Tractatus Logico-Philosophicus · Chapter
6.1264 explained
Wittgenstein distinguishes between significant propositions, which assert something and are proven by showing it is so, and logical propositions, which are themselves forms of proof.
What happens
Wittgenstein distinguishes between significant propositions, which assert something and are proven by showing it is so, and logical propositions, which are themselves forms of proof. He states that every logical proposition is a modus ponens presented in signs, and that modus ponens cannot be expressed by a proposition.
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Narrative arc
Story tension across the book.
- Setup
- Escalation
- Breaking point
- Aftermath
- Closing
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Follow the arc while readingThemes in this chapter
- Logic and Tautology
Discusses the nature of logical propositions as forms of proof and modus ponens
- Limits of Language and Thought
Highlights the inexpressibility of modus ponens by a proposition, showing a limit of expression
Characters to notice
- Mr. Wittgenstein
Author of the proposition
Key passages
“The significant proposition asserts something, and its proof shows that it is so; in logic every proposition is the form of a proof.”
A meaningful proposition makes a claim, and its demonstration confirms that claim; but in logic, each proposition itself constitutes a demonstration.
Clarifies the contrast between empirical propositions and logical ones
“Every proposition of logic is a modus ponens presented in signs. (And the modus ponens can not be expressed by a proposition.)”
Each logical proposition is a rule of inference (modus ponens) shown through symbols, but this rule itself cannot be stated as a proposition.
Emphasizes the inexpressible nature of logical form
