ginning (in the
reception of the simple ideas of perception, a, b, c, d), and at the end
(in judging how the concepts a b c and a b d stand related to each other),
the understanding is completely determined.]

More certain than our _sensitive_ knowledge of the existence of external
objects, are our immediate or _intuitive_ knowledge of our own existence
and our mediate or _demonstrative_ knowledge of the existence of God.
Every idea that we have, every pain, every thought assures us of our own
existence. The existence of God, however, as the infinite cause of all
reality, endowed with intelligence, will, and supreme power, is inferred
from the existence and constitution of the world and of ourselves. Reality
exists; the real world is composed of matter in motion and thinking beings,
and is harmoniously ordered. Since it is impossible for any real being to
be produced by nothing, and since we obtain no satisfactory answer to the
question of origin until we rise to something existent from all eternity,
we must assume as the cause of that which exists an Eternal Being, which
possesses in a higher degree all the perfections which it has bestowed upon
the creatures. As the cause of matter and motion, and as the source of all
power, this Being must be omnipotent; as the cause of beauty and order in
the world, and, above all, as the creator of thinking beings, it must be
omniscient. But these perfections are those which we combine in the idea
of God.

Intuitive knowledge is the highest of the three degrees of knowledge. It is
gained when the mind perceives the agreement or disagreement of two ideas
at first sight, without hesitation, and without the intervention of any
third idea. This immediate knowledge is self-evident, irresistible, and
exposed to no doubt. Knowledge is demonstrative when the mind perceives the
agreement (or disagreement) of two ideas, not by placing them side by side
and comparing them, but through the aid of other ideas. The intermediate
links are called proofs; their discovery is the work of the reason, and
quickness in finding them out is termed sagacity. The greater the number
of the intermediate steps, the more the clearness and distinctness of the
knowledge decreases, and the more the possibility of error increases.
In order for an argument (_e. g_., that a = d) to be conclusive, every
particular step in it (a = b, b = c, c = d) must possess intuitive
certainty. Mathematics is not the only example of