A REPLY TO SOME CHARGES AGAINST LOGIC 409 



but it may be so expressed, and then it will be found to consist 

 of two affirmative propositions which bring out the real force of 

 the statements far better than the negative form into which they 

 have been forced. 



All reasoning is by non-logical methods, 

 Some reasoning is correct reasoning ; 

 Therefore Some correct reasoning is by non-logical methods. 



A similar analysis applies to the other arguments given to 

 illustrate this point. 



Dr. Mercier brings forward several arguments to illustrate 

 the point that logicians exclude signs of quantity other than 

 all, no, some, but that, nevertheless, perfectly valid arguments 

 can be drawn when other signs of quantity are used. The 

 accusation is entirely false. Not to mention logicians such as 

 Dr. Bosanquet, who certainly would not adhere to the rule, 

 formal logicians such as De Morgan and Dr. Keynes 1 explicitly 

 admit other signs of quantity. De Morgan, indeed, works out 

 at length a treatment of the numerically definite syllogism which 

 is based upon the recognition of other signs of quantity. 2 



To illustrate Dr. Mercier's treatment of this point we may 

 examine an argument which he triumphantly concludes "is in 

 flat violation of seven out of the eight rules of the syllogism," 

 and yet " is undeniably and incontestably valid." 



If Some of them are infantry 



and Others are cavalry, 



and Others are artillery, 



and The rest are naval officers ; 



then None of them is a civilian. 



Now with regard to the claim, first that this argument 

 " contains no middle term," and secondly that " no term in the 

 premisses is distributed," it is clear that the middle term is 

 " them " about some of whom various predications are made in 

 the successive premisses, and that this term is distributed since 

 the last premiss in combination with any of the others is 

 sufficient to give ultra total distribution of the middle term. 3 

 "The rest" refers to all those not mentioned in the other 

 premiss, or premisses, and therefore ensures that the whole of 



1 See De Morgan, Formal Logic, p. 141 seq. ; Keynes, op. cit. p. 377. 



2 Op. cit., ch. viii. 



3 For recognition of this see Hamilton, Logic, ii. p. 362, and De Morgan, 

 op. cit. p. 127, and Keynes § 327. 



