A new Symbolic Treatment of the Old Logic. 201 



A new Symbolic Treatment of the Old Logic. By 

 Joseph John Murphy. Communicated by the 

 Rev. Robert Harley, M.A., F.R.S., Corresponding 

 Member. 



(Received January I4.th^ i8gi») 



" All knowledge is relative : " that is to say, all knowledge 

 is knowledge of relations ; and every proposition is the asser- 

 tion of a relation. The old logic is the theory of the formal 

 properties of a particular set of relations, which have been 

 variously defined as those of inclusion and exclusion — 

 those of identity and difference — and those of coexistence 

 and non-coexistence. All these are in effect the same — 

 the three following propositions are evidently synonymous 

 expressions, though expressed in three different ways: — 



The species Man is included in the class Rational. 

 The species Man is indentical with part of the class Rational, 

 The other attributes of Man coexist with the attribute 

 Rationality. 



In the present essay, the first of these three expressions 

 of the relation is adopted. The relations treated of are 

 defined to be those of total and partial inclusion and exclu- 

 sion as between classes, and between groups of cases. 



In logic, as in mathematics, literal symbols may be used 

 both for the terms between which the relations subsist, and 

 for the relations themselves. The former are called absolute, 

 the latter relative terms. We cannot do without symbols 

 for the former, if we are to use notation at all ; but whether 

 we use relative symbols will depend on our immediate 

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