INTRODUCTION. 



for it gives to all the formulae of reasoning a dual 

 character. It asserts also that b'etween presence or 

 absence, existence or non-existence, affirmation or ne- 

 gation, there is no third alternative. As Aristotle said, 

 there can be no mean between opposite assertions : we 

 must either affirm or deny. Hence the somewhat incon- 

 venient name by which it has been generally known 

 The Law of Excluded Middle. 



It may be held that these laws are not three inde- 

 pendent and distinct laws, they rather express three 

 different aspects of the same truth, and each law doubt- 

 less presupposes and implies the other two. But it has 

 not hitherto been found possible to state these characters 

 of identity and difference in less than the three-fold 

 formula. The reader may perhaps desire some infor- 

 mation as to the mode in which these laws have been 

 stated, or the way in which they have been regarded, 

 by philosophers in different ages of the world. Abundant 

 information on this and many other points of logical 

 history will be found in Ueberweg's * System of Logic/ 

 of which an excellent translation has been published by 

 Mr. T. M. Lindsay d . I must confess however that the 

 history of logical doctrines has seemed to me one of the 

 most confusing and least beneficial studies in which a 

 person can engage ; and over-abundant attention perhaps 

 has been paid to it by Hamilton, Mansel, and many 

 German logicians. 



The Nature and Authority of the Laws of Identity 

 and Difference. 



I must at least allude to the profoundly difficult 

 question concerning the nature and authority of these 



d Ueberweg's 'System of Logic/ trans! . by Lindsay, London, 1871, 

 pp. 228-281. 



