and only a few can feel it.
Intuitive minds, on the contrary, being thus accustomed to judge
at a single glance, are so astonished when they are presented with
propositions of which they understand nothing, and the way to which is
through definitions and axioms so sterile, and which they are not
accustomed to see thus in detail, that they are repelled and
disheartened.
But dull minds are never either intuitive or mathematical.
Mathematicians who are only mathematicians have exact minds,
provided all things are explained to them by means of definitions
and axioms; otherwise they are inaccurate and insufferable, for they
are only right when the principles are quite clear.
And men of intuition who are only intuitive cannot have the
patience to reach to first principles of things speculative and
conceptual, which they have never seen in the world and which are
altogether out of the common.
2. There are different kinds of right understanding; some have
right understanding in a certain order of things, and not in others,
where they go astray. Some draw conclusions well from a few
premises, and this displays an acute judgment.
Others draw conclusions well where there are many premises.
For example, the former easily learn hydrostatics, where the
premises are few, but the conclusions are so fine that only the
greatest acuteness can reach them.
And in spite of that these persons would perhaps not be great
mathematicians, because mathematics contain a great number of
premises, and there is perhaps a kind of intellect that can search
with ease a few premises to the bottom and cannot in the least
penetrate those matters in which there are many premises.
There are then two kinds of intellect: the one able to penetrate
acutely and deeply into the conclusions of given premises, and this is
the precise intellect; the other able to comprehend a great number
of premises without confusing them, and this is the mathematical
intellect. The one has force and exactness, the other comprehension.
Now the one quality can exist without the other; the intellect can
be strong and narrow, and can also be comprehensive and weak.
3. Those who are accustomed to judge by feeling do not
understand the process of reasoning, for they would understand at
first sight and are not used to seek for principles. And others, on
the contrary, who are accustomed to reason from principles, do not
at all understand matters of feeling, seeking principles and being
unable to see at a glance.
4. Mathematics, intuition.- True eloquence makes light of
eloquence, true morality makes light of morality; that is to say,
the morality of the judgement, which has no rules, makes light of
the morality of the intellect.
For it is to judgement that perception belongs, as science belongs
to intellect. Intuition is the part of judgement, mathematics of
intellect.
To make light of philosophy is to be a true philosopher.
