of axioms allowed them.
And here it is plain, that several other truths, not allowed to be
axioms, partake equally with them in this self-evidence. This we shall
see, if we go over these several sorts of agreement or disagreement
of ideas which I have above mentioned, viz. identity, relation,
co-existence, and real existence; which will discover to us, that not
only those few propositions which have had the credit of maxims are
self-evident, but a great many, even almost an infinite number of other
propositions are such.

4. As to Identity and Diversity all Propositions are equally
self-evident.

I. For, FIRST, The immediate perception of the agreement or disagreement
of IDENTITY being founded in the mind's having distinct ideas, this
affords us as many self-evident propositions as we have distinct ideas.
Every one that has any knowledge at all, has, as the foundation of it,
various and distinct ideas: and it is the first act of the mind (without
which it can never be capable of any knowledge) to know every one of
its ideas by itself, and distinguish it from others. Every one finds in
himself, that he knows the ideas he has; that he knows also, when any
one is in his understanding, and what it is; and that when more than one
are there, he knows them distinctly and unconfusedly one from another;
which always being so, (it being impossible but that he should perceive
what he perceives,) he can never be in doubt when any idea is in his
mind, that it is there, and is that idea it is; and that two distinct
ideas, when they are in his mind, are there, and are not one and the
same idea. So that all such affirmations and negations are made
without any possibility of doubt, uncertainty, or hesitation, and must
necessarily be assented to as soon as understood; that is, as soon as we
have in our minds [determined ideas,] which the terms in the proposition
stand for. [And, therefore, whenever the mind with attention considers
any proposition, so as to perceive the two ideas signified by the terms,
and affirmed or denied one of the other to be the same or different; it
is presently and infallibly certain of the truth of such a proposition;
and this equally whether these propositions be in terms standing for
more general ideas, or such as are less so: v.g. whether the general
idea of Being be affirmed of itself, as in this proposition, 'whatsoever
is, is'; or a more particular idea be affirmed of itself, as 'a man is a
man'; or,