Definition:Variable/Propositional Logic

Definition

A statement variable is a variable which is used to stand for an arbitrary and unspecified statement.

For a statement variable, a lowercase letter is usually used, for example:

$p, q, r, \ldots{}$, and so on

or lowercase Greek letters, for example:

$\phi, \psi, \chi$ and so on.

The citing of a statement variable can be interpreted as an assertion that the statement represented by that symbol is true.

That is:

$p$

means

$p \text { is true}$

Also known as

Equivalent terms for statement variable are:

• sentential variable
• propositional variable
• proposition symbol or propositional symbol.

The latter name is also used for the letters of the language of propositional logic, which are intended to represent statement variables.

Also see

• Definition:Statement Label: Note the difference between this and a statement variable:

The first is used to identify a particular statement.

The latter is used to represent an arbitrary instance of any statement at all.

• Definition:Propositional Symbol: when propositional logic is developed as a formal language, a statement variable is specified precisely.

Sources

• 1946: Alfred Tarski: Introduction to Logic and to the Methodology of Deductive Sciences (2nd ed.) ... (previous) ... (next): $\S \text{II}.12$: Laws of sentential calculus
• 1959: A.H. Basson and D.J. O'Connor: Introduction to Symbolic Logic (3rd ed.) ... (previous) ... (next): $\S 2.3$: Basic Truth-Tables of the Propositional Calculus
• 1964: Donald Kalish and Richard Montague: Logic: Techniques of Formal Reasoning ... (previous) ... (next): $\text{I}$: 'NOT' and 'IF': $\S 1$
• 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $1$: The Propositional Calculus $1$: $2$ Conditionals and Negation
• 1973: Irving M. Copi: Symbolic Logic (4th ed.) ... (previous) ... (next): $2$ Arguments Containing Compound Statements: $2.3$: Argument Forms and Truth Tables
• 1980: D.J. O'Connor and Betty Powell: Elementary Logic ... (previous) ... (next): $\S \text{I}: 1$: The Logic of Statements $(1)$
• 1988: Alan G. Hamilton: Logic for Mathematicians (2nd ed.) ... (previous) ... (next): $\S 1$: Informal statement calculus: $\S 1.1$: Statements and connectives
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): variable: 2.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): variable: 2.