"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.

"Every man has the right to have his ideas
examined one at a time." (Ezra Pound)

Even very established scholars sometimes describe themselves as “students of” their subjects. This isn’t an expression of (even false) humility; they are merely acknowledging that they “study” things. Something similar can be said of words like “test” and “examine”, which can be applied both to people and to ideas. At first pass, these seem to be radically different senses of “student” and “examine”, but I think it’s worth noting their connections. Students and scholars are, after all, engaged in the same cultural activity, namely, “learning.” Though here, again, we’re tempted to say that the word is used in two very different senses, I think it’s important to keep in mind that, not only is our instruction based on our scholarship, we are, in part, instructing our students in the craft of scholarship. Examination is an integral part of academic life, even when it’s not part of the process of assigning a grade.

That said, I sometimes suspect that scholars resent the exam-like conditions of, for example, the peer-review process. While it makes sense to want to put “school” behind you, that desire is easier for people who leave the university (for one of the professions or the arts or anything else) to declare than it is for academics to wanly announce. In fact, academics ideally chose their career path because they genuinely respect the exam situation. We might say that the university ought to attract people who, precisely, don’t resent examination, i.e., people who see the value of testing the knowledge of someone whose job it is to know things. The deepest way of addressing this problem, then, is to explain why no one, not even a student, should resent being examined.

Why are exams a good thing?

We can begin with the easy cases. We want our doctors to know what they’re doing. We want them to get very good educations, and we want their licenses to practice medicine to depend on this education. We’re not satisfied with their merely getting into, or even dutifully attending, medical school. We want to know that they actually learned what their teachers were trying to teach them. So we expect those teachers to examine our future doctors’ understanding of the current state of medical knowledge. These days, many of us are discovering (some of us, to our surprise) the depth of our respect for medicine, and this implies a respect for the institutions that train our medical professionals. We believe that they’ve done a good job of ensuring that the people who treat us when we are ill know what they’re doing.

This is why I don’t like it when established academics side with students who “hate school” (allegedly out of their “love of learning”). It’s perfectly legitimate, and often no doubt reasonable, to dislike going to school. All social institutions are imperfect, and none can fulfill its mission entirely without some residual nuisance and boredom, but higher education is for people who have actively put up with those imperfections for the sake of a greater goal, indeed, a higher purpose.

Testing a student is merely a somewhat artificial instance of testing ideas. Ezra Pound invoked his “right” to have his ideas tested (he had his reasons), but there is also, among academics in any case, a duty to let them be tested. At the limit, we might posit a Socratic duty to oneself to examine one’s own ideas, lest one’s own life be not worth living. But, as I reminded us above, the unexamined doctor is certainly not worthy of a medical practice. Highly educated professionals deserve our respect because they once allowed themselves to be examined by people who were qualified to tell them they were wrong. Academics, I never tire of saying, are people who are permanently committed to this regime of “testing” by their peers.

"A picture is laid against reality like a ruler."
(Ludwig Wittgenstein)

There hasn’t been a lot of rain around here lately. Today is another beautiful April day in partially re-opened Copenhagen, cruelly “mixing memory and desire,” and I can’t recall when it last rained. But I can consult the weather archive of the Danish Meteorological Institute to learn that it has rained on three days in April so far, no doubt “stirring dull roots” each time it did. In fact, DMI reports that 1.2 mm, 1.6 mm, and 0.3 mm fell on April 1, 2 and 12, respectively. At the time, someone might have said, simply, “It’s raining.” But now they can say, rather confidently, “On April 1, it rained 1.2 mm.” What gives them this confidence? What does that statement mean?

The best way to understand a measurement is to understand the measuring instrument. In this case, I assume DMI uses some sort of rain gauge. It’s always useful to hear how scientists explain things to children, and it turns out that the measurement refers to the depth of the water at the bottom of a regularly shaped container (one that is the same size from the opening at the top all the way to bottom) that has been left out in the rain. An official rain gauge is a little more sophisticated in order to make the measurement more precise, but that doesn’t change what the measurement means. You can stick a ruler into the container, or pour the water into a properly calibrated graduated cylinder, or just collect the water in that graduated cylinder in the first place (by way of a funnel whose opening is as big as your original container). It amounts to the same thing.

Now, “it is raining,” may (on occasion, as Quine points out) be a true sentence, but it refers to a big and rather vague fact. How can I be sure that “it” rained 1.2 mm in Frederiksberg on April 1? And what does this even mean? This is where we get into even more detailed descriptions of our methods of data collection. But again, it can probably be explained to school children without much trouble.

If you want to measure how much rain fell on your neighborhood, you could, in principle, use a straight-sided, flat-bottomed container that covered every square meter. Then you just measure how deep the water is. On April 1 in Frederiksberg, they say, you would have found it was 1.2 mm. That’s not workable in practice of course, but it has the virtue of getting us to imagine collecting all the water that fell on a given day in the entire neighborhood. Maybe it rained a little more in my backyard than yours? If we had relied on my gauge and then, yes, generalized our results we may have overestimated the total rainfall. And that’s not to mention all the little accidents — wind, birds, leaves — that could have interfered with or abetted the water getting into my gauge or yours. If we collect all the water, we wouldn’t have to worry about this since it all ends up on the ground we’re interested in.

To simulate this — to collect a representative sample of the rain — we set up a number of rain gauges all over the neighborhood. We measure the depth in each of them, and then we average the results. We may even weight them according to how they are spaced around town. The more seriously we take this business, the more accurate our result, and the more confident we can be when we declare that 1.2 mm of rain fell on Frederiksberg on April 1, 2020.

