Definition

A definition delimits or describes the meaning of a concept or term by stating the essential properties of the entities or objects denoted by that concept or term. The word or phrase to be defined is the definiendum (plural: definienda) and the phrase defining it is the definiens (plural: definientia).

For example, in the definition "a bachelor is an unmarried man", the definiendum is "bachelor", and the definiens is "unmarried man". In this example, the words "a", "is", "an" are easily replacable by another sign (which expresses that the first term is defined by the terms following the sign ":="): "bachelor" := "unmarried man". Often, as in this example, the definition is a statement that expresses a logical equivalence between the definiendum and the definiens.

Kinds of definition
A number of different kinds and techniques of definition can be distinguished, including:


 * A dictionary definition or lexical definition reports the meaning of a word or expression as it is normally used, usually by supplying an approximately equivalent expression in which the original word does not occur. For example, bachelor might be defined as an unmarried man; and fry as to cook in hot oil. (Notice the addition of "an" and "to" in each case, so that the defining expression is not perfectly inter-substitutable with the original: You can say John is a bachelor, but not John is a an unmarried man. This is normal practice, and is done simply for ease of reading.)  With some words, like the and if, which cannot be effectively paraphrased, dictionaries will often describe their proper use without offering an equivalent expression. (On the circularity and groundedness of dictionary definitions, see the symbol grounding problem and the "dictionary-go-round").


 * A definition by genus and difference “is one in which a word or concept that indicates a species -- a specific type of item, not necessarily a biological category -- is described first by a broader category, the genus, then distinguished from other items in that category by differentia.” (E.g., a bachelor (species) is a man (genus) who is not married (differentium), and to fry (species) is to cook (genus) in hot oil (differentium).)


 * Contextual definition. Some words cannot be clearly defined on their own, but it is possible to offer a schema for defining every sentence in which they occur--that is, a way of replacing every sentence containing the expression with another sentence not containing the expression.  Russell's famous Theory of Descriptions was an attempt (now widely believed to be incorrect) to do this for all definite descriptions&mdash;expressions of the form the (unique) x.  On Russell's account, any sentence containing (for example) the expression "the present king of France" was to be rearranged like this: The present king of France is bald means There is exactly one thing which is currently a king of France, and that thing is bald.  Notice that the defined expression, a noun phrase, is replaced by a sentence (There is . . . France) and a noun phrase (that thing) which appears in the position of the original.


 * An intensional definition specifies all and only the properties required of something in order that falls under the term defined (its necessary and sufficient conditions). This, like the following is typically used to characterize ways of specifying sets.  For example, the set of primes less than 20, or {x:x is prime and x < 20}, is an intensional definition of a set.


 * An extensional definition of a concept or term formulates its meaning by specifying its extension, that is, every object that falls under the definition of the concept or term in question.


 * An enumerative definition of a concept or term is a special type of extensional definition that gives an explicit and exhaustive listing of all the objects that fall under the concept or term in question. Enumerative definitions are only possible for finite sets and only practical for relatively small sets.


 * An ostensive definition gives the meaning of a term by pointing out the thing denoted by it, or pointing out examples of the kind of thing meant by it. So you can explain who Jones is by pointing him out to me; or what a dog is by pointing at several and expecting me to "catch on."


 * An operational definition of a quantity is a specific process whereby it is measured.


 * A theoretical definition gives the meaning of a word in terms of the theories of a specific discipline.


 * A recursive definition or inductive definition is one that defines a word in terms of itself, so to speak, albeit in a useful way. Normally this consists of two (or three) steps: (I) Several specific objects (a "base set") are stated to fall under the term X being described. (II) All and only the things bearing a certain relation to members of X are also stated to be members of X.  For instance, we could define natural number as folows: (I) 1 is a natural number.  (II) The successor of a natural number is also a natural number, and nothing else is.  ("Nothing else is", the closure step, is sometimes considered a separate step.)  For this to work well, the definition in any given case must be well-founded, avoiding a circle or an infinite regress. (See the following.)


 * A circular definition is one that assumes a prior understanding of the term being defined. For instance, we can define "oak" as a tree which has catkins and grows from an acorn, and then define "acorn" as the nut produced by an oak tree. To someone not knowing either which trees are oaks or which nuts are acorns, the definition is usually fairly useless. (see tautology)


 * A stipulative definition is the specification of a meaning adopted or assumed specifically for the purposes of argument or discussion in a given context. For example, I might want to explain to you how beer is made, but not be sure whether sake is a kind of beer nor how it is made.  So I might stipulate at the beginning that By 'beer,' I mean only beer brewed from barley.


 * A precising definition "is a definition that extends the dictionary definition (lexical definition) of a term for a specific purpose by including additional criteria that narrow down the set of things meeting the definition."


 * A persuasive definition "is a type of definition in which a term is defined in such a way as to be an argument for a particular position (as opposed to a lexical definition, which aims to be neutral to all usages), and is deceptive in that it has the surface form of a dictionary definition."

Determining meaning: extension, intension, ambiguity, and vagueness
Just as arguments can be good or bad, definitions can be good or bad. A definition gives us the meaning of a word. To understand this more deeply requires an elucidation of a few features of meaning, the principal ones being extension, intension, ambiguity, and vagueness. The distinction between the extension and the intension of a word is very similar to the distinction between a word's denotation and connotation. For example, the extension of the word "bachelor" would be all and only the bachelors in the world. The extension of this word would include several hundreds of millions of men. The intension of the word is more brief because it includes just two properties: the property of being a man, and the property of being unmarried. Essentially, all bachelors are unmarried men, and only bachelors are unmarried men.
 * An ostensive definition points out examples by which one gains a sense of the meaning of a word.
 * An extensional definition exhaustively lists every referent of a word (the completion of an ostensive exploration).
 * An intensional definition gives the properties of the referents of the word under investigation, usually allowing a more compact definition than a complete enumeration.

