Tractatus Logico-Philosophicus · Chapter
4.0621 explained
Wittgenstein argues that the negation sign '~' does not correspond to anything in reality, as demonstrated by the equivalence of double negation (~~p = p).
What happens
Wittgenstein argues that the negation sign '~' does not correspond to anything in reality, as demonstrated by the equivalence of double negation (~~p = p). Although 'p' and '~p' have opposite senses, they correspond to the same reality, showing that negation is not a characteristic of a proposition's sense.
Themes in this chapter
Logical Atomism
The discussion of negation and its lack of correspondence to reality exemplifies the logical atomist view that complex propositions are built from simple elements.
Nonsense and Meaning
The analysis of negation touches on the boundaries of meaningful language, as the sign '~' does not represent an object in reality.
Characters to notice
- Mr. Wittgenstein
Author of the proposition, analyzing the nature of negation and its relation to reality.
Key passages
“That, however, the signs “ p ” and “ ~ p ” can say the same thing is important, for it shows that the sign “ ~ ” corresponds to nothing in reality.”
The fact that 'p' and 'not-p' can express the same fact is significant because it demonstrates that the negation symbol does not represent any actual feature of the world.
Wittgenstein emphasizes that logical operators like negation are not reflections of real objects or properties.
“The propositions “ p ” and “ ~ p ” have opposite senses, but to them corresponds one and the same reality.”
Although 'p' and 'not-p' have contradictory meanings, they both refer to the same state of affairs in reality.
This highlights the distinction between the sense of a proposition and the reality it depicts.