The defintion of a word

Although
the borderline between various linguistic units is not always sharp
and clear, we shall try to define every new term on its first
appearance at once simply and unambiguously, if not always very
rigorously. The approximate definition of the term word
has already been given in the opening page of the book.

The
important point to remember about
definitions
is that they should indicate the most essential characteristic
features of the notion expressed by the term under discussion, the
features by which this notion is distinguished from other similar
notions. For instance, in defining the word one must distinguish it
from other linguistic units, such as the phoneme, the morpheme, or
the word-group. In contrast with a definition, a description
aims at enumerating all the essential features of a notion.

To
make things easier we shall begin by a preliminary description,
illustrating it with some examples.

The
word
may be described as the basic unit of language. Uniting meaning and
form, it is composed of one or more morphemes, each consisting of one
or more spoken sounds or their written representation. Morphemes as
we have already said are also meaningful units but they cannot be
used independently, they are always parts of words whereas words can
be used as a complete utterance (e. g. Listen!).
The
combinations of morphemes within words are subject to certain linking
conditions. When a derivational affix is added a new word is formed,
thus, listen
and
listener
are
different words. In fulfilling different grammatical functions words
may take functional affixes: listen
and
listened
are
different forms of the same word. Different forms of the same word
can be also built analytically with the help of auxiliaries. E.g.:
The
world should listen then as I am listening now (Shelley).

When
used in sentences together with other words they are syntactically
organised. Their freedom of entering into syntactic constructions is
limited by many factors, rules and constraints (e. g.: They
told me this story but
not *They
spoke me this story).

The
definition of every basic notion is a very hard task: the definition
of a word is one of the most difficult in linguistics because the

27

simplest
word has many different aspects. It has a sound form because it is a
certain arrangement of phonemes; it has its morphological structure,
being also a certain arrangement of morphemes; when used in actual
speech, it may occur in different word forms, different syntactic
functions and signal various meanings. Being the central element of
any language system, the word is a sort of focus for the problems of
phonology, lexicology, syntax, morphology and also for some other
sciences that have to deal with language and speech, such as
philosophy and psychology, and probably quite a few other branches of
knowledge. All attempts to characterise the word are necessarily
specific for each domain of science and are therefore considered
one-sided by the representatives of all the other domains and
criticised for incompleteness. The variants of definitions were so
numerous that some authors (A. Rossetti, D.N. Shmelev) collecting
them produced works of impressive scope and bulk.

A
few examples will suffice to show that any definition is conditioned
by the aims and interests of its author.

Thomas
Hobbes (1588-1679),
one
of the great English philosophers, revealed a materialistic approach
to the problem of nomination when he wrote that words are not mere
sounds but names of matter. Three centuries later the great Russian
physiologist I.P. Pavlov (1849-1936)
examined
the word in connection with his studies of the second signal system,
and defined it as a universal signal that can substitute any other
signal from the environment in evoking a response in a human
organism. One of the latest developments of science and engineering
is machine translation. It also deals with words and requires a
rigorous definition for them. It runs as follows: a word is a
sequence of graphemes which can occur between spaces, or the
representation of such a sequence on morphemic level.

Within
the scope of linguistics the word has been defined syntactically,
semantically, phonologically and by combining various approaches.

It
has been syntactically defined for instance as “the minimum
sentence” by H. Sweet and much later by L. Bloomfield as “a
minimum free form”. This last definition, although structural in
orientation, may be said to be, to a certain degree, equivalent to
Sweet’s, as practically it amounts to the same thing: free forms
are later defined as “forms which occur as sentences”.

