# 5.5302 explained — Tractatus Logico-Philosophicus

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

## What happens

Wittgenstein criticizes Russell's definition of identity, arguing that it fails because it cannot express the possibility of two objects sharing all properties, which, though never true, remains a meaningful proposition.

## Themes in this chapter

### Critique of Traditional Philosophy

Wittgenstein challenges Russell's logical definition of identity, showing its inadequacy.

### Nonsense and Meaning

The proposition that two objects share all properties is never true but remains significant, highlighting the boundary between sense and nonsense.

## Character check-ins

### Bertrand Russell

Russell's definition of identity is critiqued by Wittgenstein.

### Mr. Wittgenstein

Wittgenstein presents the critique of Russell's definition.

## Key lines

> Russell’s definition of “ = ” won’t do; because according to it one cannot say that two objects have all their properties in common.

Russell's definition of identity is inadequate because it does not allow for the meaningful statement that two objects share every property.

_Wittgenstein points out a logical flaw in Russell's identity definition._

> (Even if this proposition is never true, it is nevertheless significant .)

Although the statement that two objects have all properties in common is never actually true, it still carries meaning.

_Emphasizes the distinction between truth and meaningfulness._

## Links

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