26 THE PRINCIPLES OF SCIENCE. 



Beneke had employed the principle of substitution, and 

 had used the word itself in forming a theory of the 

 syllogism. My imperfect acquaintance with the German 

 language had prevented me from acquiring a complete 

 knowledge of Beneke's views, but there is no doubt 

 that Mr. Lindsay is right in saying that he, and probably 

 other previous logicians, were in some degree familiar 

 with the principle 8 . Even Aristotle's dictum may be 

 regarded as an imperfect statement of the principle of 

 substitution ; and, as I have pointed out, we have only 

 to modify that dictum in accordance with the quantifi- 

 cation of the predicate in order to arrive at the complete 

 process of substitution *. 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 11 . 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 



8 Ueberweg's 'System of Logic,' transl. by Lindsay, pp. 442-446, 



571, 572. 



* ' Substitution of Similars,' p. 9. 



a 'Port-Royal Logic,' transl. by Spencer Baynes, pp. 212-219. 

 Part III. chap. x. and xi. 



