ble at
all, it must be looked for under the mathematical or
demonstrative method; by tracing from ideas clearly
conceived the consequences which were formally involved
in them. The question was, therefore, of these
ideas, these verae ideae, as he calls them,--what were they,
and how were they to be obtained: if they were to
serve as the axioms of his system, they must, he felt,
be self-evident truths, of which no proof was required;
and the illustration which he gives of the character of
such ideas is ingenious and Platonic.

In order to produce any mechanical instrument, he
says, we require others with which to manufacture it;
and others again to manufacture those; and it would
seem thus as if the process must be an infinite one,
and as if nothing could ever be made at all. Nature,
however, has provided for the difficulty in creating of
her own accord certain rude instruments, with the help
of which we can make others better; and others again
with the help of those. And so he thinks it must be
with the mind, and there must be somewhere similar
original instruments provided also as the first outfit of
intellectual enterprise. To discover them, he examines
the various senses in which men are said to know
anything, and he finds that these senses 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. These two in Ethics are classed together.

As we have correctly conceived the laws of such
phenomena, and see them following in their sequence
m the order of nature.

3. 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