5.52 If E has as its values all the values of a function fx for all values
of x, then N(E) = P(dx) . fx.
5.521 I dissociate the concept all from truth-functions. Frege and Russell
introduced generality in association with logical productor logical sum.
This made it difficult to understand the propositions '(dx) . fx' and '(x)
. fx', in which both ideas are embedded.
5.522 What is peculiar to the generality-sign is first, that it indicates a
logical prototype, and secondly, that it gives prominence to constants.
5.523 The generality-sign occurs as an argument.
5.524 If objects are given, then at the same time we are given all objects.
If elementary propositions are given, then at the same time all elementary
propositions are given.
5.525 It is incorrect to render the proposition '(dx) . fx' in the words,
'fx is possible ' as Russell does. The certainty, possibility, or
impossibility of a situation is not expressed by a proposition, but by an
expression's being a tautology, a proposition with a sense, or a
contradiction. The precedent to which we are constantly inclined to appeal
must reside in the symbol itself.
5.526 We can describe the world completely by means of fully generalized
propositions, i.e. without first correlating any name with a particular
object.
5.5261 A fully generalized proposition, like every other proposition, is
composite.
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