E.
Sapir takes into consideration the syntactic and semantic aspects
when he calls the word “one of the smallest completely satisfying
bits of isolated ‘meaning’, into which the sentence resolves
itself”. Sapir also points out one more, very important
characteristic of the word, its indivisibility:
“It cannot be cut into without a disturbance of meaning, one or two
other or both of the several parts remaining as a helpless waif on
our hands”. The essence of indivisibility will be clear from a
comparison of the article a
and
the prefix a-
in
a
lion and
alive.
A lion is
a word-group because we can separate its elements and insert other
words between them: a
living lion, a dead lion. Alive is
a word: it is indivisible, i.e. structurally impermeable: nothing can
be inserted between its elements. The morpheme a-
is
not free, is not a word. The

28

situation
becomes more complicated if we cannot be guided by solid spelling.’
“The Oxford English Dictionary», for instance, does not
include the
reciprocal pronouns each
other and
one
another under
separate headings, although
they should certainly be analysed as word-units, not as word-groups
since they have become indivisible: we now say with
each other and
with
one another instead
of the older forms one
with another or
each
with the other.¹

Altogether
is
one word according to its spelling, but how is one to treat all
right, which
is rather a similar combination?

When
discussing the internal cohesion of the word the English linguist
John Lyons points out that it should be discussed in terms of two
criteria “positional
mobility”
and
“un­interrupt­abili­ty”.
To illustrate the first he segments into morphemes the following
sentence:

the
—
boy
—
s
—
walk
—
ed
—
slow
—
ly
—
up
—
the
—
hill

The
sentence may be regarded as a sequence of ten morphemes, which occur
in a particular order relative to one another. There are several
possible changes in this order which yield an acceptable English
sentence:

slow
—
ly
—
the
—
boy
—
s
—
walk
—
ed
—
up
—
the
—
hill
up —
the
—
hill
—
slow
—
ly
—
walk
—
ed
—
the
—
boy
—
s

Yet
under all the permutations certain groups of morphemes behave as
‘blocks’ —
they
occur always together, and in the same order relative to one another.
There is no possibility of the sequence s
—
the
—
boy,
ly —
slow,
ed —
walk.
“One
of the characteristics of the word is that it tends to be internally
stable (in terms of the order of the component morphemes), but
positionally mobile (permutable with other words in the same
sentence)”.²

A
purely semantic treatment will be found in Stephen Ullmann’s
explanation: with him connected discourse, if analysed from the
semantic point of view, “will fall into a certain number of
meaningful segments which are ultimately composed of meaningful
units. These meaningful units are called words.»³

The
semantic-phonological approach may be illustrated by A.H.Gardiner’s
definition: “A word is an articulate sound-symbol in its aspect of
denoting something which is spoken about.»⁴

The
eminent French linguist A. Meillet (1866-1936)
combines
the semantic, phonological and grammatical criteria and advances a
formula which underlies many subsequent definitions, both abroad and
in our country, including the one given in the beginning of this
book: “A word is defined by the association of a particular meaning
with a

¹Sapir
E. Language.
An Introduction to the Study of Speech. London, 1921,
P.
35.

² Lyons,
John. Introduction
to Theoretical Linguistics. Cambridge: Univ. Press, 1969.
P. 203.

³ Ullmann
St. The
Principles of Semantics. Glasgow, 1957.
P.
30.

⁴ Gardiner
A.H. The
Definition of the Word and the Sentence //
The
British Journal of Psychology. 1922.
XII.
P. 355
(quoted
from: Ullmann
St.,
Op.
cit., P. 51).

29

particular
group of sounds capable of a particular grammatical employment.»¹

This
definition does not permit us to distinguish words from phrases
because not only child,
but
a
pretty child as
well are combinations of a particular group of sounds with a
particular meaning capable of a particular grammatical employment.

We
can, nevertheless, accept this formula with some modifications,
adding that a word is the smallest significant unit of a given
language capable of functioning alone and characterised by positional
mobility
within
a sentence, morphological
uninterruptability
and semantic
integrity.²
All these criteria are necessary because they permit us to create a
basis for the oppositions between the word and the phrase, the word
and the phoneme, and the word and the morpheme: their common feature
is that they are all units of the language, their difference lies in
the fact that the phoneme is not significant, and a morpheme cannot
be used as a complete utterance.

Another
reason for this supplement is the widespread scepticism concerning
the subject. It has even become a debatable point whether a word is a
linguistic unit and not an arbitrary segment of speech. This opinion
is put forth by S. Potter, who writes that “unlike a phoneme or a
syllable, a word is not a linguistic unit at all.»³
He calls it a conventional and arbitrary segment of utterance, and
finally adopts the already mentioned
definition of L. Bloomfield. This position is, however, as
we have already mentioned, untenable, and in fact S. Potter himself
makes ample use of the word as a unit in his linguistic analysis.

