In
logic, a logical constant of a
language is a
symbol that has the same
semantic value under every
interpretation of
. Two important types of logical constants are
logical connective
In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. They can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary co ...
s and
quantifiers. The
equality
Equality may refer to:
Society
* Political equality, in which all members of a society are of equal standing
** Consociationalism, in which an ethnically, religiously, or linguistically divided state functions by cooperation of each group's elite ...
predicate (usually written '=') is also treated as a logical constant in many
systems of logic
A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system.
A form ...
.
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:
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
In logic, mathematics and linguistics, And (\wedge) is the truth-functional operator of logical conjunction; the ''and'' of a set of operands is true if and only if ''all'' of its operands are true. The logical connective that represents this ...
).
Defining logical constants is a major part of the work of
Gottlob Frege and
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, ar ...
. 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,
heymust be treated as part of the language, not as part of what the language speaks about."
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, ar ...
(1937) Preface to ''The Principles of Mathematics'', pages ix to xi The text of this book uses
relations R, their
converses
Chuck Taylor All-Stars or Converse All Stars (also referred to as "Converse", "Chuck Taylors", "Chucks", "Cons", "All Stars", and "Chucky Ts") is a model of casual shoe manufactured by Converse (shoe company), Converse (a subsidiary of Nike, In ...
and
complements as
primitive notions, also taken as logical constants in the form aRb.
See also
*
Non-logical symbol
*
Logical value
*
Logical connective
In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. They can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary co ...
References
External links
Stanford Encyclopedia of Philosophy entry on logical constants
Philosophical logic
Concepts in logic
Syntax (logic)
Logical truth
Logic symbols
{{logic-stub