INTRODUCTION. 27 



an indefinite extent of logical arguments immediately 

 deducible from the principle of substitution of which 

 the ancient syllogism forms but a small and not even 

 the most important part. 



The Logic of Relatives. 



There is a difficult and important branch of logic 

 which may be called the Logic of Relatives. If I argue, 

 for instance, that because Daniel BernouUi was the son 

 of John, and John the brother of James, therefore Daniel 

 was the nephew of James, it is not possible to prove 

 this conclusion by any simple logical process. We re- 

 quire at any rate to assume that the son of a brother is 

 a nephew. A simple logical relation is that which exists 

 between properties and circumstances of the same object 

 or class. But objects and classes of objects may also be 

 related according to aU the properties of time and space. 

 I believe it may be shown, indeed, that where an inference 

 concerning such relations is drawn, a process of substi- 

 tution is really employed and an identity must exist ; 

 but I wih 1 not undertake to prove the assertion in this 

 work. The relations of time and space are logical 

 relations of a complicated character demanding much 

 abstract and difficult investigation. The subject has been 

 treated with such great ability by Professors Peirce x , 

 De Morgan y, Ellis z , and Harley, that I will not in the 



x ' Description of a Notation for the Logic of Relatives, resulting from 

 an Amplification of the Conceptions of Boole's Calculus of Logic/ By 

 C. S. Peirce. ' Memoirs of the American Academy,' vol. ix. Cam- 

 bridge, U.S., 1870. 



y 'On the Syllogism, No. IV, and on the Logic of Relations.' By 

 Augustus De Morgan. 'Transactions of the Cambridge Philosophical 

 Society,' vol. x. part ii. 1860. 



z ' Observations on Boole's Laws of Thought/ By the late R. 

 Leslie Ellis ; communicated by the Rev. Robert Harley, F.R.S. 'Report 



