Inlogic, alogical constant orconstant symbol of alanguage is asymbol that has the samesemantic value under everyinterpretation of. Two important types of logical constants arelogical connectives andquantifiers. Theequality predicate (usually written '=') is also treated as a logical constant in manysystems of logic.
One of the fundamental questions in thephilosophy of logic is "What is a logical constant?";[1] that is, what special feature of certain constants makes themlogical in nature?[2]
Some symbols that are commonly treated as logical constants are:
| Symbol | Meaning in English |
|---|---|
| T | "true" |
| F, ⊥ | "false" |
| ¬ | "not" |
| ∧ | "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 thelogical and).
Defining logical constants is a major part of the work ofGottlob Frege andBertrand Russell. Russell returned to the subject of logical constants in the preface to the second edition (1937) ofThe 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."[3] The text of this book usesrelationsR, theirconverses andcomplements asprimitive notions, also taken as logical constants in the formaRb.
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