The
weak point of all the above definitions is that they do not establish
the relationship between language and thought, which is formulated if
we treat the word as a dialectical unity of form and content, in
which the form is the spoken or written expression which calls up a
specific meaning, whereas the content is the meaning rendering the
emotion or the concept in the mind of the speaker which he intends to
convey to his listener.

Summing
up our review of different definitions, we come to the conclusion
that they are bound to be strongly dependent upon the line of
approach, the aim the scholar has in view. For a comprehensive word
theory, therefore, a description seems more appropriate than a
definition.

The
problem of creating a word theory based upon the materialistic
understanding of the relationship between word and thought on the one
hand, and language and society, on the other, has been one of the
most discussed for many years. The efforts of many eminent scholars
such as V.V. Vinogradov, A. I. Smirnitsky, O.S. Akhmanova, M.D.
Stepanova, A.A. Ufimtseva —
to
name but a few, resulted in throwing light

¹Meillet
A. Linguistique
historique et linguistique generate. Paris,
1926.
Vol.
I. P. 30.

² It
might be objected that such words as articles, conjunctions and a few
other words
never occur as sentences, but they are not numerous and could be
collected into a
list of exceptions.

³ See:
Potter
S. Modern
Linguistics. London, 1957.
P.
78.

30

on this problem and achieved a
clear presentation of the word as a basic unit of the language. The
main points may now be summarised.

The
word
is the
fundamental
unit
of language.
It is a dialectical
unity
of form
and
content.
Its content or meaning is not identical to notion, but it may reflect
human notions, and in this sense may be considered as the form of
their existence. Concepts fixed in the meaning of words are formed as
generalised and approximately correct reflections of reality,
therefore in signifying them words reflect reality in their content.

The
acoustic aspect of the word serves to name objects of reality, not to
reflect them. In this sense the word may be regarded as a sign. This
sign, however, is not arbitrary but motivated by the whole process of
its development. That is to say, when a word first comes into
existence it is built out of the elements already available in the
language and according to the existing patterns.

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Definition of a Word

A word is a speech sound or a combination of sound having a particular meaning for an idea, object or thought and has a spoken or written form. In English language word is composed by an individual letter (e.g., ‘I’), I am a boy, or by combination of letters (e.g., Jam, name of a person) Jam is a boy. Morphology, a branch of linguistics, deals with the structure of words where we learn under which rules new words are formed, how we assigned a meaning to a word? how a word functions in a proper context? how to spell a word? etc.

Examples of word: All sentences are formed by a series of words. A sentence starts with a word, consists on words and ends with a word. Therefore, there is nothing else in a sentence than a word. 

Some different examples are: Boy, kite, fox, mobile phone, nature, etc.

Different Types of Word

There are many types of word; abbreviation, acronym, antonym, back formation, Clipped words (clipping), collocation, compound words, Content words, contractions, derivation, diminutive, function word, homograph, homonym, homophone, legalism, linker, conjunct, borrowed, metonym, monosyllable, polysyllable, rhyme, synonym, etc. Read below for short introduction to each type of word.

Abbreviation

An abbreviation is a word that is a short form of a long word.

Example: Dr for doctor, gym for gymnasium

Acronym

Acronym is one of the commonly used types of word formed from the first letter or letters of a compound word/ term and used as a single word.

Example: PIA for Pakistan International Airline

Antonym

An antonym is a word that has opposite meaning of an another word

Example: Forward is an antonym of word backward or open is an antonym of word close.

Back formation

Back formation word is a new word that is produced by removing a part of another word.

Example: In English, ‘tweeze’ (pluck) is a back formation from ‘tweezers’.

Clipped words

Clipped word is a word that has been clipped from an already existing long word for ease of use.

Example: ad for advertisement

Collocation

Collocation is a use of certain words that are frequently used together in form of a phrase or a short sentence.

