22 THE PRINCIPLES OF SCIENCE. [CHAP. 



process of substitution. 1 The Port-Royal logicians appear 

 to have entertained nearly equivalent views, for they 

 considered that all moods of the syllogism might be 

 reduced under one general principle. 2 Of two premises 

 they regard one as the containing proposition (propositio 

 continens), and the other as the applicative proposition. 

 The latter proposition must always be affirmative, and 

 represents that by which a substitution is made; the 

 former may or may not be negative, and is that in 

 which a substitution is effected. They also show that 

 this method will embrace certain cases of complex reason- 

 ing which had no place in the Aristotelian syllogism. 

 Their views probably constitute the greatest improvement 

 in logical doctrine made up to that time since the days 

 of Aristotle. But a -true reform in logic must consist, 

 not in explaining the syllogism in one way or another, 

 but in doing away with all the narrow restrictions of 

 the Aristotelian system, and in showing that there exists 

 an infinite variety of logical arguments immediately 

 deducible from the principle of substitution of which the 

 ancient syllogism forms but a small and not even the 

 most important part. 



The Logic of Relatives. 



There is a difficult and important branch of logic 

 which may be called the Logic of Eelatives. If I argue, 

 for instance, that because Daniel Bernoulli was the son 

 of John, and John the brother of James, therefore Daniel 

 was the nephew of James, it is not possible to prove 

 mis conclusion by any simple logical process. We re- 

 quire at any rate to assume that the son of a brother is 

 a nephew. A simple logical relation is that which exists 

 between properties and circumstances of the same object 

 or class. But objects and classes of objects may also be 

 related according to all the properties of time and space. 

 I believe it may be shown, indeed, that where an inference 

 concerning such relations is drawn, a process of sub- 

 stitution is really employed and an identity must exist ; 



1 Substitution of Similars ( 1 869), p. 9. 



'Port-Royal Logic, transl. by 3pencer Baynes, pp. 2 12- -219. 

 Part III. chap. x. and xi. 



