OF THE LAWS OF THOUGHT. Ib9 



that of the particular system examined in this chapter. And yet 

 writers on logic have been all but unanimous in their assertion, not 

 merely of the supremacy, but of the universal sufficiency of syllogis- 

 tic inference in deductive reasoning." These statements, that con- 

 version and syllogism are branches of a much more general processj 

 have of course no meaning except on the supposition that the "much 

 more general process" is not reducible to conversion and syllogism. 

 If reducible to these, it would not be a more general process. Now 

 we take our stand firmly on the position, that a chain of valid reason- 

 ing, which cannot be broken into parts, every one of which shall be 

 an instance either of conversion or of syllogism, is not possible. We 

 are prepared to show this in the case of every one of the examples of 

 his "more general process" which Professor Boole gives in his work. 

 Nay, we go farther, and as was intimated above, hold it to be abso- 

 lutely demonstrable, that, from the nature of the case, inference 

 cannot be of any other description than conversion or syllogism. 



To make this out, let it be remarked that the conclusion of an 

 argument exhibits a relation between two terms, say Xand Y. It 

 is an important assumption in Professor Boole's doctrine, that a 

 proposition may exhibit a relation between many terms. This is not 

 exactly true. A proposition may involve a relation between a variety 

 of terms implicitly ; but explicitly exhibits a relation only between 

 two. Take, for instance, the proposition — " Men who do not possess 

 courage and practise self-denial are not heroes." Here, on Professor 

 Boole's method, a variety of concepts are supposed to be before the 

 mind, as, men, tliose who practise self-denial, tliose ivho possess courage, 

 and heroes. But in reality, when we form the judgment expressed 

 in the proposition given, the separate concepts, men, those who prac- 

 tise self-denial, those ivho jyossess courage, are not before the mind ; 

 but simply the two concepts, men who do not possess courage and 

 practise self-denial, and heroes. What is a judgment but an act of 

 comparison ? And the comparison is essentially a comparison 

 of two concepts, each of which may no doubt involve in its expression 

 a plurality of concepts, but these necessarily bound together by the 

 comparing mind into a unity. Now, if the conclusion of an argu- 

 ment exhibits a relation between two terms JT and Y, this conclusion 

 must be drawn (what other way is possible ?) either through an 

 immediate comparison of ^ and Twith one another, or by a mediate 

 comparison of them through something eise. If it be drawn by an 



