5.501 When a bracketed expression has propositions as its terms--and the
order of the terms inside the brackets is indifferent--then I indicate it
by a sign of the form '(E)'. '(E)' is a variable whose values are terms of
the bracketed expression and the bar over the variable indicates that it is
the representative of ali its values in the brackets. (E.g. if E has the
three values P,Q, R, then (E) = (P, Q, R). ) What the values of the
variable are is something that is stipulated. The stipulation is a
description of the propositions that have the variable as their
representative. How the description of the terms of the bracketed
expression is produced is not essential. We can distinguish three kinds of
description: 1.Direct enumeration, in which case we can simply substitute
for the variable the constants that are its values; 2. giving a function fx
whose values for all values of x are the propositions to be described; 3.
giving a formal law that governs the construction of the propositions, in
which case the bracketed expression has as its members all the terms of a
series of forms.
5.502 So instead of '(-----T)(E, ....)', I write 'N(E)'. N(E) is the
negation of all the values of the propositional variable E.
5.503 It is obvious that we can easily express how propositions may be
constructed with this operation, and how they may not be constructed with
it; so it must be possible to find an exact expression for this.
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