Definition. Marking out something from everything else, the primary
meaning of the Latin verb definio being to trace out a boundary.
Distinctions have been drawn between nominal and real definition, and
the latter has been divided into essential and accidental. But with such
distinctions pure logic has nothing to do.
All that it looks to is the definition of a
concept, or, coming to the same thing, of a term which is the
expression of a concept. And this is procured by assigning to it
the genus and the difference. Given the genus to which that denoted by a
term belongs, and the difference between it and the other species of the
genus, and we have its definition. The notion is presented to us
definite and circumscribed, and all that we know or can discover about
it will come within this enclosure.
As the differentia is itself a
generic notion, it might be viewed as the genus, and the other elements
of the definition as the species, e. g. red-flowering currant. Here we
should ordinarily think and speak of currant as the genus and
red-flowering as the species. But it is plainly possible, if we happen
to be thinking of the effect of colour
in flowers, to view red-flowering as the genus, having for its species
roses and many others, amongst which will be currant. And this
consideration will bring us to the simple and ultimate view of
definition, which shows it to consist of the coincidence of two genera
at a given place, thus producing depth as well as breadth in our notion,
giving it solidity and determinate character.
It is plain that only species is definable. The genus to which we refer
it may no doubt be defined also, but only by calling in the aid of a
higher genus in which it is contained, and so viewing it as a species.
The summum genus obviously cannot be defined, for want at once of a
differentia and of a genus higher than itself; nor can the individual,
as that presents us with no adequate differentia.
Definitions have, exclusively of those called nominal, with which
science has nothing to do, been divided into real and genetic. The real
definition is of the thing viewed as already existing, e.g. "A circle is
a line returning upon itself, of which all the parts are equidistant
from a given point." The genetic definition is of the process by which
the thing comes into being, e. g. " A circle is formed when we draw
around, and always at the same distance from, a fixed point, a movable
point which leaves its trace, until the termination of the movement
coincides with the commencement." (1)
(1) HAMILTON, Logic, vol. II. pp. 12, 13.