What is "logical constant"

n. (context logic English) A word or phrase which has an invariant logical meaning and which is useful for forming argument forms.

In logic, a logical constant of a language L is a symbol that has the same semantic value under every interpretation of 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 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 (e.g., the use of the symbol "&" rather than "∧" to denote the logical and).