Concept

Logical constant

Overview

In logic, a logical constant or constant symbol of a language

{\displaystyle {\mathcal {L}}}

is a symbol that has the same semantic value under every interpretation of

{\displaystyle {\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?

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).

Defining logical constants is a major part of the work of Gottlob Frege and Bertrand Russell. 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, [they] must be treated as part of the language, not as part of what the language speaks about." The text of this book uses relations R, their converses and complements as primitive notions, also taken as logical constants in the form aRb.

Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).

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If a relational theory of instants is constructed, in which an "instant" is defined as a group of events simultaneous with each other and not all simultaneous with any event outside the group, then if our resulting series of instants is to be compact, it must be possible, if _x_ wholly precedes _y_, to find an event _z_, simultaneous with part of _x_, which wholly precedes some event which wholly precedes _y_. Now…
Bertrand Russell, Our Knowledge of the External World as a Field for Scientific Method in Philosophy
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This omission has had a very great effect upon philosophy; it is hardly too much to say that most metaphysics, since Spinoza, has been largely determined by it. The way this has occurred is, in outline, as follows: Speaking generally, adjectives and common nouns express qualities or properties of single things, whereas prepositions and verbs tend to express relations between two or more things. Thus the neglect of…
Bertrand Russell, The Problems of Philosophy
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This is nothing else than the necessity of abstract logic, which is the presupposition involved in the very fact of interrelated existence as disclosed in each immediate occasion of experience. The key to the pattern means this fact:—that from a select set of those general conditions, exemplified in any one and the same occasion, a pattern involving an infinite variety of other such conditions, also exemplified in…
Alfred North Whitehead, Science and the modern world
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Philosophers who discussed Logical constant

Gottlob Frege

Related ideas

Place in the tradition

Part of Non-classical logic.

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