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'.
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'.
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.