I.] INTEODUCTION. 21 



Whitworth has extended the same system to the screws 

 and screw-bolts used in connecting together the parts of 

 machines, by establishing a series of standard screws. 



Anticipations of the Princi/yle of Substitution. 



In such a subject as logic it is hardly possible to put 

 forth any opinions which have not been in some degree 

 previously entertained. The germ at least of ever}" 

 doctrine will be found in earlier writers, and novelty must 

 arise chiefly in the mode of harmonising and developing 

 ideas. When I first employed the process and name of 

 substitution in logic,^ I was led to do so ft-om analogy with 

 the familiar mathematical process of substituting for a 

 symbol its value as given in an equation. In writing my 

 first logical essay I had a most imperfect conception of the 

 importance and generality of the process, and I described, 

 as if they were of equal importance, a number of other 

 laws which now seem to be but particular cases of the one 

 general rule of substitution. 



j\ly second essay, " The Substitution of Similars," was 

 written shortly after I had become aware of the great 

 simplification which may be effected by a proper appli- 

 cation of the principle of substitution. 1 was not then 

 acquainted with the fact that the German logician 

 Beneke had employed the principle of substitution, and 

 had used the word itself in forming a theory of the 

 syllogism. ^ly imperfect acquaintance with the German 

 language had prevented me from acquiring a complete 

 knowledge of Beneke's views ; but there is no doubt that 

 Professor Lindsay is right in saying that he, and probably 

 other logicians, were in some degree familiar witli 

 the principle.- Even iiristotle's dictum may be regarded 

 as an imperfect statement of the principle of substitu- 

 tion ; and, as I have pointed out, we have only to 

 modify that dictum in accordance with the quantifica- 

 tion of the predicate in order to arrive at the complete 



^ Pure Logic, pp. iS, 19. 



- Ucberweg's ^System of Logic, transl. hy Linflsay, pp. 442—446, 

 571, 572. The anticipations of the principle of substitution to be 

 I'lunil in tlie works of Loibiiitz, Rt'iisch, aixl jiLThap-i otii'.-r German 

 lo;^ician;<, will be noticed in the preface to this second edition. 



