We need first to distinguish between two kinds of definition, nominal and real.
The Aristotelian tradition distinguishes 'nominal'
and 'real' or 'essential' definitions. To bring out this
distinction one must consider answers to questions
which begin: 'What is ... ?' 'What does it mean
to ... ?' For example, 'What is "positive health"?'
This question is asking for the definition of a term, a
word or words; as such it is asking for a nominal
definition. One way of identifying the request for a
nominal definition is to consider whether what we
are asking about (as in the example given) should be
enclosed in inverted commas. If however, like jesting
Pilate, we ask without quotes 'What is truth?' we are
not asking about the meaning of a word, for we all
know what the word 'truth' means, but about the
nature of what the word refers to. And, of course,
that nature is very complex, which is why Pilate did
not wait for the answer. This second sort of inquiry
is an inquiry into 'realist' or 'essentialist' definitions.
There are many methods of nominal definition.
One method - beloved of writers of essays - is to
look the word up in a dictionary. This method of
definition is called 'lexical' because it is concerned
only with words, or 'reportive' since it reports
current usage of words in terms of their approximate
synonyms. At some point, however, we must get
outside the enclosure of words or we shall not really
know what any word means; lexical, reportive or 'word-word' definitions presuppose the existence of
'word-thing' definitions. (R. S. Downie, 'Definition', Journal of Medical Ethics, Vol. 20, No. 3 (Sep., 1994), pp. 181-184: 181.)
'Real' has no honorific status : it indicates merely a definition of the thing (Latin re) rather than just the word.
Those who were first concerned with definition were
concerned with the nature of things and not mainly
of words. For example, Plato's dialogues are
typically concerned with establishing a definition -
of justice in the Republic, of courage in the Laches, of
love in the Symposium, and of knowledge in the
Theaetetus. But these definitions are of the things and
not of the words. Similarly, Aristotle offers a range of
definitions, of motion, happiness, virtue and so on,
but again he is concerned with what these things are
and not simply with the words. Indeed, Aristotle
defines 'definition' as the statement which gives the
essence, and he is clearly thinking of the essence
of the thing or the type of thing, and not mainly, or
not at all, of the word. And it is not just the ancient
Greeks who take this line on definition, nor indeed
is it just philosophers. Linnaeus provided real
definitions of plants through his system of botanical
classification, and the World Health Organisation
(WHO) in 1946 offered a much criticised definition:
Health is a state of complete physical, mental and
social well-being, and not merely the absence of
disease or infirmity. Clearly, the WHO were not
offering a definition of the word 'health', but of the
very essence of health itself. What is it that Linnaeus
and the WHO were trying to do?
Linnaeus was attempting to classify. In the
traditional logic the classification is in terms of
'genus' and 'species', where the class that is to be
divided is called the 'genus' and the sub-classes are
called the 'species'. Classification involves devising a
process of dividing such that all the sub-classes are
mutually exclusive. This process of classification
employs some technical terms which are widely
agreed: they are 'difference', 'property', and
'accident'. A quality is said to be a 'difference' if it
serves to distinguish the class of entities of which it is
a quality from other species of the same genus, or in
other words, if it is used in the definition of the class.
A quality is said to be a 'property' if it is a quality
possessed by every member of the class, yet is not
used to distinguish the class from other species of the
same genus. Finally, a quality is said to be an
accident if it may indifferently belong or not to all or
any members of the class. This terminology may
be archaic but the ideas are perfectly familiar and
are perhaps expressible as 'defining characteristics'
and 'accompanying characteristics'. For example,
we might wonder whether certain symptoms are
defining characteristics of a disease or just accompanying
ones, sometimes or always. (R. S. Downie, 'Definition', Journal of Medical Ethics, Vol. 20, No. 3 (Sep., 1994), pp. 181-184: 182-3.)
Comments and examples
Not everyone accepts the objective existence of genus and species. Are these classifications which we project on to the world or do they exist 'out there', independently of human conceptual schemes? Too big and complex a question to deal with here - at least for me.
I can, however, illustrate the distinction between the two kinds of definition:
Nominal: 'Bear: Any of several large, heavily built mammals constituting the family Ursidea (order Carnivoral), with thick fur and a plantigrade gait' (OED).
This is satisfactory for a range of descriptive and explanatory purposes.
A real definition might, by contrast, specify Ursidea in terms of its mitochondrial DNA.
An organism possessing such DNA belongs to the bear family.