The Complete Aristotle (eng.)

of its subject’, an ‘essential’ attribute, and a
‘commensurate and universal’ attribute. I call ‘true in every
instance’ what is truly predicable of all instances-not of one to
the exclusion of others-and at all times, not at this or that time
only; e.g. if animal is truly predicable of every instance of man,
then if it be true to say ‘this is a man’, ‘this is an animal’ is
also true, and if the one be true now the other is true now. A
corresponding account holds if point is in every instance
predicable as contained in line. There is evidence for this in the
fact that the objection we raise against a proposition put to us as
true in every instance is either an instance in which, or an
occasion on which, it is not true. Essential attributes are (1)
such as belong to their subject as elements in its essential nature
(e.g. line thus belongs to triangle, point to line; for the very
being or ‘substance’ of triangle and line is composed of these
elements, which are contained in the formulae defining triangle and
line): (2) such that, while they belong to certain subjects, the
subjects to which they belong are contained in the attribute’s own
defining formula. Thus straight and curved belong to line, odd and
even, prime and compound, square and oblong, to number; and also
the formula defining any one of these attributes contains its
subject-e.g. line or number as the case may be.
    Extending this classification to all other attributes, I
distinguish those that answer the above description as belonging
essentially to their respective subjects; whereas attributes
related in neither of these two ways to their subjects I call
accidents or ‘coincidents’; e.g. musical or white is a ‘coincident’
of animal.
    Further (a) that is essential which is not predicated of a
subject other than itself: e.g. ‘the walking [thing]’ walks and is
white in virtue of being something else besides; whereas substance,
in the sense of whatever signifies a ‘this somewhat’, is not what
it is in virtue of being something else besides. Things, then, not
predicated of a subject I call essential; things predicated of a
subject I call accidental or ‘coincidental’.
    In another sense again (b) a thing consequentially connected
with anything is essential; one not so connected is ‘coincidental’.
An example of the latter is ‘While he was walking it lightened’:
the lightning was not due to his walking; it was, we should say, a
coincidence. If, on the other hand, there is a consequential
connexion, the predication is essential; e.g. if a beast dies when
its throat is being cut, then its death is also essentially
connected with the cutting, because the cutting was the cause of
death, not death a ‘coincident’ of the cutting.
    So far then as concerns the sphere of connexions scientifically
known in the unqualified sense of that term, all attributes which
(within that sphere) are essential either in the sense that their
subjects are contained in them, or in the sense that they are
contained in their subjects, are necessary as well as
consequentially connected with their subjects. For it is impossible
for them not to inhere in their subjects either simply or in the
qualified sense that one or other of a pair of opposites must
inhere in the subject; e.g. in line must be either straightness or
curvature, in number either oddness or evenness. For within a
single identical genus the contrary of a given attribute is either
its privative or its contradictory; e.g. within number what is not
odd is even, inasmuch as within this sphere even is a necessary
consequent of not-odd. So, since any given predicate must be either
affirmed or denied of any subject, essential attributes must inhere
in their subjects of necessity.
    Thus, then, we have established the distinction between the
attribute which is ‘true in every instance’ and the ‘essential’
attribute.
    I term ‘commensurately universal’ an attribute which belongs to
every instance of its subject, and to every instance essentially
and as such; from which it clearly follows that all commensurate
universals inhere necessarily in their subjects. The essential
attribute, and the attribute that belongs to its subject as such,
are identical. E.g. point and straight belong to line essentially,
for they belong to line as such; and triangle as such has two right
angles, for it is essentially equal to two right angles.
    An attribute belongs commensurately and