There are seven[1] different kinds of philosophical relation, viz.
RESEMBLANCE, IDENTITY, RELATIONS OF TIME AND PLACE, PROPORTION IN
QUANTITY OR NUMBER, DEGREES IN ANY QUALITY, CONTRARIETY and CAUSATION.
These relations may be divided into two classes; into such as depend
entirely on the ideas, which we compare together, and such as may be
changed without any change in the ideas. It is from the idea of a
triangle, that we discover the relation of equality, which its three
angles bear to two right ones; and this relation is invariable, as long
as our idea remains the same. On the contrary, the relations of
contiguity and distance betwixt two objects may be changed merely by an
alteration of their place, without any change on the objects themselves
or on their ideas; and the place depends on a hundred different
accidents, which cannot be foreseen by the mind. It is the same case
with identity and causation. Two objects, though perfectly resembling
each other, and even appearing in the same place at different times,
may be numerically different: And as the power, by which one object
produces another, is never discoverable merely from their idea, it is
evident cause and effect are relations, of which we receive information
from experience, and not from any abstract reasoning or reflection.
There is no single phænomenon, even the most simple, which can be
accounted for from the qualities of the objects, as they appear to us;
or which we could foresee without the help of our memory and
experience.
[1] Part I. Sect. 5.
It appears, therefore, that of these seven philosophical relations,
there remain only four, which depending solely upon ideas, can be
the objects of knowledge and certainty. These four are RESEMBLANCE,
CONTRARIETY, DEGREES IN QUALITY, and PROPORTIONS IN QUANTITY OR NUMBER.
Three of these relations are discoverable at first sight, and fall more
properly under the province of intuition than demonstration. When any
objects resemble each other, the resemblance will at first strike the
eye, or rather the mind; and seldom requires a second examination. The
case is the same with contrariety, and with the degrees of any quality.
No one can once doubt but existence and non-existence destroy each
other, and are perfectly incompatible and contrary. And though it be
impossible to judge exactly of the degrees of any quality, such as
colour, taste, heat, cold, when the difference betwixt them is very
small: yet it is easy to decide, that any of them is superior or
inferior to another, when their difference is considerable. And this
decision we always pronounce at first sight, without any enquiry or
reasoning.