Example: Make the bed,

Compound words

Compound words are created by placing two or more words together. When compound word is formed the individual words lose their meaning and form a new meaning collectively. Both words are joined by a hyphen, a space or sometime can be written together. 

Example: Ink-pot, ice cream,

Content word

A content word is a word that carries some information or has meaning in speech and writing.

Example:  Energy, goal, idea.

Contraction

A Contraction is a word that is formed by shortening two or more  words and  joining them by an apostrophe.

Example:  ‘Don’t’ is a contraction of the word ‘do not’.

Derivation

Derivation is a word that is derived from within a language or from another language.

Example: Strategize (to make a plan) from strategy (a plan).

Diminutive

Diminutive is a word that is formed by adding a diminutive suffix with a word.

Example: Duckling by adding suffix link with word duck.

Function word

Function word is a word that is mainly used for expressing some grammatical relationships between other words in a sentence.

Example: (Such as preposition, or auxiliary verb) but, with, into etc.

Homograph

Homograph is a word that is same in written form (spelled alike) as another word but with a different meaning, origin, and occasionally pronounced with a different pronunciation

Example:  Bow for ship and same word bow for shooting arrows.

Homonym

Homonyms are the words that are spelled alike and have same pronunciation as another word but have a different meaning.

Example: Lead (noun) a material and lead (verb) to guide or direct.

Homophone

Homophones are the words that have same pronunciation as another word but differ in spelling, meaning, and origin.

Example: To, two, and too are homophones.

Hyponym

Hyponym is a word that has more specific meaning than another more general word of which it is an example.

Example: ‘Parrot’ is a hyponym of ‘birds’.

Legalism

Legalism is a type of word that is used in law terminology.

Example: Summon, confess, judiciary

Linker/ conjuncts

Linker or conjuncts are the words or phrase like ‘however’ or ‘what’s more’ that links what has already been written or said to what is following.

Example: however, whereas, moreover.

Loanword/ borrowed

A loanword or borrowed word is a word taken from one language to use it in another language without any change.

Example: The word pizza is taken from Italian language and used in English language

Metonym

Metonym is a word which we use to refer to something else that it is directly related to that.

Example: ‘Islamabad’ is frequently used as a metonym for the Pakistan government.

Monosyllable

Monosyllable is a word that has only one syllable.

Example: Come, go, in, yes, or no are monosyllables.

Polysyllable

Polysyllable is a word that has two or more than two syllables.

Example: Interwoven, something or language are polysyllables.

Rhyme

Rhyme is a type of word used in poetry that ends with similar sound as the other words in stanza.

Example; good, wood, should, could.

Synonym

Synonym is a word that has similar meaning as another word.

Example: ‘happiness’ is a synonym for ‘joy’.

What Is the Definition of Word?

A word is a speech sound or a combination of sounds, or its representation in writing, that symbolizes and communicates a meaning and may consist of a single morpheme or a combination of morphemes.

The branch of linguistics that studies word structures is called morphology. The branch of linguistics that studies word meanings is called lexical semantics.

Etymology

​From Old English, «word»

