And since demonstrative knowledge is only present when we
have a demonstration, it follows that demonstration is an inference
from necessary premisses. So we must consider what are the premisses
of demonstration-i.e. what is their character: and as a preliminary,
let us define what we mean by an attribute 'true in every instance
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.
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