An example of the first kind of imperfect definitions is the following:
Man is a rational animal. It is impossible to consider this as a complete
definition of the word Man, since (as before remarked) if we adhered to it
we should be obliged to call the Houyhnhnms men; but as there happen to be
no Houyhnhnms, this imperfect definition is sufficient to mark out and
distinguish from all other things, the objects at present denoted by
“man;” all the beings actually known to exist, of whom the name is
predicable. Though the word is defined by some only among the attributes
which it connotes, not by all, it happens that all known objects which
possess the enumerated attributes, possess also those which are omitted;
so that the field of predication which the word covers, and the employment
of it which is conformable to usage, are as well indicated by the
inadequate definition as by an adequate one. Such definitions, however,
are always liable to be overthrown by the discovery of new objects in
nature.
Definitions of this kind are what logicians have had in view, when they
laid down the rule, that the definition of a species should be _per genus
et differentiam_. Differentia being seldom taken to mean the whole of the
peculiarities constitutive of the species, but some one of those
peculiarities only, a complete definition would be _per genus et
differentias_, rather than _differentiam_. It would include, with the name
of the superior genus, not merely _some_ attribute which distinguishes the
species intended to be defined from all other species of the same genus,
but _all_ the attributes implied in the name of the species, which the
name of the superior genus has not already implied. The assertion,
however, that a definition must of necessity consist of a genus and
differentiæ, is not tenable. It was early remarked by logicians, that the
_summum genus_ in any classification, having no genus superior to itself,
could not be defined in this manner. Yet we have seen that all names,
except those of our elementary feelings, are susceptible of definition in
the strictest sense; by setting forth in words the constituent parts of
the fact or phenomenon, of which the connotation of every word is
ultimately composed.