Mr. Murpiiv on a 



A New System of Logical Notation. By Joseph John 

 Murphy.— Communicated by the Rev. Robert Harley, 

 M.A., F.R.S., Corresponding Member. 



{Received October .23rd, 1888.) 



In the present state of the science, no apology is needed 

 for offering a new system of logical notation. The use of 

 notation in logic is not to work problems, but to illustrate 

 principles ; and for this purpose the more systems of notation 

 we have the better, so long as they are not absurd, and not 

 mere reproductions of other systems. 



The chief feature of the notation now proposed is that 

 the signification of all the literal symbols is purely qualita- 

 tive, unless they are expressly quantified ; so that x does 

 not mean "all .r" or " every ;r," but only "some .r" or " an;t'." 

 Consequently the equation 



x=y 



means "some x (or some one x) is j'," provided that both x 

 and y are the names of things having real existence : — if 

 either is non-existent, the proposition has no significance. 



For all, Boole's symbol i is used ; consequently \x is 

 the expression for " all (or every) x " ; and " all x is y " is 

 written 



ia"=_y. 

 The inverse of this is given by transposing the coefficient 

 of quantity and assigning to it a negative index, when we get 



that is to say "only y is x" or "nothing but y is x." The 

 expression 



IX = i~V 

 would mean " all x is nothing but j," and would be true, 



