# Definition:Definition

## Definition

A definition lays down the meaning of a concept.

It is a statement which tells the reader what something is.

It can be understood as an equation in (usually) natural language.

Some authors distinguish between particular types of definition, particularly of symbols:

### Stipulative Definition

A stipulative definition is a definition which defines how to interpret the meaning of a symbol.

It stipulates, or lays down, the meaning of a symbol in terms of previously defined symbols or concepts.

The symbol used for a stipulative definition is:

$\text {(the symbol being defined)} := \text {(the meaning of that symbol)}$

This can be written the other way round:

$\text {(a concept being assigned a symbol)} =: \text {(the symbol for it)}$

when it is necessary to emphasise that the symbol has been crafted to abbreviate the notation for the concept.

### Ostensive Definition

An ostensive definition is a definition which shows what a symbol is, rather than use words to explain what it is or what it does.

As an example of an ostensive definition, we offer up:

The symbol used for a stipulative definition is $:=$, as in:
$\text {(the symbol being defined)} := \text {(the meaning of that symbol)}$

## Also defined as

In the words of 1910: Alfred North Whitehead and Bertrand Russell: Principia Mathematica:

A definition is a declaration that a certain newly-introduced symbol or combination of symbols is to mean the same as a certain other combination of symbols of which the meaning is already known.

## Warning: If or Iff

It is a standard convention, when making a definition in mathematics, to use if to introduce the definiens, when in fact the intent is generally iff, that is: if and only if.

This convention is specifically not followed on $\mathsf{Pr} \infty \mathsf{fWiki}$, where the mandatory style is to use if and only if.

## Also see

You can't get much more circular than defining the definition of definition.