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In logic, a logical constant or constant symbol of a formal language is a symbol that has the same semantic value under every interpretation of . Two important types of logical constants are logical connectives and quantifiers. The equality predicate (usually written '=') is also treated as a logical constant in many formal system.
One of the fundamental questions in the philosophy of logic is "What is a logical constant?"; that is, what special feature of certain constants makes them logical in nature?Rudolf Carnap (1958). Introduction to symbolic logic and its applications. New York: Dover.
Some symbols that are commonly treated as logical constants are:
| T | "true" |
| F, ⊥ | "false" |
| ¬ | "logical negation" |
| ∧ | "and" |
| ∨ | "or" |
| → | "implies", "if...then" |
| ∀ | "for all" |
| ∃ | "there exists", "for some" |
| = | "equals" |
| "necessarily" | |
| "possibly" |
Many of these logical constants are sometimes denoted by alternate symbols (for instance, the use of the symbol "&" rather than "∧" to denote the logical and).
Defining logical constants is a major part of the work of Gottlob Frege and Bertrand Russell. Russell returned to the subject of logical constants in the preface to the second edition (1937) of The Principles of Mathematics noting that logic becomes linguistic: "If we are to say anything definite about them, they must be treated as part of the language, not as part of what the language speaks about."Bertrand Russell (1937) Preface to The Principles of Mathematics, pages ix to xi The text of this book uses relations R, their converses and complements as , also taken as logical constants in the form aRb.
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