398 THE SCIENCE OF LOGIC 



combination of a categorical with a hypothetical premiss gives the 

 Mixed Hypothetical Syllogism ; the combination of a categorical 

 with a disjunctive premiss gives the Mixed Disjunctive Syllogism ; 

 and, finally, the combination of a hypothetical with a disjunctive 

 premiss gives the peculiar form of syllogism called the Dilemma. 

 This classification gives us the following species : 



I (a) Categorical. 

 () Hypothetical. 

 (&amp;lt;:) Disjunctive. 

 Syllogisms 



((a) Hypothetical. 

 (b) Disjunctive. 

 (c) Dilemma. 



The axioms and canons of the pure categorical syllogism 

 which will be considered in the present and immediately follow 

 ing chapters apply almost without any modification to pure 

 hypothetical and pure disjunctive syllogisms. But mixed syllo 

 gisms will receive separate treatment subsequently. 



150. THE SYLLOGISM AND THE LAWS OF THOUGHT. The 

 formally valid syllogism must presuppose and involve the funda 

 mental laws of thought (12-16): these are involved in every 

 formally correct thinking process. 1 The separate constituent 

 judgments involve the principles of identity, contradiction, and 

 excluded middle. The formal dependence of the conclusion on the 

 premisses may be expressed in a hypothetical judgment (148), and 

 every such judgment is an application of the principle of suffici 

 ent reason. So, too, is the reasoning in hypothetical syllogisms 

 (149) an explicit application of the latter principle. 



The syllogism, therefore, is an expression or application of 

 the laws of thought But it must not be inferred that these laws 

 give sufficiently clear expression to the immediate rational grounds 

 on which syllogistic inference is based, or that the rules or .canons 

 which are to guide us in this process may be directly and immedi 

 ately derived from those fundamental laws. These rules or 

 canons cannot be derived from the laws of thought without the 

 aid of certain other principles which may be appropriately called 

 the Mediate Axioms of the syllogism. The characteristic feature 

 of syllogistic reasoning is a middle term, with which two extremes 

 are compared, in regard to extension and intension, through 



1 Cf. KKYNKS, op. cit., p. 467. 



