Tractatus Logico-Philosophicus · Chapter
4.461 explained
Wittgenstein distinguishes between propositions that show what they say, and tautologies and contradictions which say nothing.
What happens
Wittgenstein distinguishes between propositions that show what they say, and tautologies and contradictions which say nothing. Tautologies are unconditionally true and contradictions are never true; both are without sense, analogous to a point from which two arrows go in opposite directions.
Themes in this chapter
Nonsense and Meaning
Tautologies and contradictions are described as without sense, illustrating the limits of meaningful language.
Logic and Tautology
Tautology is defined as unconditionally true, and contradiction as never true, both lacking truth-conditions.
Characters to notice
- Mr. Wittgenstein
Author of the proposition, explaining the nature of tautology and contradiction.
Key passages
“The proposition shows what it says, the tautology and the contradiction that they say nothing.”
A proposition displays its meaning, while tautologies and contradictions display that they have no meaning.
Clarifies the distinction between sense and senselessness.
“The tautology has no truth-conditions, for it is unconditionally true; and the contradiction is on no condition true.”
A tautology is true under all circumstances, so it has no conditions for truth; a contradiction is false under all circumstances.
Explains the logical status of tautologies and contradictions.
“Tautology and contradiction are without sense. (Like the point from which two arrows go out in opposite directions.)”
Tautologies and contradictions lack meaning, similar to a point where two arrows point in opposite directions.
Uses a visual metaphor to illustrate the lack of informative content.
“I know, e.g. nothing about the weather, when I know that it rains or does not rain.”
Knowing that it either rains or does not rain gives no actual information about the weather.
Example showing that tautologies convey no factual knowledge.