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?"; that is, what special feature of certain constants makes them logical in nature?
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." The text of this book uses relations R, their converses and complements as primitive notions, also taken as logical constants in the form aRb.
See also
- Logical connective
- Logical value
- Non-logical symbol
References
- Peacocke, Christopher (May 6, 1976). "What is a Logical Constant?". The Journal of Philosophy. 73 (9): 221–240. doi:10.2307/2025420. JSTOR 2025420. Retrieved Jan 12, 2022.
- Carnap, Rudolf (1958). Introduction to symbolic logic and its applications. New York: Dover.
- Bertrand Russell (1937) Preface to The Principles of Mathematics, pages ix to xi
External links
- Stanford Encyclopedia of Philosophy entry on logical constants
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In logic a logical constant or constant symbol of a language L displaystyle mathcal L is a symbol that has the same semantic value under every interpretation of L displaystyle mathcal L 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 that is what special feature of certain constants makes them logical in nature Some symbols that are commonly treated as logical constants are Symbol Meaning in EnglishT true F false not and or implies if then for all there exists for some equals displaystyle Box necessarily displaystyle Diamond possibly Many of these logical constants are sometimes denoted by alternate symbols for instance the use of the symbol amp 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 The text of this book uses relations R their converses and complements as primitive notions also taken as logical constants in the form aRb See alsoLogical connective Logical value Non logical symbolReferencesPeacocke Christopher May 6 1976 What is a Logical Constant The Journal of Philosophy 73 9 221 240 doi 10 2307 2025420 JSTOR 2025420 Retrieved Jan 12 2022 Carnap Rudolf 1958 Introduction to symbolic logic and its applications New York Dover Bertrand Russell 1937 Preface to The Principles of Mathematics pages ix to xiExternal linksStanford Encyclopedia of Philosophy entry on logical constants This logic related article is a stub You can help Wikipedia by expanding it vte
