Generalization

"Any general statement is like
a cheque drawn on a bank."
(Ezra Pound)

To generalize is to promise specifics. If you are going to say that all swans are white, you’re going to have to produce at least one white swan, and you’re going to have to be open to examining the color of other people’s (preferably randomly chosen) swans. Your statement isn’t just about swans “in general”; it’s about every certifiable swan on the planet. Most importantly, if someone brings you a black waterbird, you had better be prepared to discuss whether it’s a swan or some kind of duck. Indeed, your statement applies to every bird of any color. If the bird is a swan, you’re saying, it’s going to be white; if it’s not white, it is not a swan. Maybe you’ve already guessed where this is going: your generalization actually applies to every blesséd thing, which, you are saying is either white or not a swan, but never not white and also a swan. “All swans are white,” that is, also depends, as so much does, upon a red wheelbarrow, which isn’t even a chicken.

Now, as it turns out, there are black swans, both literally and figuratively. (There are even ugly ducklings.) So it would be more accurate, perhaps, to say that most swans are white, or that adult mute swans (Cygnus olor) are mostly white, while adult black swans (Cygnus atratus) are indeed mostly black. If you’re familiar with Toulmin’s model of argumentation you will immediately recognize these as qualifiers that define the strength and scope of your generalization. You are making it clear exactly what your generalization means, what it can be used for, and, in fact, how useful it is likely to be be. You are gerrymandering its meaning to maximize its truth, we might say.

A pragmatist will tell you that “the truth is what works,” and this is no less true of generalizations than statements of particular fact. The interesting thing about generalizations is that they “work” in so far as they are right about those particular facts, and often ones that we haven’t yet observed. These are the specifics I said you owe your reader every time you make a general statement. You don’t have to pay your debt in full in the paper itself (and, in a sense, that isn’t even possible), but you are implicitly claiming to be able to “specify” the meaning of your generalization with reference to some unambiguous matters of fact. This is often couched in the language of “making predictions”. The general statements of your theory predict the specific statements of your hypotheses, and it should even let your readers make predictions — i.e., frame hypotheses — of their own. They theory “works” if it gets those predictions right.

Of course, we don’t submit all our generalizations to rigorous testing like this. I am just trying to make clear what we mean by general statements, namely, that a range of specific statements are true. When you say something of a general kind, you usually imply that you have access to specifics, that you have experienced the relevant particulars. You are also claiming that if counterexamples exist you would have been likely to have seen them. So make sure that you are able to construct examples as well as counterexamples of the generalities you invoke in your writing. You never know when someone will take you seriously enough to test you. You want to be ready when it happens.

The value of a general statement, said Ezra Pound in the ABC of Reading, “depends on what is there to meet it. If Mr. Rockefeller draws a cheque for a million dollars it is good. If I draw one for a million it is a joke, a hoax, it has no value. If it is taken seriously, the writing of it becomes a criminal act” (p. 25). Sometimes it’s an honest mistake, of course; you thought you had enough money to cover it. But sometimes you know full well that the bank will not honor your check. In scholarship, the same thing can happen. You may have looked at a lot swans, but never gone to Australia. Or you may just be passing along what you were told as a child. Or you may be perfectly aware of the Australian black swan and just hope that your reader never goes there. Some scholars generalize based on nothing more than hearsay and gut feeling. Some scholars overgeneralize from observations that they haven’t made enough of. And some scholars simply fabricate their results, writing checks they know their data can’t cash.

I don’t think you need my moral guidance here.

1 thought on “Generalization

  1. Thomas:

    This reminds me of the saying, “Theoretical statistics is the theory of applied statistics.” At first this may sound like an empty truism, but I think it has some content. The point is that, when studying the theoretical properties of some statistical method, you should think about where and how it will be applied.

    The principle should hold not just for statistics but for other activities whose fundamental purpose is to be in service to other goals. Other such activities, in addition to statistics, include writing, architecture, and civil engineering.

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