EXTENSION OF THE ORDINARY LOGIC. 91 



Notation for the Logic of Relatives/' extracted from the 

 Memoirs of the American Academy, vol. ix. 



In applying algebraic notation to the ordinary logic, in 

 however extended and generalized a form, the terms 

 denote objects and classes of objects ; there is no need of 

 terms denoting relations between these ; and the ordinary 

 logic, as generalized and extended by Boole and Jevons, 

 has consequently been called the logic of absolute terms. 

 Nevertheless all logic belongs to the logic of relatives. 

 The logic of relatives is related to the ordinary logic, not 

 as relative is related to absolute, but as the entire science 

 is related to its simplest part. It is in accordance with 

 all analogies drawn from the history of science, that the 

 simplest part of a science should thus be studied alone and 

 brought to comparative perfection, before any one suspects 

 that its problems are not isolated, but constitute only the 

 simplest part of an infinitely wider subject. 



From the present point of view, the old logic is defined 

 as that part of logical science which deals with the rela- 

 tions of inclusion and exclusion. 



In order to exhibit inclusion as a particular case of re- 

 lation, we shall need a symbol for it. De Morgan uses L 

 as the symbol of relation generally, and I propose to use 

 L in this sense, keeping the Homan capitals for absolute 

 terms. 



Combination in logic is analogous, though not closely 

 so, to multiplication (see Boole and Jevons, passim) . 

 What is the corresponding mathematical analogue of 

 logical relation? The Rev. Robert Harley maintains that 

 it is function generally (see the British Association Trans- 

 actions, 1866 and 1870); and I have no doubt he is 

 right. But within the very limited scope of the present 

 inquiry it will not be misleading if we treat relation as 

 analogous, though not closely so, to ratio, and the sym- 



