# 3.333 explained — Tractatus Logico-Philosophicus

> Chapter companion for Tractatus Logico-Philosophicus by Ludwig Wittgenstein.

## What happens

Wittgenstein argues that a function cannot be its own argument because the functional sign already contains the prototype of its argument, leading to a distinction between inner and outer functions that resolves Russell's paradox by showing that the apparent self-reference is only a notational confusion.

## Themes in this chapter

### Logical Atomism

The analysis of functions and their arguments reflects the logical atomist project of decomposing propositions into their fundamental components.

### Critique of Traditional Philosophy

Wittgenstein's dissolution of Russell's paradox by clarifying the nature of functional signs exemplifies his critique of philosophical problems arising from linguistic confusion.

## Character check-ins

### Mr. Wittgenstein

Author of the argument that a function cannot be its own argument, resolving Russell's paradox.

### Bertrand Russell

His paradox is referenced as the problem that is resolved by the distinction between inner and outer functions.

## Key lines

> A function cannot be its own argument, because the functional sign already contains the prototype of its own argument and it cannot contain itself.

A function cannot take itself as input because the notation for the function already includes the pattern for its input, and it cannot include itself.

_Wittgenstein explains the impossibility of self-application for functions based on the structure of the functional sign._

> Herewith Russell’s paradox vanishes.

With this clarification, Russell's paradox disappears.

_Wittgenstein claims that his analysis resolves Russell's paradox by exposing it as a misunderstanding of functional notation._

## Links

- HTML: https://www.betterreads.online/discover/tractatus_logico_philosophicus_se/chapters/3-333
- Book: https://www.betterreads.online/discover/tractatus_logico_philosophicus_se
- All chapters: https://www.betterreads.online/discover/tractatus_logico_philosophicus_se/chapters