CHAP. XV.] ARISTOTELIAN LOGIC. 227 



conditional propositions. The distinction is nearly identical with 

 that of primary and secondary propositions in the present work. 

 The discussion of the theory of categorical propositions is, in all 

 the ordinary treatises of Logic, much more full and elaborate than 

 that of hypothetical propositions, and is occupied partly with 

 ancient scholastic distinctions, partly with the canons of deduc- 

 tive inference. To the latter application only is it necessary to 

 direct attention here. 



2. Categorical propositions are classed under the four fol- 

 lowing heads, viz. : 



TYPE. 



1st. Universal affirmative Propositions : All Y's are X'a. 



2nd. Universal negative No F's are X'a. 



3rd. Particular affirmative Some Y'a are X's. 



4th. Particular negative ^ Some F's are not X'a. 



To these forms, four others have recently been added, so as 

 to constitute in the whole eight forms (see the next article) sus- 

 ceptible, however, of reduction to six, and subject to relations 

 which have been discussed with great fulness and ability by Pro- 

 fessor De Morgan, in his Formal Logic. A scheme somewhat 

 different from the above has been given to the world by Sir W. 

 Hamilton, and is made the basis of a method of syllogistic in- 

 ference, which is spoken of with very high respect by authorities 

 on the subject of Logic.* 



The processes of Formal Logic, in relation to the above system 

 of propositions, are described as of two kinds, viz., " Conversion" 

 and " Syllogism." By Conversion is meant the expression of 

 any proposition of the above kind in an equivalent form, but with 

 a reversed order of terms. By Syllogism is meant the deduction 

 from two such propositions having a common term, whether 

 subject or predicate, of some third proposition inferentially in- 

 volved in the two, and forming the " conclusion." It is main- 

 tained by most writers on Logic, that these processes, and ac- 

 cording to some, the single process of Syllogism, furnish the 

 universal types of reasoning, and that it is the business of the 

 mind, in any train of demonstration, to conform itself, whether 



* Thomson's Outlines of the Laws of Thought, p. 177. 

 Q2 



