386 THE SCIENCE OF LOGIC 



sary relation ; so that (4) every such inference is from the general 

 to the particular, in this sense, that it is the application in some 

 form or other, according to the Dictum de omni, or a correspond 

 ing axiom for each of the other figures of some general rule or 

 principle to some less general group of cases, or to some single 

 case, brought under the former (170-3). 



These, therefore, we gather to be the essential characteristics 

 of the categorical syllogism. The first of them is common to all 

 mediate inferences. How far the third and fourth are also essential 

 to mediate inference, or, at least, how far all mediate inference is 

 dependent on the intuition of some universal and necessary truth 

 regarding the subject-matter of that inference, or whether it is 

 possible to have mediate inference from particular or indefinite 

 (93) propositions, 1 without the tacit intervention of any universal 

 principle we shall determine below (194). The second character 

 istic seems to be peculiar to the syllogism, so that forms of mediate 

 inference not possessing it would be non-syllogistic. Are there 

 any such? 



In referring to the Axioms of Identity and Diversity (157) 

 which are certainly presupposed by all syllogistic reasoning we 

 pointed out that the &quot;identity&quot; and &quot;diversity&quot; in question 

 were not to be understood as a mathematical &quot;equality&quot; or 

 &quot;inequality&quot; of two magnitudes or multitudes. It is a relation 

 of &quot; identity&quot; or &quot;diversity,&quot; of two objective concepts, in regard 

 to their extension and intension, that we have seen to underlie 

 the whole theory of the categorical syllogism. The judgments 

 entering into it connect two objects of thought, by means of the 

 logical copula &quot;is (not),&quot; &quot;are (not),&quot; as subject and attribute, as 

 logical, extensive whole and logical part, or as intensive whole and 

 intensive part, according to the predicative, extensive, or inten 

 sive interpretations, given to these judgments. 



Now, it is conceivable at all events, that the mind may establish, 

 between its concepts, relations other than that of &quot;subject to 

 attribute &quot;. And we have in fact encountered some such already, 

 e.g. ground and consequent in the hypothetical judgment. These 

 relations may reveal others, by way of mediate inference, in 

 virtue of certain principles distinct from, but just as immediately 

 and intuitively evident as, the axioms that govern the various 



1 Care must be taken not to confound these with definite, individual or singular 

 propositions, which formulate what are usually called &quot; particular &quot; (i.e. individual) 

 facts. 



