# Logical constant

In logic, a **logical constant** or **constant symbol** of a 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 systems of logic.

One of the fundamental questions in the philosophy of logic is "What is a logical constant?";^{[1]} that is, what special feature of certain constants makes them *logical* 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 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."^{[3]} The text of this book uses relations *R*, their converses and complements as primitive notions, also taken as logical constants in the form *aRb*.

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