# 5.5 explained — Tractatus Logico-Philosophicus

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

## What happens

Wittgenstein defines every truth-function as the result of repeatedly applying the negation operation to elementary propositions, where the operation denies all propositions in the right-hand bracket.

## Themes in this chapter

### Logical Atomism

The operation on elementary propositions reflects the atomic structure of language and truth.

### Logic and Tautology

The definition of truth-functions through negation relates to the formal nature of logical operations.

## Character check-ins

### Mr. Wittgenstein

Author of the proposition defining truth-functions via successive negation.

## Key lines

> Every truth-function is a result of the successive application of the operation ( − − − − − T ) ( ξ , . . . . . ) to elementary propositions.

All truth-functions are generated by repeatedly applying a specific negation operation to basic propositions.

_Clarifies the generative process of truth-functions from elementary propositions._

> This operation denies all the propositions in the right-hand bracket and I call it the negation of these propositions.

The operation negates every proposition listed in the right-hand bracket, which I term the negation of those propositions.

_Defines the operation as a form of joint negation._

## Links

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