Examples and Observations

• «[A word is the] smallest unit of grammar that can stand alone as a complete utterance, separated by spaces in written language and potentially by pauses in speech.»
  -David Crystal, The Cambridge Encyclopedia of the English Language. Cambridge University Press, 2003
• «A grammar . . . is divided into two major components, syntax and morphology. This division follows from the special status of the word as a basic linguistic unit, with syntax dealing with the combination of words to make sentences, and morphology with the form of words themselves.» -R. Huddleston and G. Pullum, The Cambridge Grammar of the English Language. Cambridge University Press, 2002
• «We want words to do more than they can. We try to do with them what comes to very much like trying to mend a watch with a pickaxe or to paint a miniature with a mop; we expect them to help us to grip and dissect that which in ultimate essence is as ungrippable as shadow. Nevertheless there they are; we have got to live with them, and the wise course is to treat them as we do our neighbours, and make the best and not the worst of them.»
  -Samuel Butler, The Note-Books of Samuel Butler, 1912
• Big Words
  «A Czech study . . . looked at how using big words (a classic strategy for impressing others) affects perceived intelligence. Counter-intuitvely, grandiose vocabulary diminished participants’ impressions of authors’ cerebral capacity. Put another way: simpler writing seems smarter.»
  -Julie Beck, «How to Look Smart.» The Atlantic, September 2014
• The Power of Words
  «It is obvious that the fundamental means which man possesses of extending his orders of abstractions indefinitely is conditioned, and consists in general in symbolism and, in particular, in speech. Words, considered as symbols for humans, provide us with endlessly flexible conditional semantic stimuli, which are just as ‘real’ and effective for man as any other powerful stimulus.
• Virginia Woolf on Words
  «It is words that are to blame. They are the wildest, freest, most irresponsible, most un-teachable of all things. Of course, you can catch them and sort them and place them in alphabetical order in dictionaries. But words do not live in dictionaries; they live in the mind. If you want proof of this, consider how often in moments of emotion when we most need words we find none. Yet there is the dictionary; there at our disposal are some half-a-million words all in alphabetical order. But can we use them? No, because words do not live in dictionaries, they live in the mind. Look once more at the dictionary. There beyond a doubt lie plays more splendid than Antony and Cleopatra; poems lovelier than the ‘Ode to a Nightingale’; novels beside which Pride and Prejudice or David Copperfield are the crude bunglings of amateurs. It is only a question of finding the right words and putting them in the right order. But we cannot do it because they do not live in dictionaries; they live in the mind. And how do they live in the mind? Variously and strangely, much as human beings live, ranging hither and thither, falling in love, and mating together.»
  -Virginia Woolf, «Craftsmanship.» The Death of the Moth and Other Essays, 1942
• Word Word
  «Word Word [1983: coined by US writer Paul Dickson]. A non-technical, tongue-in-cheek term for a word repeated in contrastive statements and questions: ‘Are you talking about an American Indian or an Indian Indian?’; ‘It happens in Irish English as well as English English.'»
  -Tom McArthur, The Oxford Companion to the English Language. Oxford University Press, 1992

A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols).^[1][2] Definitions can be classified into two large categories: intensional definitions (which try to give the sense of a term), and extensional definitions (which try to list the objects that a term describes).^[3] Another important category of definitions is the class of ostensive definitions, which convey the meaning of a term by pointing out examples. A term may have many different senses and multiple meanings, and thus require multiple definitions.^[4][a]

In mathematics, a definition is used to give a precise meaning to a new term, by describing a condition which unambiguously qualifies what a mathematical term is and is not. Definitions and axioms form the basis on which all of modern mathematics is to be constructed.^[5]

Basic terminology

In modern usage, a definition is something, typically expressed in words, that attaches a meaning to a word or group of words. The word or group of words that is to be defined is called the definiendum, and the word, group of words, or action that defines it is called the definiens.^[6] For example, in the definition «An elephant is a large gray animal native to Asia and Africa», the word «elephant» is the definiendum, and everything after the word «is» is the definiens.^[7]

The definiens is not the meaning of the word defined, but is instead something that conveys the same meaning as that word.^[7]

There are many sub-types of definitions, often specific to a given field of knowledge or study. These include, among many others, lexical definitions, or the common dictionary definitions of words already in a language; demonstrative definitions, which define something by pointing to an example of it («This,» [said while pointing to a large grey animal], «is an Asian elephant.»); and precising definitions, which reduce the vagueness of a word, typically in some special sense («‘Large’, among female Asian elephants, is any individual weighing over 5,500 pounds.»).^[7]

Intensional definitions vs extensional definitions

An intensional definition, also called a connotative definition, specifies the necessary and sufficient conditions for a thing to be a member of a specific set.^[3] Any definition that attempts to set out the essence of something, such as that by genus and differentia, is an intensional definition.

An extensional definition, also called a denotative definition, of a concept or term specifies its extension. It is a list naming every object that is a member of a specific set.^[3]

Thus, the «seven deadly sins» can be defined intensionally as those singled out by Pope Gregory I as particularly destructive of the life of grace and charity within a person, thus creating the threat of eternal damnation. An extensional definition, on the other hand, would be the list of wrath, greed, sloth, pride, lust, envy, and gluttony. In contrast, while an intensional definition of «Prime Minister» might be «the most senior minister of a cabinet in the executive branch of parliamentary government», an extensional definition is not possible since it is not known who the future prime ministers will be (even though all prime ministers from the past and present can be listed).

