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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 Texts in Mathematics

Graduate Studies in Mathematics

Mathematics Encyclopedia

World

Index

Hellenica World - Scientific Library

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