sometimes' is 'not-
always.'" In like manner we can re-define disjunction and the other truth-functions, as applied to propositions containing apparent variables, in terms of the definitions and primitive ideas for propositions containing no apparent variables. Propositions containing no apparent variables are called "elementary propositions." From these we can mount up step by step, using such methods as have just been indicated, to the theory of truth-functions as applied to propositions containing one, two, three, ... variables, or any number up to
, where
is any assigned finite number.
[38]The method of deduction is given in Principia Mathematica, vol. I. * 9.
[39]For linguistic reasons, to avoid suggesting either the plural or the singular, it is often convenient to say "