# 6.24 explained — Tractatus Logico-Philosophicus

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

## What happens

Wittgenstein describes the method of mathematics as one of substitution, where equations express the substitutability of expressions, and new equations are derived by replacing expressions according to existing equations.

## Themes in this chapter

### Logic and Tautology

The method of substitution in mathematics aligns with the tautological nature of logical propositions, as equations are derived through formal transformations.

## Character check-ins

### Mr. Wittgenstein

Author of the proposition; explains the method of mathematics as substitution.

## Key lines

> The method by which mathematics arrives at its equations is the method of substitution.

Mathematics derives its equations through the process of substituting one expression for another.

_Highlights the formal, rule-governed nature of mathematical reasoning._

> For equations express the substitutability of two expressions, and we proceed from a number of equations to new equations, replacing expressions by others in accordance with the equations.

Equations show that two expressions can be swapped, and we generate new equations by swapping expressions based on existing equations.

_Explains the iterative, mechanical process of mathematical derivation._

## Links

- HTML: https://www.betterreads.online/discover/tractatus_logico_philosophicus_se/chapters/6-24
- Book: https://www.betterreads.online/discover/tractatus_logico_philosophicus_se
- All chapters: https://www.betterreads.online/discover/tractatus_logico_philosophicus_se/chapters