propositionsstatements

Propositions and statements are central concepts in logic and the philosophy of language. A proposition is the content that can be true or false; it is the semantic meaning expressed by a declarative sentence. A statement is a linguistic expression that asserts something and can be assigned a truth value. In many contexts the terms are used interchangeably, but some logicians distinguish the abstract proposition from the sentence that states it.

In propositional logic, basic units are propositions (often written as p, q, r). These units can be combined with logical connectives such as and, or, not, implies, and if and only if to form compound propositions. The truth value of a compound proposition is determined by the truth values of its components, and truth tables are used to analyze them. Propositions are considered truth-apt: they can be true or false, unlike questions or commands.

Examples: The proposition “The Earth orbits the Sun” is true; “If it rains, the ground is wet” is a conditional proposition whose truth value depends on the actual weather; “The square root of two is irrational” is a classic proposition with a definite truth value. Note that not every sentence expresses a proposition: imperatives (“Close the door”) and questions do not. Ambiguity and context can affect whether a sentence expresses a single proposition.

Across disciplines, “proposition” and “statement” are used to refer to the content of assertions. In mathematics, theorems and axioms are typically stated as propositions or statements that can be evaluated for truth within a given theory.