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In
logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from prem ...
, a logical constant of a
language Language is a structured system of communication. The structure of a language is its grammar and the free components are its vocabulary. Languages are the primary means by which humans communicate, and may be conveyed through a variety of ...
\mathcal is a
symbol A symbol is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, object, or relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise very different conc ...
that has the same semantic value under every
interpretation Interpretation may refer to: Culture * Aesthetic interpretation, an explanation of the meaning of a work of art * Allegorical interpretation, an approach that assumes a text should not be interpreted literally * Dramatic Interpretation, an event ...
of \mathcal. 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 ...
s and quantifiers. The equality 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). Defining logical constants is a major part of the work of
Gottlob Frege Friedrich Ludwig Gottlob Frege (; ; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic p ...
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, a ...
. 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,
hey Hey or Hey! may refer to: Music * Hey (band), a Polish rock band Albums * ''Hey'' (Andreas Bourani album) or the title song (see below), 2014 * ''Hey!'' (Julio Iglesias album) or the title song, 1980 * ''Hey!'' (Jullie album) or the title ...
must 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, a ...
(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 (a subsidiary of Nike, Inc. since 2003) that was i ...
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 ...


References


External links


Stanford Encyclopedia of Philosophy entry on logical constants
Philosophical logic Concepts in logic Syntax (logic) Logical truth Logic symbols {{logic-stub