Tractatus Logico-Philosophicus · Chapter
3.313 explained
Wittgenstein defines an expression as being represented by a variable whose values are the propositions containing that expression.
What happens
Wittgenstein defines an expression as being represented by a variable whose values are the propositions containing that expression. In the limiting case, the variable becomes constant and the expression becomes a proposition. He terms such a variable a 'propositional variable.'
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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
- Logical Atomism
The propositional variable is a tool for analyzing propositions into their constituent expressions, reflecting the atomistic structure of language.
- Limits of Language and Thought
The variable as a representation of expressions shows how language can generalize over possible propositions, highlighting the boundaries of what can be said.
Characters to notice
- Mr. Wittgenstein
Author of the Tractatus, introducing the concept of the propositional variable.
Key passages
“An expression is thus presented by a variable, whose values are the propositions which contain the expression.”
An expression is represented by a variable, and the possible values of that variable are the propositions that include the expression.
Clarifies the relationship between expressions and variables in logical notation.
“(In the limiting case the variable becomes constant, the expression a proposition.)”
In the extreme case, the variable is fixed to a single value, so the expression itself becomes a complete proposition.
Describes the boundary condition where a variable ceases to vary and becomes a specific proposition.
“I call such a variable a 'propositional variable.'”
I name this kind of variable a 'propositional variable.'
Introduces the technical term for a variable whose values are propositions.
