4 io SCIENCE PROGRESS 



the class has been indicated. It may at once be granted that 

 the argument is not, as stated, a syllogism, and therefore need not 

 contain only three propositions and only three terms. That it 

 draws a negative conclusion from affirmative premisses is more 

 apparent than real, for it requires the assumption of the premiss 

 "none of these (ranks) are civilian," and this at once gives us 

 a negative premiss as well as a distributed term. 



Dr. Mercier in his attack on the syllogism has committed two 

 mistakes : (i) he assumes that the traditional syllogistic rules arc- 

 intended to apply to all possible reasonings, and (2) he considers 

 that the middle term is not essential for valid deductive 

 reasoning. The second is much the more serious mistake, and 

 must be dealt with at greater length. With regard to the first 

 it is sufficient to point out that rules formulated with reference 

 to a specific form of reasoning do not necessarily apply to 

 forms outside it. If the validity of obversion be admitted it is 

 clear that the premisses of every valid syllogism may be 

 expressed as negatives from which the affirmative conclusion 

 will still follow. 1 But the reasoning has then ceased to be 

 syllogistic as traditionally defined. 2 



In spite of all Dr. Mercier's efforts to dispense with the 

 middle term, there is in all his arguments a true middle term — 

 that is, an element of identical reference, which, whether ex- 

 plicitly stated or not, is the essential condition upon which the 

 validity of the argument depends. Without such an element 

 of identical reference it would be impossible to draw any con- 

 clusion from the bringing of a special case under a general 

 principle. But all reasoning consists in the application of 

 general rules to particular cases, and hence always involves 

 a middle term. 3 



Moreover, although it may be admitted that the syllogism 

 as traditionally treated is not the exclusive form of reasoning, 



1 On this point cf. Keynes, op. cit. §§ 205-206. 



3 Dr. Mercier seems not to know that Aristotle — to whose evil influence he 

 attributes all the errors of Logic — defined the syllogism as : \6yos ev 2> ndevrcov 

 Tivu>v ertpov ti tu>v Kfiptvov «'£ dvdyicqs <rv/i/3aiWi tu ravra elvai, although it is true 

 that in his investigation of the forms of the syllogism he interpreted it much 

 more narrowly (see Anal. Pri., i. 24 b i8). 



3 In the case of arguments, in the Third Figure, where the middle term is a 

 singular name, this is not immediately apparent, but, since any syllogistic argu- 

 ment can be restated in the First Figure, its essential structure can always be 

 made evident. 



