Where does function collide?

In mathematics a function is a rule that assigns to each element of one set exactly one element of another, written f: X to Y. The modern definition, which fixes a function by its input-output pairs rather than by any formula, is usually credited to Dirichlet in the 1830s and was traced by Youschkevitch in his 1976 history The concept of function up to the middle of the 19th century. The referent is a mapping between two sets, the unit is an ordered pair of an input and its one output, and what individuates a function is its domain, its codomain, and the assignment itself, not the expression used to describe it. This is a formal object with no cause, no purpose, and no behaviour in time. It differs from the computing meaning, which runs on a machine, and from the biological meaning, which does a job for an organism.[1]

Unit

A mapping assigning each input exactly one output

Recovery means

Not applicable

Measured by

Not measured; specified by its domain, its codomain, and the rule that assigns outputs to inputs

In computing a function, also called a subroutine or procedure, is a named, reusable block of instructions that takes arguments and returns a value. Wheeler described the mechanism in 1952 in The use of sub-routines in programmes, showing how one stored sequence of instructions could be called from many points in a program and returned from. The referent is a unit of executable code, the unit is a call that maps arguments to a result, and it is individuated by its name, its interface, and the effect of running it. Unlike the mathematical function, a code function is a process that executes, may take time, and can change the state of the machine. A pure function that only maps inputs to a return value is the special case closest to the mathematical meaning, and even it is a thing that runs rather than a set of pairs.[2]

Unit

A callable block of code mapping arguments to a return value

Recovery means

Not applicable

Measured by

Not measured; identified by its name, its signature, and the behaviour of executing it

In sociology, the function of an element of society is the contribution it makes to the working of the larger social system. Merton set out the idea in 1949 in Social Theory and Social Structure, distinguishing manifest functions, the consequences people intend and recognise, from latent functions, the consequences that are neither intended nor noticed, and adding dysfunctions, contributions that lessen a system's adjustment. The referent is a social pattern such as an institution or a custom, the unit is a consequence for the wider system, and the function is what the pattern does for the whole, not what any single person wants. This is the functionalist inheritance from Durkheim, and it differs sharply from the formal meanings: it names an effect within a society, not a mapping and not a piece of code.[3]

Unit

The contribution a social pattern makes to a social system

Recovery means

Not applicable

Measured by

Inferred from the consequences a social pattern has for the system, both manifest and latent

In biology and physiology, the function of an organ or trait is what it does for the organism, the job it performs, as against its structure. Cummins gave an influential analysis in 1975 in Functional Analysis: the function of a component is the contribution it makes to some capacity of the containing system, so the function of the heart is to pump blood, because pumping is how it contributes to circulation. The referent is a part of a living system, the unit is a causal contribution to a capacity of the whole, and function here answers what the part does, not how it came to exist. A rival account, Wright's 1973 etiological view in Functions, ties a trait's function to why it was selected. Either way this meaning is about a living thing and its capacities, unlike the mathematical mapping or the code that runs.[4][5]

Unit

The causal contribution an organ or trait makes to a capacity of the organism

Recovery means

Not applicable

Measured by

Identified by the capacity a part contributes to, or by the selection history that maintained it

In narratology, function refers to Propp's unit of the folktale, an act of a character defined by its place in the plot, of which he found thirty-one in a fixed order. This meaning comes from Propp (1968) in Morphology of the Folktale.[6]

Unit

Recovery means

Measured by