*xii PREFACE TO THE SECOND EDITION. 



find a copy of his book in London, even in the British 

 Museum Library; it is not mentioned in the printed 

 catalogue of the Bodleian Library ; Messrs. Asher have 

 failed to obtain it for me by advertisement in Germany ; 

 and Professor Adamson has been equally unsuccessful. 

 From the way in which the principle of substitution is 

 mentioned by Keusch, it would seem likely that other 

 logicians of the early part of the eighteenth century were 

 acquainted with it ; but, if so, it is still more curious that 

 recent historians of logical science have overlooked the 

 doctrine. 



It is a strange and discouraging fact, that true views of 

 logic should have been discovered and discussed from one 

 to two centuries ago, and yet should have remained, like 

 George Bentham's work in this century, without influ- 

 ence on the subsequent progress of the science. It may 

 be regarded as certain that none of the discoverers of 

 the quantification of the predicate, Bentham, Hamilton, 

 Thomson, De Morgan, and Boole, were in any way assisted 

 by the hints of the principle contained in previous writers. 

 As to my own views of logic, they were originally moulded 

 by a careful study of Boole's works, as fully stated in my 

 first logical essay. 1 As to the process of substitution, it 

 was not learnt from any work on logic, but is simply the 

 process of substitution perfectly familiar to mathematicians, 

 and with which I necessarily became familiar in the course 

 of my long-continued study of mathematics under the late 

 Professor De Morgan. 



I find that the Theory of Number, which I explained in 

 the eighth chapter of this work, is also partially anticipated 

 in a single scholium of Leibnitz. He first gives as an 

 axiom the now well-known law of Boole, as follows : 



" Axioma I. Si idem secum ipso sumatur, uihil consti- 

 tuitur novuin, seu A + A oc A" Then follows this 



1 Pure Logic, or the Logic of Quality apart from Quantity ; with 

 Remarks on Boole's System, and on the Relation of Logic and Mathomatict. 

 London, 1864, p. 3. 



