Sir William did not know the distinction between the two kinds of
knowledge, and what he meant to say was that "All knowledge
obtained by observation and experience is relative, and only
relatively true."

His knowledge of this relativity was not obtained by observation
or from reason. It could not possibly have been obtained in that
way. It came from intuition, and it was absolute and exact. A
man may have absolute and exact knowledge and yet not be able to
put it into words that exactly express it to another. Hamilton
had this knowledge. But it was not clearly formulated even in
his own mind. He had two separate and distinct meanings for the
word "knowledge," without being conscious of it.

We have yet to coin a proper word to express what comes to us
through intuition. The old English word "wisdom" originally did.
The old verb "wis" was meant what a man knew without being told
it, as "ken" meant knowledge by experience. Try and prove by
reason that a straight line is the shortest distance between two
points, or that a part can never be greater than the whole, and
your reason has an impossible task. "You must take them for
axioms," it says. You must take them because you wis them, not
because you know (ken) them.

Intuitional knowledge must not be confounded with the relative
knowledge that flows through the reason: that "If the sum of two
numbers is one and their difference is five," the numbers are
minus two and plus three.

The point cannot be too strongly enforced that there is a