Pascals Pensees | Page 8

that mathematicians are not intuitive is
that they do not see what is before them, and that, accustomed to the
exact and plain principles of mathematics, and not reasoning till they
have well inspected and arranged their principles, they are lost in
matters of intuition where the principles do not allow of such
arrangement. They are scarcely seen; they are felt rather than seen;
there is the greatest difficulty in making them felt by those who do not
of themselves perceive them. These principles are so fine and so
numerous that a very delicate and very clear sense is needed to perceive
them, and to judge rightly and justly when they are perceived, without
for the most part being able to demonstrate them in order as in
mathematics; because the principles are not known to us in the same
way, and because it would be an endless matter to undertake it. We
must see the matter at once, at one glance, and not by a process of
reasoning, at least to a certain degree. And thus it is rare that
mathematicians are intuitive, and that men of intuition are
mathematicians, because mathematicians wish to treat matters of
intuition mathematically, and make themselves ridiculous, wishing to
begin with definitions and then with axioms, which is not the way to
proceed in this kind of reasoning. Not that the mind does not do so, but
it does it tacitly, naturally, and without technical rules; for the
expression of it is beyond all men, 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;[2] 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
judgment, which has no rules, makes light of the morality of the
intellect.
For it is to judgment that perception belongs, as science belongs to
intellect. Intuition is the part of judgment, mathematics of intellect.
To make light of philosophy is to be a true philosopher.
5
Those who judge of a work by rule[3] are in regard to others as those
who have a watch are in regard to others. One says, "It is two hours
ago"; the other says, "It is only three-quarters of an hour." I look at my
watch, and say to the one, "You are weary," and to the other, "Time
gallops with you"; for it is