# 6.22 explained — Tractatus Logico-Philosophicus

> Chapter companion for Tractatus Logico-Philosophicus by Ludwig Wittgenstein.

## 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.

## Themes 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.

## Character check-ins

### Mr. Wittgenstein

Author of the proposition; presents the analogy between logical tautologies and mathematical equations.

## Key lines

> 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._

## Links

- HTML: https://www.betterreads.online/discover/tractatus_logico_philosophicus_se/chapters/6-22
- Book: https://www.betterreads.online/discover/tractatus_logico_philosophicus_se
- All chapters: https://www.betterreads.online/discover/tractatus_logico_philosophicus_se/chapters