474 D R - A - N - WHITEHEAD ON 



. . ' . . On(ExWy).. [' ". ^ '^Jmv^^ 



Again, (Ex<l>'y) means there exists an entity ivhich is denoted by the non- 

 propositional function <f>'z, when z has the particular value y. For example, if u is a 

 class, there is such an entity as its cardinal number, denoted by Nc'w ; but if u is not 

 a class, there is no such entity as its cardinal number.* 



On Symbols of the Type R ; ( ). 



Relations. R'(xyz) means x, y, z form an instance in which the triadic relation R 

 holds, the special "positions" of x, y, z in this instance of that relationship being 

 indicated by their order of occurrence in the symbol ^'(xyz). Again, R ; ( ' yz) means 

 there exists an entity, x say, such that ~R'(xyz). The symbolic definitions of R ; ( ' 

 and of analogous symbols, are 



Df 



z) . = . ( W ) . R(xyz) Df 



Df 

 Df 

 2) . E'(a^) Df 



and so on. Again, R ; ( ; yz) denotes the class of terms, such as x (say), which satisfy 

 K,-(xyz), and ~R'(-;z) denotes the class of terms, such as y (say), such that there exists a 

 term, x say, such that ~R'(xyz) holds. The symbolic definitions of R : (;yz) and of 

 analogous entities, and of R ; (';) and of analogous entities, are 



Df 

 Df 

 Df 

 Df 

 Dt 



Df 



and so on : 



Df 



Df 

 Df 



The difficult question of the import of a proposition, which contains a non-propositional function (with 

 some particular entity as argument) to which no entity corresponds, has recently been elucidated by 

 RUSSELL, cf. 'Mind,' October, 1905. All propositions containing such a function are untrue, unless the 

 function is merely a constituent of a subsidiary proposition whose truth is not implied by the proposition 

 in question. 



