GENERAL RULES OR CANONS OF THE SYLLOGISM 311 



Simple, however, as the present rule appears, the apparent 

 exceptions to it are, nevertheless, so striking that they have led 

 logicians from time to time to raise doubts about its validity. 

 But the rule is certainly valid, and the exceptions are only ap 

 parent. For example, in the syllogism, Whatever is not material 

 is not mortal ; The human soul is not material ; . . The human 

 soul is not mortal : the two premisses are, as they stand, negative 

 in form; but the middle term is, in reality, &quot; not-material&quot; ; it is 

 only by regarding this as the class-concept to the extension of 

 which the human soul is asserted in the minor to belong, that 

 the conclusion in question can be drawn about the latter. The 

 minor premiss is thus in reality affirmative: its force or function, 

 as it stands, is affirmative, viz. to assert that a thing belongs to 

 a certain class. The substitution of the term &quot; immaterial &quot; will 

 at once convince us of this. What we have to remember, there 

 fore, is this, that it is not so much the affirmative or negative 

 form of the premisses we must look to : this may always be 

 altered by the simple process of obversion. We must look rather 

 to their function in the context, remembering that a proposition 

 which is negative in form is sometimes really affirmative in force 

 and function. 



The present rule does not state simply and absolutely that 

 from two propositions which are negative in form nothing can 

 follow, but that no inference may be drawn about either of two ex 

 tremes, S and P, from comparing these in two really negative judg 

 ments with a single third term. 



The premisses of the syllogism given above, as it stands, may 

 be expressed symbolically thus : No not-M is P ; S is not M. 

 Here, with the two negative propositions, we have four terms 

 not-M, P, 5, M ; i.e. we have not a syllogism at all. In order 

 to make the given propositions premisses of a syllogism, with 

 a common middle term, we must obvert the minor, thus making 

 it an affirmative proposition. From which we see that before 

 we can, by valid syllogistic reasoning, draw a conclusion, the pre 

 misses must conform to the present rule. 



Similarly, for example, from the two propositions No M is 

 P ; No M is S we can draw no conclusion about either P or 

 S. But by obverting the minor, or both, premisses, we get a 

 valid syllogism, whose terms are M, P, and not-S, or M, not-P 

 and not-S, and from whose respective premisses we can infer 

 that Some not-S is not P or that Some not-S is not-P. 



