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,
