Tractatus Logico-Philosophicus · Chapter
5.525 explained
Wittgenstein criticizes Russell's translation of the existential proposition '(∃x).fx' as 'fx is possible,' arguing that modality (possibility, impossibility, certainty) is not expressed by a proposition's content but by the logical status
What happens
Wittgenstein criticizes Russell's translation of the existential proposition '(∃x).fx' as 'fx is possible,' arguing that modality (possibility, impossibility, certainty) is not expressed by a proposition's content but by the logical status of the expression itself—whether it is a tautology, a significant proposition, or a contradiction. The necessary precedent for such logical distinctions must be inherent in the symbol, not appealed to externally.
Themes in this chapter
Nonsense and Meaning
The distinction between tautology, significant proposition, and contradiction is central to Wittgenstein's view of meaningful expression.
Limits of Language and Thought
Modality is not a matter of propositional content but of the logical form inherent in symbols, reflecting the limits of what can be said.
Characters to notice
- Mr. Wittgenstein
Author of the Tractatus; presents a critique of Russell's interpretation of existential propositions.
- Bertrand Russell
Mentioned as the target of Wittgenstein's criticism regarding the rendering of '(∃x).fx' as 'fx is possible.'
Key passages
“It is not correct to render the proposition “ ( ∃ x ) . f x ”—as Russell does—in the words “ f x is possible .””
Russell's translation of '(∃x).fx' as 'fx is possible' is mistaken.
Wittgenstein rejects the modal interpretation of existential quantification.
“Certainty, possibility or impossibility of a state of affairs are not expressed by a proposition but by the fact that an expression is a tautology, a significant proposition or a contradiction.”
Modal concepts like certainty, possibility, and impossibility are not conveyed by the content of a proposition, but rather by whether the expression is a tautology, meaningful, or contradictory.
Modality is a feature of logical form, not of propositional content.
“That precedent to which one would always appeal, must be present in the symbol itself.”
The logical standard that one might seek to invoke must be inherent within the symbol itself.
The necessary logical distinctions are internal to the symbol, not externally imposed.