# 5.41 explained — Tractatus Logico-Philosophicus

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

## What happens

This proposition states that the results of truth-operations on truth-functions are identical when they correspond to the same truth-function of elementary propositions, emphasizing the determinacy of logical form.

## Themes in this chapter

### Logic and Tautology

The identity of truth-operations on truth-functions underlies the tautological nature of logical propositions.

## Key lines

> For all those results of truth-operations on truth-functions are identical, which are one and the same truth-function of elementary propositions.

Whenever two sets of truth-operations applied to truth-functions yield the same truth-function of elementary propositions, their results are identical.

_Clarifies the uniqueness of logical outcomes based on underlying truth-functions._

## Links

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