294 THE SCIENCE OF LOGIC 



This definition embraces forms of syllogism to which Aris 

 totle s fundamental axiom of syllogistic reasoning the Dictum de 

 omni et nullo does not apply : though these latter forms of 

 reasoning may all be expressed absolutely speaking, though 

 not quite naturally in the typical Aristotelean syllogism to 

 which the axiom referred to does apply. We shall examine the 

 definition presently in connexion with the axiom in question. 



Meantime we must distinguish between the matter or material 

 elements, and the form m formal element, of the syllogism. 



The material elements of the syllogism are its terms (remote 

 matter), and its propositions (proximate matter). Take as a 

 typical syllogism this example: &quot;A free agent is responsible 

 for his conduct ; voters are free agents ; therefore voters are re 

 sponsible for their conduct &quot;. This reasoning is thus expressed 

 symbolically : 



M is P ... major premiss. 

 S is M ... minor premiss. 

 . . S is P ... conclusion. 



There are three propositions. These contain three terms, each 

 occurring twice: the middle term twice in the premisses and not 

 at all in the conclusion, the extreme terms once each in the con 

 clusion and once in either premiss. The predicate of the conclu 

 sion, P [&quot;responsible for conduct&quot;], is called the major term or 

 major extreme of the syllogism. The subject of the conclusion, S 

 [&quot;voters&quot;], is called the minor term or minor extreme. 



The subject and predicate of the conclusion are called re 

 spectively the minor and major terms, because as a rule, when the 

 judgment is expressed in its natural order (78), the subject is 

 more concrete, and narrower in its extension, than the predicate. 1 

 The middle term is so called because in the typical Aristotelean 

 syllogism, of which the example given is an illustration, the ex 

 tension of the concept expressed by M, the middle term, is inter 

 mediate between that of the lesser, smaller, or minor class-notion, 

 S, and that of .the larger, greater, or major class-notion, P. How 

 ever, though the nomenclature is retained and employed univers 

 ally, the relation indicated between the respective concepts in point 

 of extension does not hold in all forms of the syllogism : some 

 times the extension of 5 is not narrower than that of P ; some 

 times M is not intermediate, but is either the smallest, or the largest, 



1 Cf. JOSEPH, op. cit., pp. 235-37. 



