Analysis of Mr. Mill's System of Logic — John Stuart Mill — John Shaqi
Analysis of Mr. Mill's System of Logic
John Stuart Mill · en
Though the only accurate definition is one declaring all the facts
involved in the name, i.e. its connotation, men are usually satisfied
with anything which will serve as an index to its denotation, so as to
guard them from applying it inconsistently. This was the object of
logicians when they laid down that a species must be defined _per genus
et differentiam_, meaning by the _differentia one_ attribute included in
the essence, i.e. in the connotation. And, in fact, one attribute, e.g.
in defining man, Rationality (Swift's Houyhnhms having not been as yet
discovered) often does sufficiently mark out the objects denoted. But,
besides that a definition of this kind ought, in order to be complete,
to be _per genus et differentias_, i.e. by _all_ the connoted attributes
not implied in the name of the _genus_, still, even if all were given, a
_summum genus_ could not be so defined, since it has no superior genus.
And for merely marking out the objects denoted, Description, in which
none of the connoted attributes are given, answers as well as logicians'
so-called _essential_ definition. In Description, any one or a
combination of attributes may be given, the object being to make it
exactly coextensive with the name, so as to be predicable of the same
things. Such a description may be turned into an essential definition by
a change of the connotation (not the denotation) of the name; and, in
fact, thus are manufactured almost all scientific definitions, which,
being landmarks of classification, and not meant to declare the meaning
of the name (though, in fact, they do declare it in its new use), are
ever being modified (as is the definition of a science itself) with the
advance of knowledge. Thus, a technical definition helps to expound the
artificial classification from which it grows; but ordinary definition
cannot expound, as the Aristotelians fancied it could, the natural
classification of things, i.e. explain their division into _kinds_, and
the relations among the _kinds_: for the properties of every _kind_ are
innumerable, and all that definition can do is to state the connotation
of the name.