The sort of definition that philosophers are interested in, insofar as they are interested in definitions at all, is one that identifies a word's intension, rather than its extension. A definition of the word 'bachelor' is 'unmarried man' which could also be specified by a very long list including all unmarried men. Aside from being practically impossible, such a list is not what is generally desired. What is desired is a description of what all those things we call 'bachelors' have in common that distinguishes them from all non-bachelors. A list of all bachelors would be static, and could not expand to determine whether any new human is a bachelor or not.

There are two different ways in which the meanings of words can be unclear. Words can be unclear in the sense of being ambiguous, of being vague, or a combination of the two. Most words are, in fact, both ambiguous and vague. This is not a skeptical or even a controversial claim; to say that many, or perhaps even most, words are both ambiguous and vague is not to say that they have no meaning. It is to say, first, that many individual words have many distinct senses; and, second, that those senses are often, in ordinary language, not meant to be exhaustively precise. A word that is both ambiguous and vague, whose extreme limits are fuzzy and undefined, can still contain a rich fund of meaning.

A definition of 'definition'

 * It just can't be defined, as it's the basis for all definitions
 * It's similar to the fact that you can't prove that adding numbers actually works, by using mathematics. You've got to start somewhere by simply defining axioms.
 * All religions has basic definitions too, that can not be examined further. (If they can, they are not basic definitions).

A contribution to defining the term 'definition'
Minimum Intent: The following definition of the term 'definition' is presented as a reference, (a comparator, a norm) that must not be violated when defining scientific terms.

Axioms:

1) ‘Something’ is a term that has a most general meaning, it can mean anything (but it does not automatically include ‘everything’).

2) 'Ambient' is anything in the vicinity of, and, to a certain degree, within something.

3) ‘Event’ is something that can be distinguished from its ambient.

4) ‘Relation’ is something that has, at least, two events.

5) ‘System’ is something that has at least two relations.

6) ‘Phenomenon’ is a generic term (hypernym) for the above terms, providing that one or several of  human senses indicate (directly or indirectly, presently or in the past) the existence of a so-termed system, relation, event, ambient, or something else.

7) All other terms used within this theorem - apart from the term “definition” and the terms listed in inverted commas under 1) to 6) above - are already intrinsically known; the understanding of each of these terms is consistent with this treatise.

Theorem:

"Definition" is a fixed, static form (a model; an appearance of something as distinguished from the substance of which it is made; something autonomous from its own representation) of some relation(s) that significantly increases the probability of realisation of an intended (premeditated) change of some phenomenon. Such a change is to be achieved by an entity that is capable of utilising this definition for such a specified purpose. A definition cannot be generated, or used, without the existence of a system, which is organised and structured above a certain level of chaos. However, once it is generated and recorded, a definition can continue to exist (to be recorded) without the existence of the mentioned entity. A definition should be complemented with a minimum intent statement: a context that delimits a minimum domain of purposes for which it can be used. This statement does not exclude the possibility of using the same definition correctly for some other purpose. However, this extended use must not violate (contradict) an already established meaning; e.g. it must not cause synonymy or homonymy.

In addition, a definition must be complemented with axioms, with one or more examples, and, when needed and possible, with figures and animated representations.

Definitions are the bits necessary to construct and communicate knowledge. A definition is built up of structural components: pieces of information. Information is conveyed by means of signals of various kinds; the most frequently used include figures and terms. Although terms can be transferred by means of figures, they can also be transferred by means of sounds which are registered by the hearing senses. It is worth noting that information media can be mutually translated, e.g. visual info can be translated into information received by tactile or hearing senses. A history of the media used to record information reveals a variety of options. Alphabetic writing (in which consonant and vowel sounds are presented by letters or other symbols such as Braille characters and Morse code) is the most widespread system, but it is not the earliest, nor is it the only one. Writing has evolved from an extension of pictures that iconically represented some thing or action and then the word that bore that meaning. This approach led to so-called character script, such as that of Chinese, in which each word is represented by a separate symbol.

Contemporary definitions rely heavily on textual formulations, but figures are also very efficient at conveying comprehensive information; many sciences (e.g. mathematics, chemistry) have accepted ideograms to convey sophisticated notions. The optimal solution is an appropriate combination of text, figures, animation and sound.

The following definition is presented to provide an example of a definition:

“Figure”: (n) an arrangement of points made within two-dimensional space to present a visual static impression (a perception) of something (e.g., a figure printed on a book page, showing the front view of a home). Spuzic S and Nouwens F (2004) "A Contribution to Defining the Term ‘Definition’", Issues in Informing Science and Information Technology Education, Volume 1 (2004) pp 645 - 662

NOTE: Regarding the contribution immediately above, readers should feel free to consider whether it is an an extensional member of the set of fallacious definitons defined by the entry Fallacies of definition, in particular the section dealing with the fallacy of giving obscure definitions.

Quotation
"Nothing is more usual than for philosophers to encroach on the province of grammarians, and to engage in disputes of words, while they imagine they are handling controversies of the deepest importance and concern." &mdash; David Hume