# 5.531 explained — Tractatus Logico-Philosophicus

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

## What happens

Wittgenstein proposes a notation for identity that avoids the explicit use of the identity sign, suggesting that identity of arguments can be indicated by repeating the same variable, and difference by using distinct variables.

## Themes in this chapter

### Logical Atomism

The proposal to replace identity statements with notational conventions reflects the atomistic view that logical structure should mirror the structure of facts without extraneous signs.

## Character check-ins

### Mr. Wittgenstein

Author of the proposition, refining logical notation to eliminate the identity sign.

## Key lines

> I write therefore not “ f ( a , b ) . a = b ” but “ f ( a a ) ” (or “ f ( b b ) ”). And not “ f ( a , b ) . ~ a = b ”, but “ f ( a , b ) ”.

Instead of writing 'f(a,b) and a equals b', I write 'f(a,a)' (or 'f(b,b)'). And instead of 'f(a,b) and a does not equal b', I simply write 'f(a,b)'.

_Wittgenstein suggests that identity and difference of arguments can be shown by the use of same or different variable names, eliminating the need for an explicit identity sign._

## Links

- HTML: https://www.betterreads.online/discover/tractatus_logico_philosophicus_se/chapters/5-531
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