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The Marginalian

Blaise Pascal on the Intuitive vs. the Logical Mind and How We Come to Know Truth

“Your intuition and your intellect should be working together… making love,” Madeleine L’Engle asserted in contemplating how creativity works. Ray Bradbury believed that intuition and emotion should guide creative work, the intellect coming in only to revise after the act of creation, and Susan Sontag admonished against buying into this polarity in the first place: “The kind of thinking that makes a distinction between thought and feeling is just one of those forms of demagogy that causes lots of trouble for people.” But it’s hard to deny that in most minds there exists a combination of the two and in very few a perfect balance.

The duality of these two faculties and their interplay is what the great French physicist, philosopher, inventor, and mathematician Blaise Pascal (June 19, 1623–August 19, 1662) explores in Pensées (free ebook | public library) — the same masterwork of fragmentary reflections that gave us Pascal on the art of changing minds.

In a passage outlining the difference between the intuitive and the mathematical mind — “mathematical” meaning “logical” or “rational” — he writes:

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.

Suggesting that it is a greater failure to be unintuitive than to be unanalytical, Pascal adds:

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… Mathematicians wish to treat matters of intuition mathematically, and make themselves ridiculous.

Art from The Boy Who Loved Math, a children’s book about the life of legendary mathematician Paul Erdos.

But this mathematical (or logical) mind is only a subset of the intellect that stands opposite intuition:

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.

Pascal argues that our failure to understand the principles of reality is due to both our impatience and a certain lack of moral imagination:

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.

He considers what mediates the relationship between our intellect and our intuition:

The understanding and the feelings are moulded by intercourse; the understanding and feelings are corrupted by intercourse. Thus good or bad society improves or corrupts them. It is, then, all-important to know how to choose in order to improve and not to corrupt them; and we cannot make this choice, if they be not already improved and not corrupted. Thus a circle is formed, and those are fortunate who escape it.

Pascal makes a peculiar and rather poignant aside — doubly so in our divisive age of harsh snap-judgments directed at others via soundbites and status updates — suggesting that our inability to appreciate the singular gifts of other people is essentially a failure of our own intelligence, for the prerequisite for appreciation is comprehension:

The greater intellect one has, the more originality one finds in men. Ordinary persons find no difference between men.

One of Antoine de Saint-Exupéry’s original watercolors for The Little Prince.

Three centuries before the most beloved line from the most beloved children’s book“It is only with the heart that one can see rightly,” wrote Antoine de Saint-Exupéry. “What is essential is invisible to the eye.” — Pascal observes:

The heart has its reasons, which reason does not know… We know truth, not only by the reason, but also by the heart.

Nearly four centuries later, Pensées remains a revelatory read, full of timeless wisdom on everything from navigating uncertainty to the key to eloquence. Complement this particular portion with a fascinating read on the role of intuition in scientific discovery, Carl Sagan on the necessary balance between skepticism and openness, and Hannah Arendt on the crucial difference between truth and meaning.

Published June 19, 2015




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