350 PERSONAL PREPARATION FOR RESEARCH. 



major and middle terms, and also the minor and middle 

 terms, and are thus enabled to compare the major and 

 minor terms with each ofher, and to draw from them the 

 third proposition or conclusion. In making the com- 

 parison we must be careful to compare the major and 

 minor terms either with the whole or with the same part 

 of the middle or third term, because in the great majority 

 of cases the identities to be discovered are only partial. If 

 the major and minor terms agree with the middle one, and 

 so far as they agree with it, they agree with each other, 

 because two terms which have the same meaning as a 

 third one have the same meaning as each other. Where 

 there is equality there may be inference, and mediate as 

 well as immediate inference is based upon the principle of 

 equality. In whatever relation one object or idea exists 

 with regard to another, in that same relation must it 

 exist to the equal of that other. As also things which are 

 equal to the same are equal to each other, we can always 

 prove a proposition by proving the equivalent to it. And 

 as two things, of which one is equal and the other unequal 

 to a third, are unequal to each other, we may always dis- 

 prove a proposition by proving the absence of equivalence 

 of a term, or by disproving its equivalent. But as two terms 

 or objects, which are each unequal to a third one, may or 

 may not be equal to each other, they afford us no basis 

 of inference, and therefore neither of proof or disproof. 



Some of the rules of the syllogism or form of mediate 

 inference are as follows : That it contain three proposi- 

 tions or judgments, and no more, viz. the major premise, 

 the minor premise, and the conclusion. That at least one 

 premise must be affirmative. That three and only three 

 terms be employed. The middle term must not be am- 

 biguous, and must be distributed once at least, i.e. referred 

 to universally in one premise, if not in both. That from 



