So you want to refute–i.e., prove to be false–someone else’s generalization. There’s only one way that I can think of: show that the generalization is false. That means your evidence of its falsity must be as general as the claim itself. Pointing out exceptions to a generalization only demonstrates your inability to grasp one foundational notion of informal reasoning. Two examples of this from our dear friend, George F. Will:

>Once America’s most industrialized city, Newark attracted the attentions of New York mobsters (the movie “On the Waterfront” was filmed on New Jersey docks) whose depredations contributed to the flight of industry just as blacks were arriving from the South. Partly because of the cost that organized crime added to many city contracts, Newark spent twice as much per citizen as did other midsize cities. And the riots came, (redundant) evidence of the problematic nature of attempts to spend one’s way to domestic tranquility.

The first part of this paragraph shows how the spending in Newark was uniquely corrupt. How that then can be evidence for the claim that spending does not equal domestic tranquility baffles: it wasn’t effective spending. Unless, of course, Mr.Will means to refute the view of the person who says: “all social spending–including the corrupt cosa nostra kind–ensures tranquility–and if you find one counterexample, I will be wrong.”

Here’s the second:

>Today, per-pupil spending tops $17,000, which is 75 percent above the national average and a (redundant) refutation of the public education lobby’s not disinterested judgment that in primary and secondary education, cognitive outputs correlate with financial inputs. Seventy percent of Newark’s 11th-graders flunk the state’s math test. Booker says that under the previous mayor’s administration, every elected official sent his or her children to private schools.

Again. That’s hardly a “refutation” of that rule. It’s a counter-example. And perhaps a reminder that not just any money counts. Money well spent counts. I think that’s probably what the rule means.

But in both cases, in order to show the falsity of the generalization being refuted, Mr.Will will have to come up with a more representative counter-example than the city awash in mob corruption (on account, in part, because of its place in global trade–the port of Newark). If he wants actually to say something true, then perhaps he ought to try to do a little non-Heritage foundation research.

6 thoughts on “Refutation”

  1. this column is really the heighth of mean-spirited agenda-stumping. that will feels justified in using race riots, mob corruption, and a flagging civic economy to further his own case for the privatization of america is shameful. the window in his ivory tower is getting narrower and narrower. maybe he should just hang up a mirror to facilitate his navel-gazing.

  2. That was poetic Phil. You have a way with phrases that calls to mind the best “your mama” jokes (albeit in a slightly more literary fashion). Awwwww snappp! Will is again full of his own jackassitude.

  3. When you wrote, “Pointing out exceptions to a generalization only demonstrates your inability to grasp one foundational notion of informal reasoning,” what exactly did you mean? I’m used to scientific inquiry, in which (often, not always) an exception to a generalization falsifies the generalization.

    Also, do you notice how George Will commits the fallacy of the oversimplified cause? There may be other factors (no doubt there are) for why Newark students haven’t had perfect academic success. In fact, the comparison to make is not between Newark and other cities (which are different in many other ways besides money spent), but between Newark spending at 75% of the national average and Newark spending at a smaller rate.


  4. Dear David–

    By that I meant that exceptions to inductive generalizations don’t show much, unless they’re substantial enough to nullify all the instances in which the opposite is the case. So in the case of the Newark public schools, we have money corruptly spent, but this doesn’t show the falsity of the general idea that students benefit from public education spending (or that spending money on education doesn’t produce positive results).

    Newark as a whole, as you point out, seems a unique case of a failed government. But the failure of one particularly corrupt government can’t hardly serve as the example for any government entity. That’s just silly.

    On that score, I don’t remember Will making the causal connection about the failure of the students, as you suggest. I just remember him making the inference that the failure of such richly funded students undercuts the idea that paying more per student yields results. To that anyone with any sense would say, “no kidding. The money has to be spent properly.” Thousands of suburban public schools will demonstrate what kind of education money can buy you.

    Good points, and thanks for the comment.


  5. I see. So I guess, in science I’m thinking of a generalization that is inferred in order to illuminate a certain definite cause for the members of a class and in which the generalization becomes almost synonymous with the supposed cause. In this case, one counterexample (provided the counterexample itself truly is a member of the class) is sufficient to refute the generalization and the supposed cause. Of course, sometimes the supposed cause does not determine the properties of the members of a class, but rather it determines the likelihood that certain properties will occur. In that case, one counterexample is not capable of refuting the generalization or the supposed cause, and one must adopt a statistical approach with many trials. The scatter about the most likely property may be truly random, or it may be due to additional unknown causes. This is very much more like the Newark case, in which one might say that, while increased spending doesn’t guarantee better performance, it raises the likelihood of better performance. One way you see this commonly expressed is with the caveat, “All other things being equal…”


    Thanks for clearing up my confusion, and thanks for the comments.

  6. Dear David,

    that sounds right to me. Say when one locates what one thinks is the cause of some disease, but then a ceteris paribus counter example emerges, one would be rightly skeptical about the previously identified cause. Of course, the implication would be that the previously identified cause was taken to be both necessary and sufficient. It might then just be a sufficient cause. Enough to bring about disease x, but not necessary. Or of course it could be neither. But I’d hesitate to call that circumstance a generalization, however, so much as a causal claim. Those of course as you rightly point out apply to general groups, but because they can be undermined with one counter example, they’re not generalizations.

    In the school case, no one claims that money is the sole determining factor in educational success (i.e., both a sufficient and necessary cause). This is an absolutely ludicrous view (but again typical of the way Will characterizes “liberals”). It is not sufficient, obviously, and it is not always necessary, but it usually is, and that’s enough.

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