# 5.44 explained — Tractatus Logico-Philosophicus

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

## What happens

Wittgenstein argues that truth-functions are not material functions, using the example of double negation to show that the possibility of denial is already contained in affirmation, and that treating '~' as an object would make '~~p' say something different from 'p'.

## Themes in this chapter

### Logic and Tautology

The discussion of double negation and truth-functions relates to the nature of logical operations and tautologies.

### Nonsense and Meaning

The argument that treating '~' as an object would lead to nonsensical differences in meaning between '~~p' and 'p'.

## Character check-ins

### Mr. Wittgenstein

Author of the proposition, presenting the argument about truth-functions and denial.

## Key lines

> Truth-functions are not material functions.

Truth-functions are not like functions in material science or mathematics that operate on objects.

_Wittgenstein distinguishes logical operations from material ones._

> Does “ ~ ~ p ” deny ~ p , or does it affirm p ; or both?

Does the double negation of p deny the negation of p, affirm p, or do both?

_A rhetorical question highlighting the ambiguity if '~' were treated as an object._

> The proposition “ ~ ~ p ” does not treat of denial as an object, but the possibility of denial is already prejudged in affirmation.

The double negation does not refer to denial as a thing; rather, the possibility of denial is already built into affirmation.

_Wittgenstein argues that denial is not an object but a logical operation implicit in affirmation._

## Links

- HTML: https://www.betterreads.online/discover/tractatus_logico_philosophicus_se/chapters/5-44
- Book: https://www.betterreads.online/discover/tractatus_logico_philosophicus_se
- All chapters: https://www.betterreads.online/discover/tractatus_logico_philosophicus_se/chapters