O and equal to ONE
AND TWO. Such kinds of truths the mind perceives at the first sight of
the ideas together, by bare intuition; without the intervention of any
other idea: and this kind of knowledge is the clearest and most
certain that human frailty is capable of. This part of knowledge is
irresistible, and, like bright sunshine, forces itself immediately to be
perceived, as soon as ever the mind turns its view that way; and leaves
no room for hesitation, doubt, or examination, but the mind is presently
filled with the clear light of it. IT IS ON THIS INTUITION THAT DEPENDS
ALL THE CERTAINTY AND EVIDENCE OF ALL OUR KNOWLEDGE; which certainty
every one finds to be so great, that he cannot imagine, and therefore
not require a greater: for a man cannot conceive himself capable of a
greater certainty than to know that any idea in his mind is such as
he perceives it to be; and that two ideas, wherein he perceives a
difference, are different and not precisely the same. He that demands a
greater certainty than this, demands he knows not what, and shows
only that he has a mind to be a sceptic, without being able to be so.
Certainty depends so wholly on this intuition, that, in the next degree
of knowledge which I call demonstrative, this intuition is necessary in
all the connexions of the intermediate ideas, without which we cannot
attain knowledge and certainty.

2. II. Demonstrative.

The next degree of knowledge is, where the mind perceives the agreement
or disagreement of any ideas, but not immediately. Though wherever the
mind perceives the agreement or disagreement of any of its ideas, there
be certain knowledge; yet it does not always happen, that the mind sees
that agreement or disagreement, which there is between them, even where
it is discoverable; and in that case remains in ignorance, and at most
gets no further than a probable conjecture. The reason why the mind
cannot always perceive presently the agreement or disagreement of
two ideas, is, because those ideas, concerning whose agreement or
disagreement the inquiry is made, cannot by the mind be so put together
as to show it. In this case then, when the mind cannot so bring its
ideas together as by their immediate comparison, and as it were
juxta-position or application one to another, to perceive their
agreement or disagreement, it is fain, BY THE INTERVENTION OF OTHER
IDEAS, (one or more, as it happens) to discover the agreement or
disagreement which it se