Tractatus Logico-Philosophicus · Chapter
5.513 explained
Wittgenstein discusses the commonality among symbols that assert conjunctions and disjunctions, and argues that each proposition has only one negation because only one proposition lies entirely outside it.
What happens
Wittgenstein discusses the commonality among symbols that assert conjunctions and disjunctions, and argues that each proposition has only one negation because only one proposition lies entirely outside it. He also notes that in Russell's notation, 'q : p ∨ ~p' says the same as 'q', and 'p ∨ ~p' says nothing.
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…
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Follow the arc while readingThemes in this chapter
- Logic and Tautology
The discussion of 'p ∨ ~p' as saying nothing illustrates the nature of tautologies.
- Nonsense and Meaning
The proposition 'p ∨ ~p' says nothing, highlighting the boundary between sense and nonsense.
Characters to notice
- Mr. Wittgenstein
Author of the proposition
- Bertrand Russell
Referenced for his notation
Key passages
“What is common to all symbols, which assert both p and q , is the proposition “ p . q ”.”
The common feature of all symbols that assert both p and q is the conjunction 'p and q'.
Clarifies the shared logical form of conjunctions.
“Thus in Russell’s notation also it appears evident that “ q : p ∨ ~ p ” says the same thing as “ q ”; that “ p ∨ ~ p ” says nothing.”
In Russell's notation, 'q and (p or not p)' is equivalent to 'q' alone, because 'p or not p' is a tautology that adds no information.
Illustrates the vacuity of tautologies in logical notation.
