# 6.022 explained — Tractatus Logico-Philosophicus

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

## What happens

Wittgenstein defines the concept of number as the general form common to all numbers, equating it with the variable number, and similarly treats equality of numbers as the general form of all specific numerical equalities.

## Themes in this chapter

### Logic and Tautology

The discussion of the general form of number and equality reflects the logical structure underlying arithmetic.

## Character check-ins

### Mr. Wittgenstein

Author of the proposition, defining number and numerical equality in terms of general form.

## Key lines

> The concept number is nothing else than that which is common to all numbers, the general form of a number.

The idea of number is just what all numbers share, namely their general pattern or form.

_Wittgenstein reduces the concept of number to its logical form._

> The concept number is the variable number.

The concept of number is the same as the variable that can stand for any number.

_Number is treated as a variable in logical notation._

> And the concept of equality of numbers is the general form of all special equalities of numbers.

What it means for numbers to be equal is just the general pattern that all specific numerical equalities follow.

_Equality is also understood as a formal, logical structure._

## Links

- HTML: https://www.betterreads.online/discover/tractatus_logico_philosophicus_se/chapters/6-022
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- All chapters: https://www.betterreads.online/discover/tractatus_logico_philosophicus_se/chapters