Wednesday, 9 December 2009


7.0 Whereof we cannot speak, thereof we must remain silent.

Tractatus Logico-Philosophicus

3.333 The reason why a function cannot be its own argument is that the sign for a function already contains the prototype of its argument, and it cannot contain itself.

For let us suppose that the function F(fx) could be its own argument: in that case there would be a proposition 'F(F(fx))', in which the outer function F and the inner function F must have different meanings, since the inner one has the form φ(fx) and the outer one has the form ψ(φ(fx)). Only the letter 'F' is common to the two functions but the letter by itself signifies nothing.

This immediately becomes clear if instead of 'F(fu)' we write '(∃φ):F(φu).φu=Fu'.

That disposes of Russell's Paradox.

Tractatus Logico-Philosophicus

109. ... Philosophy is a battle against the bewitchment of our intelligence by means of our language.
- Philosophical Investigations I

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