Whether it's in comment forums or class discussions, one thing that always drives me up the wall is when someone makes a remark that's a "difference of degree" statement, and then some jerk pipes up -- always oozing smugness or sarcasm -- with a "counterexample." But unlike math class,* we are rarely arguing the existence vs. non-existence, or uniqueness vs. non-uniqueness, of anything. Thus, "counterexamples" -- really just naysaying -- don't prove squat. If I claim that men are more likely than women to be 6 feet tall, pointing out even 10,000 women who are at least that height doesn't go against what I said, since I could point out even more men.
I used to think that this was a sly rhetorical trick, or intellectual laziness, or perhaps a gut emotional reaction to a claim you don't like. But then again, maybe most of these people are just stupid and can't count. Maybe they'd score above-average on an IQ test (or maybe they wouldn't), but they aren't smart enough to engage in an honest debate -- not for want of honesty (necessarily...), but for want of logical thinking ability.
I've coached kids for the SAT for about 3 years in total, and among the reading comprehension questions, some of the harder ones test the student's ability to discern subtlety. An easy way to write this type of question is to create three outer-space answers, one answer that has a universally positive or negative quantifier ("all," "every," "none," etc.), and one that has a less extreme phrasing. The test-makers never choose extreme writers, or moderate writers on controversial issues, so the subtle answer is almost always the right one -- "The author grudgingly accepts the way our school system is structured," rather than "The author expresses his disdain for institutional education." Others might focus on "not at all" vs. "is less likely," and so on.
Now, SAT questions only make it into the real test by proving themselves to be somewhat g-loaded: they help you tell the dull from the average from the smart students. So, maybe those who repeatedly commit this error are more cretinous than crafty. Just a thought.
* Even mathematicians are comfortable saying things like, "Don't expect a typical group to be Abelian" or "These types of equations usually have closed-form solutions."
I think there is also a tendency among intellectuals toward Platonism, toward assuming that higher thinking must represent perfect essences which a single counter example (e.g., a triangle with four sides) could disprove. In turn that leads to post-modernism, where you believe hideously implausible things just because they can't be ultimately disproved -- e.g., that blacks are more found in the NBA than Mexicans because there's a stereotype that blacks are more found in the NBA than Mexicans, so everybody is under the control of the stereotype and thus obeys it so precisely that the actual reality comes to be exactly what the stereotype says the realit is.ReplyDelete