omewhere similar original instruments provided
also as the first outfit of intellectual enterprise. To discover these,
he examines the various senses in which men are said to know anything,
and he finds that they resolve themselves into three, or, as he
elsewhere divides it, four.

We know a thing--

1. i. _Ex mero auditu_: because we have heard it from some
person or persons whose veracity we have no reason to
question.

ii. _Ab experientia vaga_: from general experience: for
instance, all facts or phenomena which come to us through
our senses as phenomena, but of the causes of which we
are ignorant.

2. We know a thing as we have correctly conceived the laws
of its phenomena, and see them following in their
sequence in the order of nature.

3. Finally, we know a thing, _ex scientia intuitiva_, which
alone is absolutely clear and certain.

To illustrate these divisions, suppose it be required to find a fourth
proportional which shall stand to the third of three numbers as the
second does to the first. The merchant's clerk knows his rule; he
multiplies the second into the third and divides by the first. He
neither knows nor cares to know why the result is the number which he
seeks, but he has learnt the fact that it is so, and he remembers it.

A person a little wiser has tried the experiment in a variety of simple
cases; he has discovered the rule by induction, but still does not
understand it.

A third has mastered the laws of proportion mathematically, as he has
found them in Euclid or other geometrical treatise.

A fourth, with the plain numbers of 1, 2, and 3, sees for himself by
simple intuitive force that 1:2=3:6.

Of these several kinds of knowledge the third and fourth alone deserve
to be called knowledge, the others being no more than opinions more or
less justly founded. The last is the only real insight, although the
third, being exact in its form, may be depended upon as a basis of
certainty. Under this last, as Spinoza allows, nothing except the very
simplest truths, _non nisi simplicissimae veritates_, can be perceived;
but, such as they are, they are the foundation of all after-science; and
the true ideas, the _verae ideae_, which are apprehended by this faculty
of intuition, are the primitive instruments with which nature has
furnished us. If we ask for a test by which to distinguish them, he has
none to give us. 'Veritas,' he says to his