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A Treatise of Human Nature

PART I.3: Of Knowledge And Probability
SECT. I. OF KNOWLEDGE.
There are seven [Part I. Sect. 5.] 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
phaenomenon, even the most simple, which can be accounted for from the qualities of the
objects, as they appear to us; or which we coued foresee without the help of our memory
and experience.
It appears, therefore, that of these seven philosophical relations, there remain only four,
which depending solely upon ideas, can be the objects of knowledge said 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 eve, 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.
We might proceed, after the same manner, in fixing the proportions of quantity or
number, and might at one view observe a superiority or inferiority betwixt any numbers,
or figures; especially where the difference is very great and remarkable. As to equality or
any exact proportion, we can only guess at it from a single consideration; except in very
short numbers, or very limited portions of extension; which are comprehended in an
instant, and where we perceive an impossibility of falling into any considerable error. In
 
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