Page:Wittgenstein - Tractatus Logico-Philosophicus, 1922.djvu/141

Rh sum. Then it would be difficult to understand the propositions "$$~ (\exists x). fx$$" and "$$~ (x). fx$$" in which both ideas lie concealed. That which is peculiar to the "symbolism of generality" is firstly, that it refers to a logical prototype, and secondly, that it makes constants prominent.

The generality symbol occurs as an argument.

If the objects are given, therewith are all objects also given.

If the elementary propositions are given, then therewith all elementary propositions are also given.

It is not correct to render the proposition "$$~ (\exists x). fx$$"—as Russell does—in words "fx is possible".

Certainty, possibility or impossibility of a state of affairs are not expressed by a proposition but by the fact that an expression is a tautology, a significant proposition or a contradiction.

That precedent to which one would always appeal, must be present in the symbol itself.

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 one and only one x, which. . . .": and this x is a,

A completely generalized proposition is like every other proposition composite. (This is shown by the fact that in "$$~ (\exists x, \phi).\phi x$$" we must mention "$$\phi$$" and "$$x$$" separately. Both stand independently in signifying relations to the world as in the ungeneralized proposition.) Rh