346 THE SCIENCE OF LOGIC 



It seems to be a distinct type : it shows us that a thing is not so, without 

 showing us why it is not so : l and if we are asked to justify or validate our 

 inference that &quot; S is not P &quot; we naturally do so, not by trying to throw the in 

 ference into the first figure, but by an appeal to the reductio ad impossibile 

 (167) : by arguing that &quot;if S were P it would be M, but it is not&quot; (or, as 

 the case may be, that &quot; if S were P it would not be M, but it is &quot;) : &quot;The 

 patient has not smallpox, because if he had he would reveal certain symptoms 

 which he does not reveal &quot; ; &quot;The Christmas rose is not a true rose, because 

 if it were it would bloom in summer, but it does not,&quot; &quot; Frozen meat contains 

 no active bacilli, because if it did it would putrefy, but it does not &quot;. Those 

 are all natural justifications of syllogisms in the second figure ; and they are 

 all indirect : they proceed by showing that if the conclusions were not true 

 something contradictory of an admitted premiss would follow. And the force 

 of this reductio ad impossibile is not apprehended as an afterthought by one 

 who has argued in the second figure : it &quot; is really a part of the thought 

 grasped in the syllogism. . . . We see the validity of the conclusion by the 

 contradiction that would be involved in denying it.&quot; 2 And this it is that 

 differentiates the second figure from the first : the reasoning in the former is 

 indirect, while in the latter it is direct. In the first figure the fact that S is 

 something other than P (namely M) gives the mind an insight into the real 

 cause or ground of its not being P ; while in the second we merely see that 

 we are forced under pain of contradiction to admit that S is not P, without 

 seeing why it is not P. The perception of this contradiction is not the reason 

 of the truth of the conclusion, the reason why the conclusion is true, but is 

 only the reason why we have to admit the latter, the means whereby we 

 realize the validity of the inference. 



An axiom for the second figure, corresponding to the Dictum de omni 

 for the first, and called the Dictum de diverso, has been formulated in the 

 following, or similar, terms : If an attribute [J/J can be predicated affirma 

 tively or negatively of every member of a class [/*], any subject [S] of which 

 it can not be so predicated does not belong to that class. 



An axiom more directly based on the intension of the terms, like the 

 Nota notae, has been thus formulated by Mr. Joseph : &quot; no subject [S] can 

 Possess an attribute [P] which either excludes what it possesses or carries 

 what it excludes [M] &quot;. 3 



172. CHARACTERISTICS OF THE THIRD FIGURE. The third 

 figure (a) proves only particulars, proving each (I and O) in three 

 different modes. It is, therefore, () appropriate for disproving a 

 general rule or statement by establishing some exceptions to it 

 at least one. (c] It is the only natural figure for expressing argu- 



aniums are not fragrant, because they are scarlet, and no fragrant flowers are scarlet,&quot; 

 as compared with &quot; Some geraniums are not fragrant, because they are scarlet and 

 no scarlet flowers are fragrant&quot; (ibid., p. 290, n.) 



1 In answering this question we must bear in mind that &quot; the same verbal form 

 may be used where the thought in the speaker s mind is different. The character 

 of an argument depends not on the verbal form, but on the thought behind it.&quot; 

 JOSEPH, op. cit. t p. 290. 



3 JOSEPH, op. cit., p. 293. 3 op. cit., p. 295. 



