1660

                                    PENSEES

                                by Blaise Pascal

                          translated by W. F. Trotter

                         SECTION I

                THOUGHTS ON MIND AND ON STYLE

    1. The difference between the mathematical and the intuitive
mind.- In the one, the principles are palpable, but removed from
ordinary use; so that for want of habit it is difficult to turn
one's mind in that direction: but if one turns it thither ever so
little, one sees the principles fully, and one must have a quite
inaccurate mind who reasons wrongly from principles so plain that it
is almost impossible they should escape notice.

    But in the intuitive mind the principles are found in common use
and are before the eyes of everybody. One has only to look, and no
effort is necessary; it is only a question of good eyesight, but it
must be good, for the principles are so subtle and so numerous that it
is almost impossible but that some escape notice. Now the omission
of one principle leads to error; thus one must have very clear sight
to see all the principles and, in the next place, an accurate mind not
to draw false deductions from known principles.

    All mathematicians would then be intuitive if they had clear
sight, for they do not reason incorrectly from principles known to
them; and intuitive minds would be mathematical if they could turn
their eyes to the principles of mathematics to which they are unused.

    The reason, therefore, that some intuitive minds are not
mathematical is that they cannot at all turn their attention to the
principles of mathematics. But the reason 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; 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