5.526

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One can describe the world completely by completely generalized propositions, i.e. without from the outset co-ordinating any name with a definite object.

In order then to arrive at the customary way of expression we need simply say after an expression "there is only and only one x, which . . . .": and this x is a.

5.5261    A completely generalized proposition is like every other proposition composite. (This is shown by the fact that in "( EXISTS x we must mention φ) . φx", "φ" and "x" separately. Both stand independently in signifying relations to the world as in the ungeneralized proposition.)

A characteristic of a composite symbol: it has something in common with other symbols.

5.5262    The truth or falsehood of every proposition alters something in the general structure of the world. And the range which is allowed to its structure by the totality of elementary propositions is exactly that which the completely general propositions delimit.

(If an elementary proposition is true, then, at any rate, there is one more elementary proposition.)