Concept
Arity
Overview
In logic, mathematics, and computer science, arity ( ) is the number of arguments or operands taken by a function, operation or relation. In mathematics, arity may also be called rank, but this word can have many other meanings. In logic and philosophy, arity may also be called adicity and degree. In linguistics, it is usually named valency.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
Found by search and not yet checked by a person; they may only mention the idea in passing.
When we think of mathematics, we have in our mind a science devoted to the exploration of number, quantity, geometry, and in modern times also including investigation into yet more abstract concepts of order, and into analogous types of purely logical relations. The point of mathematics is that in it we have always got rid of the particular instance, and even of any particular sorts of entities.
Alfred North Whitehead, Science and the modern world
Close in meaning to Arity; the term itself is not named.
With this conception of the origin, nature, and functions of logical operations little remains to be said of their truth and falsity. If the whole enterprise of logical operation, of the construction and verification of hypothesis, is in the interest of the removal of ambiguity, and inhibition in conduct, the only relevant truth or falsity they can possess must be determined by their success or failure in that…
John Dewey, Creative Intelligence
Close in meaning to Arity; the term itself is not named.
The chief business of the logician is to classify arguments; for all testing clearly depends on classification. The classes of the logicians are defined by certain typical forms called syllogisms. For example, the syllogism called _Barbara_ is as follows: S is M; M is P: Hence, S is P. Or, to put words for letters— Enoch and Elijah were men; all men die: Hence, Enoch and Elijah must have died.
Charles S. Peirce, Chance, Love, and Logic
States what Arity is.
Related ideas
- Exclusive or
- Hexadecimal
- Tuple
- Philosophy
- Latin
- Logical conjunction
- Function (mathematics)
- Mathematics
- Numeral system
- Linguistics
- Truth
- Willard Van Orman Quine
- Logic
- Computer programming
- Computer science
- Complex number
- Cardinal number
- Currying
- Logical disjunction
- Absolute value
- Agda (programming language)
- ML (programming language)
- Finitary relation
- Function (computer programming)
Place in the tradition
Part of First-order logic.