Page:Russell, Whitehead - Principia Mathematica, vol. I, 1910.djvu/60

If $\scriptstyle {\alpha \in 1}$, $\scriptstyle {{\breve {\iota }}'\alpha }$ is the only member of $\scriptstyle {\alpha }$, for the only member of $\scriptstyle {\alpha }$ is the only term to which $\scriptstyle {\alpha }$ has the relation $\scriptstyle {\iota }$. Thus "$\scriptstyle {{\breve {\iota }}'\alpha }$" takes the place of "$\scriptstyle {(}$℩$\scriptstyle {x)(\phi x)}$," if $\scriptstyle {\alpha }$ stands for $\scriptstyle {{\hat {z}}(\phi z)}$. In practice, "$\scriptstyle {{\breve {\iota }}'\alpha }$" is a more convenient notation than "$\scriptstyle {(}$℩$\scriptstyle {x)(\phi x)}$," and is generally used instead of "$\scriptstyle {(}$℩$\scriptstyle {x)(\phi x)}$."

The above account has explained most of the logical notation employed in the present work. In the applications to various parts of mathematics, other definitions are introduced; but the objects defined by these later definitions belong, for the most part, rather to mathematics than to logic. The reader who has mastered the symbols explained above will find that any later formulae can be deciphered by the help of comparatively few additional definitions.