Classes of intensional definitions

A genus–differentia definition is a type of intensional definition that takes a large category (the genus) and narrows it down to a smaller category by a distinguishing characteristic (i.e. the differentia).^[8]

More formally, a genus–differentia definition consists of:

1. a genus (or family): An existing definition that serves as a portion of the new definition; all definitions with the same genus are considered members of that genus.
2. the differentia: The portion of the new definition that is not provided by the genus.^[6]

For example, consider the following genus–differentia definitions:

• a triangle: A plane figure that has three straight bounding sides.
• a quadrilateral: A plane figure that has four straight bounding sides.

Those definitions can be expressed as a genus («a plane figure») and two differentiae («that has three straight bounding sides» and «that has four straight bounding sides», respectively).

It is also possible to have two different genus–differentia definitions that describe the same term, especially when the term describes the overlap of two large categories. For instance, both of these genus–differentia definitions of «square» are equally acceptable:

• a square: a rectangle that is a rhombus.
• a square: a rhombus that is a rectangle.

Thus, a «square» is a member of both genera (the plural of genus): the genus «rectangle» and the genus «rhombus».

Classes of extensional definitions

One important form of the extensional definition is ostensive definition. This gives the meaning of a term by pointing, in the case of an individual, to the thing itself, or in the case of a class, to examples of the right kind. For example, one can explain who Alice (an individual) is, by pointing her out to another; or what a rabbit (a class) is, by pointing at several and expecting another to understand. The process of ostensive definition itself was critically appraised by Ludwig Wittgenstein.^[9]

An enumerative definition of a concept or a term is an 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 in fact only practical for relatively small sets).

Divisio and partitio

Divisio and partitio are classical terms for definitions. A partitio is simply an intensional definition. A divisio is not an extensional definition, but an exhaustive list of subsets of a set, in the sense that every member of the «divided» set is a member of one of the subsets. An extreme form of divisio lists all sets whose only member is a member of the «divided» set. The difference between this and an extensional definition is that extensional definitions list members, and not subsets.^[10]

Nominal definitions vs real definitions

In classical thought, a definition was taken to be a statement of the essence of a thing. Aristotle had it that an object’s essential attributes form its «essential nature», and that a definition of the object must include these essential attributes.^[11]

The idea that a definition should state the essence of a thing led to the distinction between nominal and real essence—a distinction originating with Aristotle. In the Posterior Analytics,^[12] he says that the meaning of a made-up name can be known (he gives the example «goat stag») without knowing what he calls the «essential nature» of the thing that the name would denote (if there were such a thing). This led medieval logicians to distinguish between what they called the quid nominis, or the «whatness of the name», and the underlying nature common to all the things it names, which they called the quid rei, or the «whatness of the thing».^[13] The name «hobbit», for example, is perfectly meaningful. It has a quid nominis, but one could not know the real nature of hobbits, and so the quid rei of hobbits cannot be known. By contrast, the name «man» denotes real things (men) that have a certain quid rei. The meaning of a name is distinct from the nature that a thing must have in order that the name apply to it.

This leads to a corresponding distinction between nominal and real definitions. A nominal definition is the definition explaining what a word means (i.e., which says what the «nominal essence» is), and is definition in the classical sense as given above. A real definition, by contrast, is one expressing the real nature or quid rei of the thing.

This preoccupation with essence dissipated in much of modern philosophy. Analytic philosophy, in particular, is critical of attempts to elucidate the essence of a thing. Russell described essence as «a hopelessly muddle-headed notion».^[14]

More recently Kripke’s formalisation of possible world semantics in modal logic led to a new approach to essentialism. Insofar as the essential properties of a thing are necessary to it, they are those things that it possesses in all possible worlds. Kripke refers to names used in this way as rigid designators.

Operational vs. theoretical definitions

A definition may also be classified as an operational definition or theoretical definition.

