logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure o ...

, a logical constant or constant symbol of a

language Language is a structured system of communication that consists of grammar and vocabulary. It is the primary means by which humans convey meaning, both in spoken and signed language, signed forms, and may also be conveyed through writing syste ...

\mathcal

is a

symbol A symbol is a mark, Sign (semiotics), sign, or word that indicates, signifies, or is understood as representing an idea, physical object, object, or wikt:relationship, relationship. Symbols allow people to go beyond what is known or seen by cr ...

that has the same semantic value under every interpretation 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. Connectives can be used to connect logical formulas. For instance in the syntax of propositional logic, the ...

s and quantifiers. The

equality Equality generally refers to the fact of being equal, of having the same value. In specific contexts, equality may refer to: Society * Egalitarianism, a trend of thought that favors equality for all people ** Political egalitarianism, in which ...

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 Philosophy of logic is the area of philosophy that studies the scope and nature of logic. It investigates the philosophical problems raised by logic, such as the presuppositions often implicitly at work in theories of logic and in their applicatio ...

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 (for instance, 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 conjunction or logical conjunction. The logical connective of this operator is typically represented as \wedge or \& or K (prefix) or \times or \cdo ...

). 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 philos ...

and

Bertrand Russell Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British philosopher, logician, mathematician, and public intellectual. He had influence on mathematics, logic, set theory, and various areas of analytic ...

. Russell returned to the subject of logical constants in the preface to the second edition (1937) of ''

The Principles of Mathematics ''The Principles of Mathematics'' (''PoM'') is a 1903 book by Bertrand Russell, in which the author presented Russell's paradox, his famous paradox and argued his thesis that mathematics and logic are identical. The book presents a view of ...

'' 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."

(1937) Preface to ''The Principles of Mathematics'', pages ix to xi The text of this book uses

relation Relation or relations may refer to: General uses * International relations, the study of interconnection of politics, economics, and law on a global level * Interpersonal relationship, association or acquaintance between two or more people * ...

s ''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") are sneakers manufactured by American fashion brand Converse (lifestyle wear), Converse (a subsidiary ...

and complements as

primitive notion In mathematics, logic, philosophy, and formal systems, a primitive notion is a concept that is not defined in terms of previously-defined concepts. It is often motivated informally, usually by an appeal to Intuition (knowledge), intuition or taken ...

s, also taken as logical constants in the form ''aRb''.

References

External links

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

See also

References

External links