# 6.03 explained — Tractatus Logico-Philosophicus

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

## What happens

Wittgenstein defines the general form of the cardinal number as a series starting from 0, where each successive number is obtained by adding 1 to the previous one.

## Themes in this chapter

### Logic and Tautology

The definition of cardinal numbers as a formal series reflects Wittgenstein's view that mathematical propositions are tautologies or formal transformations.

## Character check-ins

### Mr. Wittgenstein

Author of the proposition defining the general form of cardinal numbers.

## Key lines

> The general form of the cardinal number is: [ 0 , ξ , ξ + 1 ] .

Every natural number can be generated by starting at 0 and repeatedly applying the operation of adding 1.

_This defines the natural numbers as a recursive series, foundational to arithmetic._

## Links

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