Page:Wittengenstein - Tractatus Logico-Philosophicus, 1922.djvu/121

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TRACTATUS LOGICO-PHILOSOPHICUS

(And that which is common to the bases, and the result of an operation, is the bases themselves.)

5.241 The operation does not characterize a form but only the difference between forms.

5.242 The same operation which makes "q" from "p", makes "r" from "q", and so on. This can only be expressed by the fact that "p", "q", "r", etc., are variables which give general expression to certain formal relations.

5.25 The occurrence of an operation does not characterize the sense of a proposition.

For an operation does not assert anything; only its result does, and this depends on the bases of the operation.

(Operation and function must not be confused with one another.)

5.251 A function cannot be its own argument, but the result of an operation can be its own basis.

5.252 Only in this way is the progress from term to term in a formal series possible (from type to type in the hierarchy of Russell and Whitehead). (Russell and Whitehead have not admitted the possibility of this progress but have made use of it all the same.)

5.2521 The repeated application of an operation to its own result I call its successive application ("O' O' O' a" is the result of the threefold successive application of "O' ξ" to "a").

In a similar sense I speak of the successive application of several operations to a number of propositions.

5.2522 The general term of the formal series a, O', a, O' O' a, ... I write thus : "[a, x, O' x]". This expression in brackets is a variable. The first

term of the expression is the beginning of the
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