Later On

A blog written for those whose interests more or less match mine.

Mathematics and reasoning

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I went to a liberal arts college as an undergraduate. The goal of the “liberal arts” is to “free” (liberate) a person from the bonds and traps of current circumstances and provide a broader and more informed vision of human possibilities and the essentials of a good life—in a word, to free a person to participate in a free society. (The liberal arts are thus a primary target in an authoritarian or totalitarian society: the last thing such societies want is a citizenry that thinks for itself and asks probing questions and can readily spot fallacious reasoning. Cf. the dismantling of liberal arts programs in this country and the push to train people only on narrow commercial and technical skills: much more suited to the kind of government we are building with the corporate takeover and dismantling of civil and human rights.)

Having a liberal arts curriculum meant, among other things, four years of study of mathematics and four years of laboratory science: essential liberal arts, and exercises in asking and answering particular sorts of questions.

This morning as I shaved I got to reflecting on this, and I realized that, as Steve of Kareneio has pointed out to me, we all are prone to “motivated reasoning”: reasoning distorted by a determination (conscious or unconscious) to arrive at a certain result. It’s a natural weakness that one can see most plainly in children and certain politicians. Their focus is on achieving the goal (the result/outcome they desire) and little attention is paid to the process by which the goal is achieved—and processes that do not arrive at the goal they want are dismissed out of hand, rather than dealt with thoughtfully.

It’s a natural tendency, like (say) chewing with your mouth open or scratching vigorously at an itch. And just as we can learn to modify those behaviors, we can also learn to detach ourselves from motivated reasoning and learn how to reason rightly.

This morning I was reflecting on the freshman mathematics program at my college: reading Euclid’s Elements: going through the definitions, axioms, postulates, and theorems, retracing the building of that magnificent logical edifice. I realized that what we were learning was how to reason correctly, not in a motivated way. Because the results were not something to which we had a pre-existing emotional attachment, we could reason without distortion, and quickly spot errors in reasoning in ourselves or (more often) in others, errors form which we could learn: developing habits of correct reasoning and a sensitivity to error.

That is, no one really has an emotional attachment to whether the squares on the sides of a right triangle are equal to the square on the hypotenuse or not. We have no emotional investment in a particular outcome, so we can more easily focus on the reasoning process itself. In contrast, on the issue of the ownership of high-capacity magazines or a woman’s right to an abortion, attachment to a particular outcome is strong and it’s harder to pay attention to the reasoning process. If the result is not what one wants, the reasoning is often dismissed without examination; if the result comes out “right” (in the eyes of the person witnessing the argument) the reasoning is accepted as sound without investigating it. Almost all the focus is on the outcome to be achieved, so little attention is paid to the arguments that achieve it. To reason well on that sort of topic requires good experience with the skills of sound reasoning and a developed sensitivity to errors in reason: i.e., education in liberal arts.

This doesn’t work well. Better that citizens—free citizens—have learned the arts of freedom and thus understand how to argue soundly and how to see through bad argument. Thus the liberal arts.

Written by LeisureGuy

25 January 2013 at 9:30 am

Posted in Daily life, Education

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