CHAP. VI.] OF INTERPRETATION. 89 



represented by the constituent to which it is prefixed must be 

 taken. 



3rd. Let the coefficient be of the form -. Now, as in Arith- 



metic, the symbol represents an indefinite number, except when 



otherwise determined by some special circumstance, analogy 

 would suggest that in the system of this work the same symbol 

 should represent an indefinite class. That this is its true mean- 

 ing will be made clear from the following example : 



Let us take the Proposition, " Men not mortal do not exist ;" 

 represent this Proposition by symbols; and seek, in obedience to 

 the laws to which those symbols have been proved to be subject, 

 a reverse definition of " mortal beings," in terms of " men." 



Now if we represent " men" by y, and " mortal beings" by x, 

 the Proposition, " Men who are not mortals do not exist," will 

 be expressed by the equation 



from which we are to seek the value of x. Now the above equa- 



tion gives 



y - yx = 0, or yx = y. 



Were this an ordinary algebraic equation, we should, in the next 

 place, divide both sides of it by y. But it has been remarked in 

 Chap. u. that the operation of division cannot be performed with 

 the symbols with which we are now engaged. Our resource, then, 

 is to express the operation, and develop the result by the method 

 of the preceding chapter. We have, then, first, 



.y 



x , 



y 



and, expanding the second member as directed, 



*=y + o( l -!/) 



This implies that mortals (x) consist of all men (y), together 

 with such a remainder of beings which are not men (1 - y), as 



will be indicated by the coefficient -. Now let us inquire what 



