8. These axioms do not much influence our other knowledge. In the
next place let us consider, what influence these received maxims
have upon the other parts of our knowledge. The rules established in
the schools, that all reasonings are Ex praeognitis et
praeconcessis, seem to lay the foundation of all other knowledge in
these maxims, and to suppose them to be praecognita. Whereby, I think,
are meant these two things: first, that these axioms are those
truths that are first known to the mind; and, secondly, that upon them
the other parts of our knowledge depend.
9. Because maxims or axioms are not the truths we first knew. First,
That they are not the truths first known to the mind is evident to
experience, as we have shown in another place. (Bk. I. chap. i.) Who
perceives not that a child certainly knows that a stranger is not
its mother; that its sucking-bottle is not the rod, long before he
knows that "it is impossible for the same thing to be and not to
be?" And how many truths are there about numbers, which it is
obvious to observe that the mind is perfectly acquainted with, and
fully convinced of, before it ever thought on these general maxims, to
which mathematicians, in their arguings, do sometimes refer them?
Whereof the reason is very plain: for that which makes the mind assent
to such propositions, being nothing else but the perception it has
of the agreement or disagreement of its ideas, according as it finds
them affirmed or denied one of another in words it understands; and
every idea being known to be what it is, and every two distinct
ideas being known not to be the same; it must necessarily follow, that
such self-evident truths must be first known which consist of ideas
that are first in the mind.
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