Tractatus Logico-Philosophicus · Chapter
6.22 explained
Wittgenstein draws a parallel between logic and mathematics, stating that while logic shows the structure of the world through tautologies, mathematics does so through equations.
What happens
Wittgenstein draws a parallel between logic and mathematics, stating that while logic shows the structure of the world through tautologies, mathematics does so through equations.
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
- Logic and Tautology
Logic shows the structure of the world through tautologies, which are necessarily true.
- Limits of Language and Thought
Mathematics, like logic, expresses no thoughts but shows the form of the world.
Characters to notice
- Mr. Wittgenstein
Author of the proposition; presents the analogy between logical tautologies and mathematical equations.
Key passages
“The logic of the world which the propositions of logic show in tautologies, mathematics shows in equations.”
The logical structure of reality is revealed by logical propositions through tautologies, and by mathematics through equations.
Wittgenstein equates the expressive function of logic and mathematics in displaying the form of the world.
