Page:Wittengenstein - Tractatus Logico-Philosophicus, 1922.djvu/135

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TRACTATUS LOGICO-PHILOSOPHICUS

5.474 The number of necessary fundamental operations depends only on our notation.

5.475 It is only a question of constructing a system of signs of a definite number of dimensions — of a definite mathematical multiplicity.

5.476 It is clear that we are not concerned here with a number of primitive ideas which must be signified but with the expression of a rule.

5.5 Every truth-function is a result of the successive application of the operation (- - - - T)(\xi, . . . .) to elementary propositions.

This operation denies all the propositions in the right-hand bracket and I call it the negation of these propositions.

5.501 An expression in brackets whose terms are propositions I indicate — if the order of the terms in the bracket is indifferent — by a sign of the form "(\bar \xi)". "\xi" is a variable whose values are the terms of the expression in brackets, and the line over the variable indicates that it stands for all its values in the bracket.

(Thus if \xi has the 3 values P, Q, R, then (\bar \xi)=(P,Q, R).)

The values of the variables must be determined.

The determination is the description of the propositions which the variable stands for.

How the description of the terms of the expression in brackets takes place is unessential.

We may distinguish 3 kinds of description:

  1. Direct enumeration. In this case we can place simply its constant values instead of the variable.
  2. Giving a function "fx" whose values for all values of "x" are the propositions to be described.
  3. Giving a formal law, according to which those propositions are constructed. In this case the