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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.'

Themes 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.