Bad logic, but good statistics

Ad hominem arguments are bad logic, but good (Bayesian) statistics. A statement isn’t necessarily false because it comes from an unreliable source, though it is more likely to be false.

Some people are much more likely to know what they’re talking about than others, depending on context. You’re more likely to get good medical advice from a doctor than from an accountant, though the former may be wrong and the latter may be right. (Actors are not likely to know what they’re talking about when giving advice regarding anything but acting, though that doesn’t stop them.)

Ad hominem guesses are a reasonable way to construct a prior, but the prior needs to be updated with data. Given no other data, the doctor is more likely to know medicine than the accountant is. Assuming a priori that both are equally likely to be correct may be “fair,” but it’s not reasonable. However, as you gather data on the accuracy of each, you could change your mind. The posterior distribution could persuade you that you’ve been talking to a quack doctor or an accountant who is unusually knowledgeable of medicine.

Related post: Musicians, drunks, and Oliver Cromwell

6 thoughts on “Bad logic, but good statistics

  1. Agreed to some extent, as long as the Ad Hominem is of the form: “Bob was wrong about the economy in the previous 100 instances, so why should we take his economic forecast seriously this time?” instead of “Bob listens to music we don’t like and cheats on his wife so why should we take his economic forecasts seriously?”

    (I find most of the Ad Hominem in the wild to be variations on the second type rather than the first.)


  2. “…though it is more likely to be false.”

    I think a Bayesian would say that he believes it to be more likely. It’s perfectly reasonable (from a Bayesian perspective) to say that “Bob was wrong about the economy in the previous 100 instances, therefore I believe his currect economic forecast will be wrong?” But, this isn’t a statement (argument) about Bob’s forcast, it’s a statement about my belief.

    It’s a sublte but significant difference to say that “Bob was wrong about the economy in the previous 100 instances, therefore his currect economic forecast will be wrong?” This is ad hominem; a poor argument.

  3. What Jose above said. Calling somebody unreliable, or prone to exaggeration, or partisan, is not an ad hominem attack. That is, after all, relevant.

    Saying “Oh, he’s just a Tea Party conservative” is a perfectly rational dismissal if the argument is about climate change or US budgets. Saying the same when the discussion is about whether Chicken Vindaloo really should count as genuinely Indian cuisine is Ad Hominem. Saying “He’s Indian you know” is an important point in an argument about the food, but Ad Hominem if you use it to dismiss his argument about carbon sequestration.

  4. I think Jose is right: the argument is fallacious only when the facts about the claimer are not relevant for the truth/falsity of the claim. (That’s why it’s an informal fallacy: the logic structure itself can be cogent, but it’s not enough to know if it’s a fallacy or not).

    Therefore if the argument is an ad hominem, facts about the author should be treated as an independent event. Correspondinly, if you believe the argument to be more or less reliable depending on the source, you are assuming (implicitly) that the argument is not fallacious — and you might be wrong. BTW, your examples look more like ad verecundiam (“argument from authority”, another informal fallacy).

    And for Janne example, it can be a “perfectly rational dismissal”, but still a textbook example of an ad hominem — the stubbornness and irrationality with which someone makes an claim has no value about the truth of the claim.

  5. Good article, but can I quibble? Ad hominem arguments are invalid in standard two-valued logic systems but can be formulated in a way that would be valid in many-valued logic systems. So it might be too harsh to call them “bad logic”.

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