# 5.532 explained — Tractatus Logico-Philosophicus

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

## What happens

Wittgenstein critiques Russell's notation for existence statements, arguing that identity signs are unnecessary and can be replaced by more perspicuous logical forms that avoid pseudo-propositions about identity.

## Themes in this chapter

### Logical Atomism

Wittgenstein's reformulation of existence statements reflects the logical atomist project of analyzing propositions into elementary components without superfluous signs like identity.

### Nonsense and Meaning

By eliminating the identity sign, Wittgenstein aims to avoid pseudo-propositions that appear meaningful but are logically empty.

## Character check-ins

### Mr. Wittgenstein

Author of the Tractatus, presenting a refined logical notation that eliminates the identity sign.

### Bertrand Russell

His notation for existence statements is critiqued and reformulated by Wittgenstein.

## Key lines

> And analogously: not “ ( ∃ x , y ) . f ⁡ ( x , y ) . x = y ”, but “ ( ∃ x ) . f ⁡ ( x , x ) ”; and not “ ( ∃ x , y ) . f ⁡ ( x , y ) . ~ x = y ”, but “ ( ∃ x , y ) . f ⁡ ( x , y ) ”.

Instead of writing 'there exist x and y such that f(x,y) and x equals y', we should write 'there exists an x such that f(x,x)'. And instead of 'there exist x and y such that f(x,y) and x is not equal to y', we should simply write 'there exist x and y such that f(x,y)'.

_Wittgenstein shows how to eliminate the identity sign by using distinct variables or repeated variables, making the logical form more perspicuous._

## Links

- HTML: https://www.betterreads.online/discover/tractatus_logico_philosophicus_se/chapters/5-532
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