Tractatus Logico-Philosophicus · Chapter
3.333 explained
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
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.
Free preview opens on this chapter — companions, themes, and character notes appear beside the text.
Narrative arc
Story tension across the book — this chapter sits in Exposition.
- Setup
- Escalation
- Breaking point
- Aftermath
- Closing
This passage marks the story’s dramatic climax because it presents the moment when the protagonist’s obsessive…
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Follow the arc while readingThemes 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.
Characters to notice
- 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 passages
“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.
