xvi PREFACE TO THE SECOND EDITION. 



device is, that one slide can be drawn, out and pushed in 

 again at right angles to the other, and the overlapping 

 part of the slides then represents the probability of a 

 conclusion, derived from two premises of which the pro- 

 babilities are respectively represented by the projecting 

 parts of the slides. Thus it appears that Stanhope had 

 studied the logic of probability as well as that of certainty, 

 here again anticipating, however obscurely, the recent 

 progress of logical science. It will be seen, however, that 

 between Stanhope's Demonstrator and my Logical Machine 

 there is no resemblance beyond the fact that they both 

 perform logical inference. 



In the first edition I inserted a section (vol. i. p. 25), on 

 "Anticipations of the Principle of Substitution," and I 

 have reprinted that section unchanged in this edition 

 (p. 21). I remark therein that, " 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 

 writings, and novelty must arise chiefly in the mode of 

 harmonising and developing ideas." I point out, as 

 Professor T. M. Lindsay had previously done, that Beneke 

 had employed the name and principle of substitution, and 

 that doctrines closely approximating to substitution were 

 stated by the Port Eoyal Logicians more than 200 years 

 ago. 



I have not been at all surprised to learn, however, that 

 other logicians have more or less distinctly stated this 

 principle of substitution during the last two centuries. 

 As my friend and successor at Owens College, Professor 

 Adamson, has discovered, this principle can be traced back 

 to no less a philosopher than Leibnitz. 



The remarkable tract of Leibnitz, 1 entitled "Non inelegans 

 Specimen Demonstrandi in Abstractis," commences at once 

 with a definition corresponding to the principle : 



1 Leibnitii Opera Philosophica qua extant. Erdmann, Pars I. Berolini 

 1840, p. 94. 



