Tractatus Logico-Philosophicus · Chapter
4.442 explained
Wittgenstein discusses the propositional sign and truth-conditions, using a truth-table schema to illustrate how the final column alone expresses truth-conditions.
What happens
Wittgenstein discusses the propositional sign and truth-conditions, using a truth-table schema to illustrate how the final column alone expresses truth-conditions. He criticizes Frege's assertion sign as logically meaningless, arguing it merely indicates the author's belief in the proposition's truth, not a logical property.
Themes in this chapter
Nonsense and Meaning
Wittgenstein argues that Frege's assertion sign is logically meaningless, contributing to the theme of distinguishing sense from nonsense in logical notation.
Logic and Tautology
The discussion of truth-conditions and propositional signs relates to how logical propositions express tautologies or contradictions.
Characters to notice
- Mr. Wittgenstein
Author of the Tractatus, presenting his analysis of propositional signs and truth-conditions.
- Frege
Criticized for his assertion sign, which Wittgenstein deems logically meaningless.
- Bertrand Russell
Mentioned alongside Frege as using the assertion sign to mark propositions they hold as true.
Key passages
“Frege’s assertion sign “ ⊢ ” is logically altogether meaningless; in Frege (and Russell) it only shows that these authors hold as true the propositions marked in this way.”
Frege's assertion sign has no logical content; it merely indicates that Frege or Russell believe the proposition is true.
Wittgenstein distinguishes between logical form and psychological assertion.
“If the sequence of the truth-possibilities in the schema is once for all determined by a rule of combination, then the last column is by itself an expression of the truth-conditions.”
If the order of truth-possibilities is fixed by a rule, the final column alone suffices to represent the truth-conditions.
Wittgenstein reduces the truth-table to its essential component.