35 THE SCIENCE OF LOGIC 



or, expressed hypothetically : 



Certain M*s are (or are not) P, 

 These same Af s are S, 

 therefore, Though M is S it may be (or need not be} P. 1 



173. THE FOURTH FIGURE AND THE INDIRECT MOODS OF 

 THE FIRST FIGURE : SUMMARY OF DOCTRINE ON THE FIGURES. 

 Each of the three figures we have so far examined presents a 

 distinct type of inference. The first figure applies the conditions 

 of a general rule to cases subsumed under it. The second en 

 ables us to prove that cases do not fulfil the conditions of a rule, 

 that they differ from those of a contemplated rule : without, how 

 ever, showing us why they so differ. The third enables us to 

 disprove a necessary rule or principle by an appeal to instances 

 which refute it. In the latter the middle term is twice subject ; 

 in the second it is twice predicate ; and in the first the major 

 extreme is predicated of the middle term, while this in turn is 

 predicated of the minor extreme. We have next to determine 

 whether those syllogisms in which the minor is predicated of the 

 middle, and this in turn of the major, exemplify any further new 

 type of inference. If they do, there is something to be said for 

 treating them as moods of a new and independent figure, the 

 fourth ; but if not, their erection into a new figure, although it 

 may make for mere external symmetry in the treatment of the 

 figures, will be really calculated rather to mislead than to give a 

 true notion syllogistic inference. After a careful examination 

 of its moods, Mr. Joseph concludes 2 that it &quot; is not an independ 

 ent type ; its first three moods are merely moods of the first 

 figure with the conclusion converted, as the process of reducing 

 them assumes ; its last two moods draw conclusions which are 

 shown to be valid most naturally by reduction to the third 

 [figure] &quot;. And this appears to be about the most accurate view 

 to take of the matter. 



We have seen that Aristotle did not recognize the fourth 

 figure. Its first introduction into logic is attributed by Averroes, 

 an Arabian philosopher of the twelfth century, to G&len, a Roman 

 physician of the second century. Some logicians have not quite 

 accurately described the relation of the fourth figure to the first 

 by saying that it is merely the first figure with the conclusion 

 converted. 3 It is true that if we regard the first premiss (P M) 



1 Cf. SIGWART, Logic, i., pp. 355, 356. 2 op. cit. t p. 290. 



8 C/. BOWEN, Logic, p. 192; THOMSON, Laws of Thought, p. 178; CLARKE, 

 Logic, p. 337. 



