Let the sign 'ξ' indicate a variable whose terms are propositions. Let ξ‾ indicate the list of all those values where the order of the terms is indifferent. The bar indicates that the variable represents of all its values. The declaration describes the propositions the variable represents. If ξ has the three values P, Q, R, then (ξ‾)=(P, Q, R).
What the values of the terms are are must be fixed, but how the each term of the bracketed expression are described is indifferent. There are three ways that it can be done:
- Direct enumeration, in which case we can simply substitute constant values for the variable.
- Stating a function fx whose values for all values of x are the propositions to be described.
- Stating a formal law that governs the construction of the propositions. In that case the bracketed expression has all the terms of a series of forms as its members.
Tt is now clear that this operation may be used to construct propositions, but exactly how it can be done must be made clear as well.