Tractatus Logico-Philosophicus · Chapter
5.535 explained
Wittgenstein argues that pseudo-propositions, such as those arising from Russell's Axiom of Infinity, dissolve when properly understood.
What happens
Wittgenstein argues that pseudo-propositions, such as those arising from Russell's Axiom of Infinity, dissolve when properly understood. The intended content of the axiom would be expressed in language by an infinite number of names with distinct meanings, not by a separate proposition.
Themes in this chapter
Nonsense and Meaning
The Axiom of Infinity is treated as a pseudo-proposition that disappears when its logical form is properly understood.
Limits of Language and Thought
The discussion shows how certain philosophical problems arise from misunderstanding the limits of what can be said.
Characters to notice
- Mr. Wittgenstein
Author of the Tractatus, presenting his critique of Russell's Axiom of Infinity.
- Bertrand Russell
His Axiom of Infinity is discussed as a source of pseudo-propositions.
Key passages
“So all problems disappear which are connected with such pseudo-propositions.”
All difficulties tied to these meaningless statements vanish.
Wittgenstein claims that recognizing pseudo-propositions dissolves associated philosophical problems.
“What the axiom of infinity is meant to say would be expressed in language by the fact that there is an infinite number of names with different meanings.”
The intended content of the axiom of infinity is shown by the existence of infinitely many distinct names in language, not by a separate proposition.
The axiom's truth would manifest in the structure of language itself, not as a substantive claim.