Tractatus Logico-Philosophicus · Chapter
5.51 explained
Wittgenstein explains how the N-operator, when applied to a set with one proposition, yields its negation, and when applied to a set with two propositions, yields the joint negation (neither p nor q).
What happens
Wittgenstein explains how the N-operator, when applied to a set with one proposition, yields its negation, and when applied to a set with two propositions, yields the joint negation (neither p nor q).
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Narrative arc
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- Setup
- Escalation
- Breaking point
- Aftermath
- Closing
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Follow the arc while readingThemes in this chapter
- Logic and Tautology
The N-operator defines how truth-functions are built from elementary propositions, grounding logical necessity in tautology.
Characters to notice
- Mr. Wittgenstein
Author of the Tractatus, presenting the N-operator as a fundamental logical operation.
Key passages
“If ξ has only one value, then N ( ξ ‾ ) = ~ p (not p ), if it has two values then N ( ξ ‾ ) = ~ p . ~ q (neither p nor q ).”
When the set ξ contains a single proposition, the N-operator gives its negation; when it contains two propositions, the N-operator gives the conjunction of their negations.
This illustrates how the N-operator can generate all truth-functions by joint negation.
