INTKODUCTION. 



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 Principle 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 every 

 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, 1 I was led to do so from 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. 



My 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. I 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. 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 

 Professor Lindsay is right in saying that he, and probably 

 other logicians, were in some degree familiar with 

 the principle. 2 Even Aristotle'a 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 



1 Pure Logic, pp. 18, 19. 



2 Ueberweg's Syntem of Logic, transl. by Lindsay, pp. 442446 

 571, 572. The anticipations jf the principle of substitution to b 

 found in the works of Leibnitz, Eeusch, and perhaps other German 

 logicians, will be noticed in the preface to this second edition. 



