388 THE SCIENCE OF LOGIC 



Various attempts have been made to reduce the former argu 

 ment, (I), to a syllogism. Of these the following alone calls for 

 some notice : 



(I, a) &quot; Whatever is greater than a greater than B is greater 

 than B ; A is greater than a greater than B ; therefore, A is 

 greater than B.&quot; 



This is certainly a syllogism, and a valid one ; but, just as 

 certainly, it is not an expression of the former argument , (I) : for it 

 has not the same terms. It does bring out, however, this im 

 portant fact, to which we shall presently return (194), that the 

 argument in question (and the same is true of all mediate infer- 

 ences whatsoever] involves, and depends for its validity on, the appre 

 hension of some intuitively evident, abstract and universal truth or 

 principle, of which it is an application. The application of the 

 principle involved in the first inference, (I), is stated in the major 

 premiss of (I, a): &quot; Whatever is greater than a greater than B 

 is greater than B &quot;. This is a particular case of the general 

 mathematical axiom which we formulated above for the argu 

 ment (I) under examination. 



In a precisely similar way, we may show that the syllogism, 

 (II), given above depends on the Dictum de omni, by means of 

 this other syllogism, having for major the required application 

 of the Dictum. 



(II, a) Whoever belongs to a class of beings that are mortal is 

 himself mortal ; Socrates belongs to a class of beings that are 

 mortal ; therefore, Socrates is mortal. 



The major of this syllogism (II, a] simply states the narrower 

 application, employed in the previous syllogism (II), of the Dictum 

 de omni. Yet it would hardly be correct to say that (II) is reduced 

 to (II, a], or that the latter is another or equivalent expression of 

 the former; but rather that (II) involves (II, a) just as (I) involves 

 (I, a). 



192. SOME CLASSES OF SUCH INFERENCES. (A) The Syl 

 logism, of which (II) is an example, is, therefore, a mediate 

 inference from judgments which express each a relation of subject to 

 attribute. 



(B) The class of arguments of which (I) is an example, in 

 cludes all mediate inferences from judgments which express each a 

 relation of degree between two measurable magnitudes. Alia fortiori 

 arguments belong to this class ; e.g. &quot; A is hotter than B ; B is 

 hotter than C ; therefore, a fortiori, A is hotter than C&quot;. 



