Tractatus Logico-Philosophicus · Chapter
5.5351 explained
Wittgenstein criticizes Russell's use of tautological expressions like 'p ⊃ p' as hypotheses to ensure arguments are propositions, arguing that such hypotheses are nonsense because they do not prevent meaningless arguments and do not affect
What happens
Wittgenstein criticizes Russell's use of tautological expressions like 'p ⊃ p' as hypotheses to ensure arguments are propositions, arguing that such hypotheses are nonsense because they do not prevent meaningless arguments and do not affect the sense of the proposition.
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 Falling action.
- Setup
- Escalation
- Breaking point
- Aftermath
- Closing
This passage marks the story’s dramatic climax because it presents the moment when the protagonist’s obsessive…
Full beat labels and climax notes unlock in the reader.
Follow the arc while readingThemes in this chapter
- Nonsense and Meaning
Wittgenstein argues that placing 'p ⊃ p' as a hypothesis to ensure argument form results in nonsense, as it does not make false arguments meaningful.
- Critique of Traditional Philosophy
Direct critique of Russell's logical method in the Principles of Mathematics.
Characters to notice
- Mr. Wittgenstein
Author of the critique
- Bertrand Russell
Mentioned for his use of 'p ⊃ p' in Principles of Mathematics
Key passages
“So Russell in the Principles of Mathematics has rendered the nonsense “ p is a proposition” in symbols by “ p ⊃ p ” and has put it as hypothesis before certain propositions to show that their places for arguments could only be occupied by propositions.”
Russell symbolically expressed the nonsensical statement 'p is a proposition' as 'p ⊃ p' and used it as a hypothesis to restrict arguments to propositions.
Wittgenstein identifies Russell's symbolic translation as nonsense.
“It is nonsense to place the hypothesis p ⊃ p before a proposition in order to ensure that its arguments have the right form, because the hypotheses for a non-proposition as argument becomes not false but meaningless, and because the proposition itself becomes senseless for arguments of the wrong kind, and therefore it survives the wrong arguments no better and no worse than the senseless hypothesis attached for this purpose.”
Using 'p ⊃ p' as a hypothesis to guarantee correct argument form is futile, since a non-proposition argument makes the hypothesis meaningless rather than false, and the proposition itself is already senseless with such arguments, so the hypothesis adds nothing.
Wittgenstein explains why the hypothesis is ineffective and nonsensical.
