# 3.313 explained — Tractatus Logico-Philosophicus

> Chapter companion for Tractatus Logico-Philosophicus by Ludwig Wittgenstein.

## 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.

## Character check-ins

### Mr. Wittgenstein

Author of the Tractatus, introducing the concept of the propositional variable.

## Key lines

> 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._

## Links

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