In logic, a logical constant of a language \( {\mathcal {L}} \) is a symbol that has the same semantic value under every interpretation of\( {\mathcal {L}} \) . 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?[1]
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"
\( \Box \) "necessarily"
\( \Diamond \) "possibly"
Many of these logical constants are sometimes denoted by alternate symbols (e.g., 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.
See also
Non-logical symbol
Logical value
Logical connective
References
Carnap
External links
Stanford Encyclopedia of Philosophy entry on logical constants
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
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