Terms with multiple definitions

Homonyms

A homonym is, in the strict sense, one of a group of words that share the same spelling and pronunciation but have different meanings.^[15] Thus homonyms are simultaneously homographs (words that share the same spelling, regardless of their pronunciation) and homophones (words that share the same pronunciation, regardless of their spelling). The state of being a homonym is called homonymy. Examples of homonyms are the pair stalk (part of a plant) and stalk (follow/harass a person) and the pair left (past tense of leave) and left (opposite of right). A distinction is sometimes made between «true» homonyms, which are unrelated in origin, such as skate (glide on ice) and skate (the fish), and polysemous homonyms, or polysemes, which have a shared origin, such as mouth (of a river) and mouth (of an animal).^[16][17]

Polysemes

Polysemy is the capacity for a sign (such as a word, phrase, or symbol) to have multiple meanings (that is, multiple semes or sememes and thus multiple senses), usually related by contiguity of meaning within a semantic field. It is thus usually regarded as distinct from homonymy, in which the multiple meanings of a word may be unconnected or unrelated.

In logic and mathematics

In mathematics, definitions are generally not used to describe existing terms, but to describe or characterize a concept.^[18] For naming the object of a definition mathematicians can use either a neologism (this was mainly the case in the past) or words or phrases of the common language (this is generally the case in modern mathematics). The precise meaning of a term given by a mathematical definition is often different from the English definition of the word used,^[19] which can lead to confusion, particularly when the meanings are close. For example a set is not exactly the same thing in mathematics and in common language. In some case, the word used can be misleading; for example, a real number has nothing more (or less) real than an imaginary number. Frequently, a definition uses a phrase built with common English words, which has no meaning outside mathematics, such as primitive group or irreducible variety.

In first-order logic definitions are usually introduced using extension by definition (so using a metalogic). On the other hand, lambda-calculi are a kind of logic where the definitions are included as the feature of the formal system itself.

Classification

Authors have used different terms to classify definitions used in formal languages like mathematics. Norman Swartz classifies a definition as «stipulative» if it is intended to guide a specific discussion. A stipulative definition might be considered a temporary, working definition, and can only be disproved by showing a logical contradiction.^[20] In contrast, a «descriptive» definition can be shown to be «right» or «wrong» with reference to general usage.

Swartz defines a precising definition as one that extends the descriptive dictionary definition (lexical definition) for a specific purpose by including additional criteria. A precising definition narrows the set of things that meet the definition.

C.L. Stevenson has identified persuasive definition as a form of stipulative definition which purports to state the «true» or «commonly accepted» meaning of a term, while in reality stipulating an altered use (perhaps as an argument for some specific belief). Stevenson has also noted that some definitions are «legal» or «coercive» – their object is to create or alter rights, duties, or crimes.^[21]

Recursive definitions

A recursive definition, sometimes also called an inductive definition, is one that defines a word in terms of itself, so to speak, albeit in a useful way. Normally this consists of three steps:

1. At least one thing is stated to be a member of the set being defined; this is sometimes called a «base set».
2. All things bearing a certain relation to other members of the set are also to count as members of the set. It is this step that makes the definition recursive.
3. All other things are excluded from the set

For instance, we could define a natural number as follows (after Peano):

1. «0» is a natural number.
2. Each natural number has a unique successor, such that:
   • the successor of a natural number is also a natural number;
   • distinct natural numbers have distinct successors;
   • no natural number is succeeded by «0».
3. Nothing else is a natural number.

So «0» will have exactly one successor, which for convenience can be called «1». In turn, «1» will have exactly one successor, which could be called «2», and so on. Notice that the second condition in the definition itself refers to natural numbers, and hence involves self-reference. Although this sort of definition involves a form of circularity, it is not vicious, and the definition has been quite successful.

In the same way, we can define ancestor as follows:

1. A parent is an ancestor.
2. A parent of an ancestor is an ancestor.
3. Nothing else is an ancestor.

Or simply: an ancestor is a parent or a parent of an ancestor.

