60 DIVISION OF PROPOSITIONS. [CHAP. IV. 



of pleasure, together with all things not productive of pleasure, 

 but preventive of pain, and its symbolical expression would be 



If then we attach to this expression placed in brackets to denote 

 that both its terms are referred to, the symbols s and t limiting 

 its application to things "transferable" and " limited in supply," 

 we obtain the following symbolical equivalent for the original 

 definition, viz. : 



w = st[p + r(\-p)}. (1) 



If the expression, " Either productive of pleasure or preventive of 

 pain," were intended to point out merely those things which are 

 productive of pleasure without being preventive of pain, p (1 - r), 

 or preventive of pain, without being productive of pleasure, 

 r (1 - p) (exclusion being made of those things which are both 

 productive of pleasure and preventive of pain), the expression in 

 symbols of the definition would be 



w-*t{p(l-r) + r(l-p)}. (2) 



All this agrees with what has before been more generally stated. 

 The reader may be curious to inquire what effect would be 

 produced if we literally translated the expression, " Things pro- 

 ductive of pleasure or preventive of pain," by p + r, making the 

 symbolical equation of the definition to be 



w = st(p + r). (3) 



The answer is, that this expression would be equivalent to (2), 

 with the additional implication that the classes of things denoted 

 by stp and str are quite distinct, so that of things transferable 

 and limited in supply there exist none in the universe which are 

 at the same time both productive of pleasure and preventive of 

 pain. How the full import of any equation may be determined 

 will be explained hereafter. What has been said may show that be- 

 fore attempting to translate our data into the rigorous language 

 of symbols, it is above all things necessary to ascertain the in- 

 tended import of the words we are using. But this necessity 

 cannot be regarded as an evil by those who value correctness of 



