2 i6 SCIENCE PROGRESS 



This seems to the non-logical mind a good, sound, valid 

 argument, but the non-logical mind is mistaken. It is not only 

 not a valid argument, but it is not an argument at all, and this 

 for so many reasons that it would be tedious to enumerate them 

 all. In the first place, not one of these pseudo-propositions is a 

 "logical" proposition. No "logical" proposition can be con- 

 structed except with the verb " is " or " are," and none of these 

 propositions contains either of these. This is bad, but this is 

 not the worst ; for though we may grant, as every logician does 

 in practice grant, though he strictly denies it in principle, that 

 propositions can be formed with other verbs than " is " and 

 " are," yet neither in practice nor in principle will any logician 

 allow for a moment that any argument can be conducted, or any 

 " logical " proposition be constructed, with such quantities as 

 " many " and " few." Logic allows that it is possible, and even 

 meritorious, to affirm, deny, and argue about All soldiers, about 

 Some soldiers, and about No soldiers ; but to reason about Many 

 soldiers or Few soldiers, or even to make any statement about 

 them, is among the many impossibilities of Logic. This seems 

 a little unreasonable, but let us play the game according to 

 logical rules, and admit into our premisses no quantity but the 

 logical " Some." 



IX. If Some logicians admit the verb "were" into their propositions, 

 and Some do not ; 

 then Logicians are divided in opinion about "were." 



Here we have avoided Scylla only to be swamped in 

 Charybdis. We have got the orthodox " quantities " into the 

 premisses, but alas! in our conclusion the term " Logicians" is 

 not preceded by either of the orthodox quantities, All, Some, 

 and None. It is indesignate, and with an indesignate proposition 

 no "logical" argument can possibly be constructed. 



4. It is impossible to construct an argument in which the 

 middle term appears in the conclusion. It is possible that this 

 rule is not imperative. It has never, I believe, been actually 

 formulated, but for two thousand 3^ears every "logical" argu- 

 ment has conformed to it. Lately, however, one logician, greatly 

 daring, has allowed his middle term to appear occasionally in 

 his conclusions ; but as far as I know, no other logician has 

 ventured to adopt this revolutionary innovation. There are, 



