on the 

 &quot; reduction &quot; of the moods of the &quot; imperfect &quot; figures to those of 

 the first or &quot; perfect &quot; figure. By the Reduction of a syllogism 

 we mean, in general, the process of so rearranging its premisses 

 that the same conclusion still follows from them but now in a different 

 mood whether of the same or of a different figure. But when 

 we speak of reduction simply, we are understood to mean, with 

 Aristotle and the Scholastics, reduction from a mood of some other 

 figure to a mood of the first. The latter figure they regarded as 

 the most perfect form of syllogistic inference, and in this they were 

 right, for it is the form naturally assumed by the argument which 

 demonstrates its conclusion by showing the ratio essendi of the 

 latter. That it is the only cogent form of reasoning they did not 

 maintain ; nor would this be true, for reasonings in the other 

 figures are equally cogent. 



They do seem, however, to have taught that the cogency of 

 the syllogistic inference can be seen most clearly, and to the best 

 advantage, in the first figure, and to have concluded from this that 

 the proper way to demonstrate the validity of a syllogism in any 

 other figure was to &quot; reduce &quot; it to the first figure and apply the 

 Dictum de omni et nullo to it when so reduced. Here they 

 went too far : the cogency of syllogistic inference is not always 

 seen most clearly in the first figure. There are, as we shall see, 

 arguments which fall more naturally, some into the second, 

 others into the third figure. Besides the method of &quot; reduction,&quot; 

 moreover, there are other and easier ways of testing the validity 

 of syllogisms in figures other than the first : for instance, by 



335 



