# 5.31 explained — Tractatus Logico-Philosophicus

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

## What happens

Wittgenstein explains that the schemata from 4.31 remain significant even when the propositional variables are not elementary propositions, and that the propositional sign in 4.442 expresses a truth-function of elementary propositions regardless of the complexity of its components.

## Themes in this chapter

### Logical Atomism

The passage emphasizes that all propositions, even complex ones, are ultimately truth-functions of elementary propositions, a core tenet of logical atomism.

## Character check-ins

### Mr. Wittgenstein

Author of the Tractatus, presenting the logical structure of propositions.

## Key lines

> The schemata No. 4.31 are also significant, if “ p ”, “ q ”, “ r ”, etc. are not elementary propositions.

The truth-table schemata from 4.31 still apply even when the variables stand for complex propositions rather than simple ones.

_Wittgenstein extends the applicability of truth-functional analysis beyond elementary propositions._

> And it is easy to see that the propositional sign in No. 4.442 expresses one truth-function of elementary propositions even when “ p ” and “ q ” are truth-functions of elementary propositions.

The notation in 4.442 still represents a truth-function of basic propositions, even if its components are themselves truth-functions.

_This reinforces the idea that all propositions reduce to truth-functions of elementary propositions._

## Links

- HTML: https://www.betterreads.online/discover/tractatus_logico_philosophicus_se/chapters/5-31
- Book: https://www.betterreads.online/discover/tractatus_logico_philosophicus_se
- All chapters: https://www.betterreads.online/discover/tractatus_logico_philosophicus_se/chapters