BDFN: Basic Definition
Acronym Definition
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BDFN: Basic Definition
A definition is a statement of the meaning of a term, word or phrase. The
term to be defined is known as the definiendum (Latin: that which is to be
defined). The words which define it are known as the definiens (Latin: that
which is doing the defining).
Stipulative definition
A definition may either give the meaning that a term bears in general use (a
descriptive definition), or that which the speaker intends to impose upon it for
the purpose of his or her discourse (a stipulative definition). Stipulative
definitions differ from descriptive definitions in that they prescribe a new
meaning either to a term already in use or to a new term. A descriptive
definition can be shown to be right or wrong by comparison to usage, while a
stipulative definition cannot. A stipulative definition, however, may be more or
less useful. A persuasive definition, named by C.L. Stevenson, is a form of
stipulative definition which purports to describe the 'true' or 'commonly
accepted' meaning of a term, while in reality stipulating an altered use,
perhaps as an argument for some view, for example that some system of government
is democratic. Stevenson also notes that some definitions are 'legal' or
'coercive', whose object is to create or alter rights, duties or crimes.
Intension and extension
Main articles: Intension and Extension (metaphysics)
An intensional definition, also called a connotative definition, specifies the
necessary and sufficient conditions for a thing being a member of a specific
set. 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.
So, for example, an intensional definition of 'Prime Minister' might be the most
senior minister of a cabinet in the executive branch of government in a
parliamentary system; whereas an extensional definition would be simply a list
of all past and present Prime Ministers.
One important form of 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. So you can
explain who Alice (an individual) is by pointing her out to me; or what a rabbit
(a class) is by pointing at several and expecting me to 'catch on'. The process
of ostensive definition itself was critically appraised by Ludwig Wittgenstein.
An enumerative definition of a concept or 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 only practical for relatively small sets.
Definition by genus and differentia
Scientific classification of living things uses definition by genus and
differentia.Genus-differentia definition
Traditionally, a definition consists of the genus (the family) of thing to which
the defined thing belongs, and the differentia (the distinguishing feature which
marks it off from other members of the same family). Thus 'triangle' is defined
as 'a plane figure (genus) bounded by three straight sides (differentia).
Rules for definition by genus and differentia
Fallacies of definition
Certain rules have traditionally been given for this particular type of
definition.
A definition must set out the essential attributes of the thing defined.
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 error is known as 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.
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 no other objects (i.e. not include any things to which the defined term would
not truly apply).
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.
(See the definition of Free will in Wikipedia, for instance).
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. We cannot define a point except as
'something with no parts', nor blindness except as 'the absence of sight in a
creature that is normally sighted'.
Essence
Essence
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.
The idea that a definition should state the essence of a thing led to the
distinction between nominal and real essence, originating with Aristotle. In a
passage from the Posterior Analytics, he says that we can know the meaning of a
made-up name (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 the so-called
quid nominis or 'whatness of the name', and the underlying nature common to all
the things it names, which they called the quid rei or 'whatness of the thing'.
(Early modern philosophers like Locke used the corresponding English terms
'nominal essence' and 'real essence'). The name 'hobbit', for example, is
perfectly meaningful. It has a quid nominis. But we could not know the real
nature of hobbits, even if there were such things, and so we cannot know the
real nature or quid rei of hobbits. 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 thing must have in order that the name apply to it.
This leads to a corresponding distinction between nominal and real definition. 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 it as "a hopelessly muddle-headed notion".
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 it possesses in all possible
worlds. Kripke refers to names used in this way as Rigid designators.
Genetic definition
A genetic definition describes the process or method by which a thing is formed.
"But if you define the circle as a pattern resulting from having a segment of a
line revolve around one of its ends, this is a genetic definition because it
tells you how to make a circle."
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:
At least one thing is stated to be a member of the set being defined; this is
sometimes called a "base set".
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.
All other things are excluded from the set
For instance, we could define natural number as follows (after Peano):
"0" is a natural number.
Each natural number has a distinct successor, such that:
the successor of a natural number is also a natural number, and
no natural number is succeeded by "0".
Nothing else is a natural number.
So "0" will have exactly one successor, which for convenience we can call "1".
In turn, "1" will have exactly one successor, which we would call "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 is quite
successful.
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 leave some terms undefined. If every term of every definiens must
itself be defined, where should we stop? A dictionary, for instance, insofar as
it is a comprehensive list of lexical definitions, must resort to circularity.
Many philosophers have chosen instead to leave some terms undefined. The
scholastic philosophers claimed that the highest genera (the so-called ten
generalissima) cannot be defined, since we cannot assign any higher genus under
which they may fall. Thus we cannot define being, unity and similar concepts.
Locke supposes in An Essay Concerning Human Understanding 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. 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", claiming
instead that explanation of a term is only needed when we need to avoid
misunderstanding.
Locke and Mill also argued that we cannot define individuals. We learn names by
connecting an idea with a sound, so that speaker and hearer have the same idea
when the same word is used. This is not possible when no one else is acquainted
with the particular thing that has "fallen under our notice". 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. 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 to state a definition; rather, one simply comes to
understand the use of the term.
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