By reason, examining the agreement or
disagreement of two ideas, by the intervention of some others; or,
3. By sensation, perceiving the existence of particular things:
hence it also follows:
3. Intuitive knowledge extends itself not to all the relations of
all our ideas. Thirdly, That we cannot have an intuitive knowledge
that shall extend itself to all our ideas, and all that we would
know about them; because we cannot examine and perceive all the
relations they have one to another, by juxta-position, or an immediate
comparison one with another. Thus, having the ideas of an obtuse and
an acute angled triangle, both drawn from equal bases, and between
parallels, I can, by intuitive knowledge, perceive the one not to be
the other, but cannot that way know whether they be equal or no;
because their agreement or disagreement in equality can never be
perceived by an immediate comparing them: the difference of figure
makes their parts incapable of an exact immediate application; and
therefore there is need of some intervening qualities to measure
them by, which is demonstration, or rational knowledge.
4. Nor does demonstrative knowledge. Fourthly, It follows, also,
from what is above observed, that our rational knowledge cannot
reach to the whole extent of our ideas: because between two
different ideas we would examine, we cannot always find such mediums
as we can connect one to another with an intuitive knowledge in all
the parts of the deduction; and wherever that fails, we come short
of knowledge and demonstration.
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