Tractatus Logico-Philosophicus · Chapter
5.521 explained
Wittgenstein distinguishes the concept of 'all' from the truth-function, criticizing Frege and Russell for linking generality to logical product or sum, which obscures the meaning of existential and universal propositions.
What happens
Wittgenstein distinguishes the concept of 'all' from the truth-function, criticizing Frege and Russell for linking generality to logical product or sum, which obscures the meaning of existential and universal propositions.
Free preview opens on this chapter — companions, themes, and character notes appear beside the text.
Narrative arc
Story tension across the book.
- 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
- Critique of Traditional Philosophy
Wittgenstein challenges the Frege-Russell approach to generality, arguing it obscures the logical structure.
- Logic and Tautology
The discussion of generality and truth-functions relates to the nature of logical propositions.
Characters to notice
- Mr. Wittgenstein
Author of the Tractatus, presenting his critique of Frege and Russell's treatment of generality.
- Frege
Introduced generality in connection with logical product or sum, according to Wittgenstein.
- Bertrand Russell
Along with Frege, introduced generality in connection with logical product or sum, criticized by Wittgenstein.
Key passages
“I separate the concept all from the truth-function.”
I distinguish the notion of 'all' from the operation of truth-functions.
Wittgenstein insists that generality is not reducible to truth-functional operations.
“Frege and Russell have introduced generality in connection with the logical product or the logical sum.”
Frege and Russell linked generality to logical conjunction or disjunction.
Critique of their approach to quantification.
“Then it would be difficult to understand the propositions “ ( ∃ x ) . f x ” and “ ( x ) . f x ” in which both ideas lie concealed.”
This makes it hard to grasp existential and universal propositions, where both concepts are hidden.
The conflation obscures the logical form of quantified statements.
