Page:Wittengenstein - Tractatus Logico-Philosophicus, 1922.djvu/91

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TRACTATUS LOGICO-PHILOSOPHICUS

as it would be to say: 2+2 is at 3 o’clock equal to 4.)

4.12721 The formal concept is already given with an object, which falls under it. One cannot, therefore, introduce both, the objects which fall under a formal concept and the formal concept itself, as primitive ideas. One cannot, therefore, e.g. introduce (as Russell does) the concept of function and also special functions as primitive ideas; or the concept of number and definite numbers.

4.1273 If we want to express in logical symbolism the general proposition “b is a successor of a” we need for this an expression for the general term of the formal series: aRb, (∃x):aRx.xRb, (∃x,y):aRx.xRy.yRb,… The general term of a formal series can only be expressed by a variable, for the concept symbolized by “term of this formal series” is a formal concept. (This Frege and Russell overlooked; the way in which they express general propositions like the above is, therefore, false; it contains a vicious circle.)

We can determine the general term of the formal series by giving its first term and the general form of the operation, which generates the following term out of the preceding proposition.

4.1274 The question about the existence of a formal concept is senseless. For no proposition can answer such a question.

(For example, one cannot ask: “Are there unanalysable subject-predicate propositions?”)

4.128 The logical forms are anumerical.

Therefore there are in logic no pre-eminent numbers, and therefore there is no philosophical monism or dualism, etc.

4.2 The sense of a proposition is its agreement and disagreement with the possibilities of the
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