In medicine

In medical dictionaries, guidelines and other consensus statements and classifications, definitions should as far as possible be:

• simple and easy to understand,^[22] preferably even by the general public;^[23]
• useful clinically^[23] or in related areas where the definition will be used;^[22]
• specific^[22] (that is, by reading the definition only, it should ideally not be possible to refer to any other entity than that being defined);
• measurable;^[22]
• a reflection of current scientific knowledge.^[22][23]

Problems

Certain rules have traditionally been given for definitions (in particular, genus-differentia definitions).^{[24][25][26][27]}

1. A definition must set out the essential attributes of the thing defined.
2. Definitions should avoid circularity. To define a horse as «a member of the species equus» would convey no information whatsoever. For this reason, Locke adds that a definition of a term must not consist of terms which are synonymous with it. This would be a circular definition, a circulus in definiendo. Note, however, that it is acceptable to define two relative terms in respect of each other. Clearly, we cannot define «antecedent» without using the term «consequent», nor conversely.
3. The definition must not be too wide or too narrow. It must be applicable to everything to which the defined term applies (i.e. not miss anything out), and to nothing else (i.e. not include any things to which the defined term would not truly apply).
4. The definition must not be obscure. The purpose of a definition is to explain the meaning of a term which may be obscure or difficult, by the use of terms that are commonly understood and whose meaning is clear. The violation of this rule is known by the Latin term obscurum per obscurius. However, sometimes scientific and philosophical terms are difficult to define without obscurity.
5. A definition should not be negative where it can be positive. We should not define «wisdom» as the absence of folly, or a healthy thing as whatever is not sick. Sometimes this is unavoidable, however. For example, it appears difficult to define blindness in positive terms rather than as «the absence of sight in a creature that is normally sighted».

Fallacies of definition

Limitations of definition

Given that a natural language such as English contains, at any given time, a finite number of words, any comprehensive list of definitions must either be circular or rely upon primitive notions. If every term of every definiens must itself be defined, «where at last should we stop?»^[28][29] A dictionary, for instance, insofar as it is a comprehensive list of lexical definitions, must resort to circularity.^[30][31][32]

Many philosophers have chosen instead to leave some terms undefined. The scholastic philosophers claimed that the highest genera (called the ten generalissima) cannot be defined, since a higher genus cannot be assigned under which they may fall. Thus being, unity and similar concepts cannot be defined.^[25] Locke supposes in An Essay Concerning Human Understanding^[33] that the names of simple concepts do not admit of any definition. More recently Bertrand Russell sought to develop a formal language based on logical atoms. Other philosophers, notably Wittgenstein, rejected the need for any undefined simples. Wittgenstein pointed out in his Philosophical Investigations that what counts as a «simple» in one circumstance might not do so in another.^[34] He rejected the very idea that every explanation of the meaning of a term needed itself to be explained: «As though an explanation hung in the air unless supported by another one»,^[35] claiming instead that explanation of a term is only needed to avoid misunderstanding.

Locke and Mill also argued that individuals cannot be defined. Names are learned by connecting an idea with a sound, so that speaker and hearer have the same idea when the same word is used.^[36] This is not possible when no one else is acquainted with the particular thing that has «fallen under our notice».^[37] Russell offered his theory of descriptions in part as a way of defining a proper name, the definition being given by a definite description that «picks out» exactly one individual. Saul Kripke pointed to difficulties with this approach, especially in relation to modality, in his book Naming and Necessity.

There is a presumption in the classic example of a definition that the definiens can be stated. Wittgenstein argued that for some terms this is not the case.^[38] The examples he used include game, number and family. In such cases, he argued, there is no fixed boundary that can be used to provide a definition. Rather, the items are grouped together because of a family resemblance. For terms such as these it is not possible and indeed not necessary to state a definition; rather, one simply comes to understand the use of the term.^[b]

See also

Notes

References

External links

• Definitions, Stanford Encyclopedia of Philosophy Gupta, Anil (2008)
• Definitions, Dictionaries, and Meanings, Norman Swartz 1997
• Guy Longworth (ca. 2008) «Definitions: Uses and Varieties of». = in: K. Brown (ed.): Elsevier Encyclopedia of Language and Linguistics, Elsevier.
• Definition and Meaning, a very short introduction by Garth Kemerling (2001).