ABRIDGED AND CONJOINED SYLLOGISMS 377 



subject and once predicate the syllogism will belong to the first 

 figure, or to the fourth [or indirect form of first (173)], according 

 to the extreme which is made subject or predicate of the con 

 clusion. 



When an enthymeme belongs to tt\z first or the second order, 

 we may without much difficulty determine its figure and mood, 

 and so fill in the missing premiss. If the given premiss and the 

 conclusion have the same predicate, the argument belongs to the 

 first or to the third figure ; if they have the same subject, the 

 argument is in the first or in the second figure ; if the predicate 

 of the conclusion is subject of the given premiss the argument is 

 either in the second or in the fourth figure ; finally, if the subject 

 of the conclusion is predicate of the given premiss the argument 

 is either in the third or in the fourth figure. 



We may, furthermore, have pure hypothetical enthymemes 

 (174). If, however, we get an enthymeme containing a minor 

 premiss and a conclusion, with no term common to them, we 

 must conclude that the syllogism is a mixed one : a mixed 

 hypothetical or a mixed disjunctive. The enthymeme &quot; C is D 

 because A is B &quot; belongs to the first order, and may have for 

 major either the proposition &quot; If A is B y C is D &quot; or the proposi 

 tion &quot; Either A is not B or C is D &quot;. 



187. THE POLYSYLLOGISM. This is the name given to a 

 chain of reasoning consisting of a number of syllogisms each of 

 which proves one of the premisses of one of the two immediately 

 adjacent syllogisms. If we select any pair of successive syllogistic 

 links in such a chain, we shall find that one of them has for its 

 conclusion a premiss of the other. The former in relation to the 

 latter is called a prosyllogism ; the latter in relation to the former 

 is called an episyllogism. Every intermediate link in the whole 

 chain is therefore both a prosyllogism to the link on one side of 

 it, and an episyllogism to the link on the other side. 



Now, a chain of syllogistic reasoning may proceed either from 

 prosyllogism to episyllogism, or in the opposite direction, from 

 episyllogism to prosyllogism. A chain of reasoning which proceeds 

 onward from prosyllogism to episyllogism, i.e. each syllogism 

 of which proves, or has for its conclusion, the major or the minor 

 premiss of the succeeding syllogism, is called a PROGRESSIVE, or 

 SYNTHETIC, or EPISYLLOGISTIC, chain of reasoning. A reasoning 

 process which proceeds backward each succeeding step (syl 

 logism) proving, or giving a reason for, one of the premisses of 



