412 THE SCIENCE OF LOGIC 



particular conclusion there always intervenes some universal 

 principle which is not merely the record or register of a past infer 

 ence, but rather the logical ground of an actual one. 



Behind these universal axioms and premisses, which form real starting 

 points of our conscious, logical inferences, the Logic of Inference has neither 

 the right nor the duty to go, as Mill does, &quot; in order to inquire into their 

 grounds : the customary logical process of taking them for granted, and start 

 ing from them as the origin of our reasoning, is quite consistent ... no 

 general proposition can be a true ultimate starting point ; . . . [but] a theory 

 of the syllogism which requires for its explanation and justification that the 

 full account of it should, so to say, straggle over our whole life, if we are to 

 find scope for both its premises and its conclusion, is surely unfitted for the 

 purpose of logic. . . . Mill s explanation . . . seems . . . to be a transgres 

 sion into the province of psychology ; an attempt to determine the ultimate 

 sources of knowledge.&quot; * An unsuccessful and misleading attempt it is too ; 

 for, though Mill is right when he places the ultimate source of all our know 

 ledge in sense experience, he entirely misinterprets the nature and function of 

 the higher cognitive faculty of the mind the intellect or reason when he 

 teaches that it can merely sum up the individual experiences of sense into 

 collective judgments. 2 



199. SUMMARY OF CHAPTER. We may now conveniently 

 summarize the main conclusions we have reached in the foregoing 

 discussions. 



(1) If we understand by the &quot;syllogism&quot; that form of infer 

 ence which is usually analysed into moods, figures, etc., in text 

 books of logic, it would appear that there are other forms of 

 mediate inference which cannot be reduced to it. 



(2) These, no less than the syllogism, have their formal and 

 their material sides ; and also their own mediate axioms, which 

 are both conceptual and real. 



(3) The process by which the conclusion is reached, by the 

 application of the axiom, may in all cases be expressed in the 

 form of a syllogism proper. 



(4) Syllogistic inference is described as &quot; deductive,&quot; because 

 it compares particular cases with a general rule or principle, in 

 order to see if they fulfil the conditions of that rule or principle. 



(5) It is not possible to reason syllogistically from two inde 

 finite premisses, or even from premisses one or both of which 

 are universal, without the aid of some underlying universal axiom, 

 of which the given syllogism is a partial embodiment. 



(6) It is not possible to reason mediately from one, or from a 

 definite number, or from an indefinite multitude, of individual 



1 Cf. VENN, op. cit., pp. 377-9. 2 C/. MELLONE, op. cit., p. 385. 



