t of identity, our intuitive knowledge reaches as far as our
ideas. And we are capable of making as many self-evident propositions,
as we have names for distinct ideas. And I appeal to every one's own
mind, whether this proposition, 'a circle is a circle,' be not as
self-evident a proposition as that consisting of more general terms,
'whatsoever is, is'; and again, whether this proposition, 'blue is not
red,' be not a proposition that the mind can no more doubt of, as
soon as it understands the words, than it does of that axiom, 'it is
impossible for the same thing to be and not to be?' And so of all the
like.

5. In Co-existance we have few self-evident Propositions.

II. SECONDLY, as to CO-EXISTANCE, or such a necessary connexion between
two ideas that, in the subject where one of them is supposed, there the
other must necessarily be also: of such agreement or disagreement as
this, the mind has an immediate perception but in very few of them. And
therefore in this sort we have but very little intuitive knowledge: nor
are there to be found very many propositions that are self-evident,
though some there are: v.g. the idea of filling a place equal to the
contents of its superficies, being annexed to our idea of body, I think
it is a self-evident proposition, that two bodies cannot be in the same
place.

6. III. In other Relations we may have many.

THIRDLY, As to the RELATIONS OF MODES, mathematicians have framed many
axioms concerning that one relation of equality. As, 'equals taken from
equals, the remainder will be equal'; which, with the rest of that kind,
however they are received for maxims by the mathematicians, and are
unquestionable truths, yet, I think, that any one who considers them
will not find that they have a clearer self-evidence than these,--that
'one and one are equal to two', that 'if you take from the five fingers
of one hand two, and from the five fingers of the other hand two,
the remaining numbers will be equal.' These and a thousand other such
propositions may be found in numbers, which, at the very first hearing,
force the assent, and carry with them an equal if not greater clearness,
than those mathematical axioms.

7. IV. Concerning real Existence, we have none.

FOURTHLY, as to REAL EXISTANCE, since that has no connexion with any
other of our ideas, but that of ourselves, and of a First Being, we have
in that, concerning the real existence of all other beings, not so much
as demo