39* THE SCIENCE OF LOGIC 



The question has been raised whether those inferences, whose 

 classification as syllogistic or non-syllogistic is open to dispute, 

 are formal or material inferences. 



If by a formal inference we mean one in which the truth of 

 the conclusion follows necessarily from the premisses on the 

 assumption that these premisses are true, then they are just as 

 formal as the syllogism, i.e. their conclusions follow by the same 

 hypothetical necessity from their premisses as in the case of 

 the syllogism. They contain, of course, a material or &quot;truth&quot; 

 aspect, as well as a formal or &quot; consistency &quot; aspect. But so, too, 

 does the syllogism. In this, just as in those, the conformity of 

 the whole mental process throughout, with the reality which it 

 interprets, depends not merely on the cogency of each such form 

 of inference, 1 but on the truth of the judgments which constitute its 

 antecedents or premisses. 



193. THE POSSIBILITY OF MEDIATE INFERENCE FROM PAR 

 TICULAR JUDGMENTS. We have seen that a certain small number 

 of immediate inferences of minor importance can be derived from 

 particular or indefinite judgments (i 16-21, 140.). Even in those 

 cases, however, the mental process does not take place without 

 the aid of certain self-evident, necessary, universal truths, which 

 are embodied, as &quot; laws of thought,&quot; in all our judgments (n). 

 The syllogism, as we saw, cannot be valid unless it has at least 

 one universal premiss (156). Moreover, the recognition of a 

 syllogism as formally valid is merely the recognition of an in 

 dividual case or application of some self-evident universal axiom, 

 which the mind apprehends as embodied in the special case 

 before it. And the same is true of all forms of mediate inference 

 (192): all alike derive their cogency as forms of reasoning from 



takes &quot; deductive &quot; inference as wider than &quot; syllogistic &quot; inference (of which latter 

 he takes the narrower view, excluding hypothetical and disjunctive arguments ; cf. 

 148, 174), and as including those forms of inference (referred to above) which are 

 based upon intuitions of necessary relations seen to hold universally in the domains 

 of time, space, magnitude, multitude, etc. Such principles as these cannot, he 

 thinks, be reduced to &quot; logical &quot; principles, nor vice versa : &quot; There are some who 

 have represented logic as at bottom a branch of mathematics ; and others seem 

 inclined to suppose that mathematics can be reduced to formal logic. ... I ought 

 perhaps to say that I do not understand how either theory can be true &quot; (ibid., p. 

 512). If we take &quot; logical &quot; inference as resting on self-evident intuitions of Being, 

 then &quot; mathematical &quot; inference will be &quot; logical &quot; and something more, inasmuch 

 as it demands as basis not merely self-evident intuitions about Being, but also intui 

 tions about a special category of Being, viz. Quantity. 



1 Or, in other words, on the truth of the self-evident axiom of the form of in 

 ference in question. 



