# 6.21 explained — Tractatus Logico-Philosophicus

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

## What happens

Wittgenstein asserts that mathematical propositions do not express thoughts, distinguishing them from genuine propositions that picture facts.

## Themes in this chapter

### Nonsense and Meaning

Mathematical propositions are shown to lack the sense of genuine propositions, as they do not picture states of affairs.

### Logic and Tautology

Mathematical propositions are akin to tautologies, expressing no factual content or thought.

## Character check-ins

### Mr. Wittgenstein

Author of the proposition that mathematical propositions express no thoughts.

## Key lines

> Mathematical propositions express no thoughts.

Mathematical statements do not convey any factual content or represent possible states of affairs.

_Wittgenstein distinguishes mathematical propositions from empirical ones, aligning them with logical tautologies._

## Links

- HTML: https://www.betterreads.online/discover/tractatus_logico_philosophicus_se/chapters/6-21
- Book: https://www.betterreads.online/discover/tractatus_logico_philosophicus_se
- All chapters: https://www.betterreads.online/discover/tractatus_logico_philosophicus_se/chapters