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1660

translated by W. F. Trotter

PENSÉES

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
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