Tractatus Logico-Philosophicus · Chapter
5.44 explained
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 so
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'.
Free preview opens on this chapter — companions, themes, and character notes appear beside the text.
Narrative arc
Story tension across the book — this chapter sits in Falling action.
- Setup
- Escalation
- Breaking point
- Aftermath
- Closing
This passage marks the story’s dramatic climax because it presents the moment when the protagonist’s obsessive…
Full beat labels and climax notes unlock in the reader.
Follow the arc while readingThemes 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'.
Characters to notice
- Mr. Wittgenstein
Author of the proposition, presenting the argument about truth-functions and denial.
Key passages
“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.