Suppose I want to know whether the population approves of our prime minister’s handling of the COVID-19 outbreak. At one level, we could make a simple, qualitative observation based on the impression we get from watching the news and talking to friends and neighbors: “The prime minister is very popular at the moment.” This is like saying, “There hasn’t been a lot of rain around here lately,” and may or may not be true. But our question is actually more interesting and requires measurement. We can survey the population and compare the result to previous surveys. We have to make sure that our surveys ask enough people and sample from different segments of the population. We also have to ask whether the pollsters themselves have biases, and we have to average among the different surveys that have been done. It can be very complicated, but the procedure can be described, if not to school children, then certainly to university students. But underneath it all are the surveys themselves, the “instruments” that gathered the responses from each of the people that were polled.

Andrew Gelman is tireless in his insistence on the importance of good measurement in social science. “Purity of heart is no protection,” he tells us: “the math doesn’t care. If you conduct power = .06 research, or if you try to study ovulation and you get the dates of ovulation wrong, or if you study sex ratios without understanding scales of variation, or if you study himmicanes without getting control of your data, etc., then you will fail to learn about reality. You will be doing bad science. Science has its own logic.” You’re probably a good person. But that’s not enough.

I began this series with Ezra Pound’s idea that “the arts provide data for ethics.” I will return to this idea in greater detail in my next post, but I want to end by emphasizing, as Pound did, the connection between good science and serious art. It lies in the precision of the observation, the accuracy of our measurements. “The serious artist,” says Pound, “is scientific in that he presents the image of his desire, of his hate, of his indifference as precisely that, as precisely the image of his own desire, hate or indifference. The more precise his record the more lasting and unassailable his work of art” (Literary Essays, p. 46). As a social scientist you also maintain a record of “images”, mental pictures of social facts, and you do well to be just as precise. A great deal depends upon it.

"Sometimes it is raining, sometimes not."
(W.V.O. Quine)

One of the most famous images in modern American poetry is that of a red wheelbarrow glazed with rain. “So much depends upon” it, said William Carlos Williams, without saying exactly what or how. It’s reasonable to assume that he was alluding to imagination, which was the subject of the book in which the poem first appeared. “To whom then am I addressed?” he asks in Spring and All, and answers, “To the imagination.” Nothing much depends on the wheelbarrow or the chickens, but a great deal depends on our ability to imagine them. And the poem shows us that we can imagine them. The importance of this ability — what Kant called Einbildungskraft, which more literally means “the power to form pictures” — can be seen in our near inability to imagine not having it. Imagine not having an imagination at all! You might as well try to imagine what it’s like to be a wheelbarrow.

Or the rain. In my last post, I proposed to reflect on the “data of epistemology”. What is given to us to think about when we think about knowledge, what knowledge is, what it means to “know something”? Can anything be taken for given in philosophy in the first place? In a wonderful essay from 1993, W.V.O. Quine suggested that there are, indeed, “epistemological givens”. They’re not quite as bereft of meaning as the “sense data” of the British empiricists, and not as impossibly technical as the “protocol sentences” of the logical positivists. But they have the same kind of finality. He was thinking about reports of a particular kind of experience, sentences that we understand immediately, and which we can quickly and easily decide whether are true. “It’s cold.” “That’s milk.” “That’s a dog.” And, yes, “It’s raining.”

He called them “observation sentences” and he sang their praises. We might say he thought a great deal depended on them.

Each of us learned some of his observation sentences in early childhood, and each of us learned most of them later. We learn some of them from other ones by analogy, recombining their parts. We learn to form compounds of simple ones, using grammatical particles. As adults we learn many more through the mediation of sophisticated theory. Thus, take the sentence ‘There is some copper in the solution’. We understand it by construction from its separate words, but it becomes an observation sentence for a chemist who has learned to spot the presence of copper by a glance at a solution. What qualifies sentences of both sorts as observational, for a given individual, is just his readiness to assent outright on the strength of appropriate neural intake, irrespective of what he may have been engaged in at the time. (108)

Notice that Quine is here giving us a clear paradigm for epistemological analysis. There is a difference between my statement, “There is copper in the solution,” and the chemist’s observation, expressed in the very same sentence. Being a scientist means being able to make observations of a particular kind, which non-scientists are then consigned to “understand by construction”. Of course, even the scientist must “build us his world,” as Ezra Pound said of the poet. But the materials that scientists build their worlds out of when they are talking to each other are very different from the ones they use when they are talking to us.

All of us, Quine argues, at least whenever we actually know what we are talking about, are building our worlds out of observations. While I don’t find the language of “neural intake” very compelling, Quine insists that it offers a better starting point than, say, things and people, or situations (my preference, I think), because “nerve endings afford a clearly individuated, homogeneous domain” in the causal chain of perception. But that’s not something I’m going to quibble about here. The point is simply that we all know the conditions under which we would grant that it is raining, the conditions under which the sentence “It is raining” is true. Just as we know a white chicken and a red wheelbarrow when we see one. It’s what let you imagine them again just now.

Academic writers do well to bear this in mind. Some of your sentences can be traced back to your observations. You and your peers are qualified to make some observations and not others and some of your claims are grounded, or “bottom out”, or terminate, in these sentences. The essential thing is that they be utterly familiar to your intended readers, your peers. When you say “There is copper in the solution,” they know exactly what you have seen. They can picture it. They understand the sentence as readily as the rest of us understand “It is raining,” and that, at the end of the day, is what makes it an observation. You can imagine it.

"The essential thing in a poet is that he build us his world."
(Ezra Pound)

"Discipline is implied."
(William Carlos Williams)

Ludwig Wittgenstein famously begins his Tractatus Logico-Philosophicus with a simple but sweeping proposition. “The world is everything that is the case,” he declares. The reader will later be told that this proposition is actually meaningless; it is not a statement “about” the world at all. It just shows us what the words mean. We might say it defines the word “world”, but surely it also defines “everything” and “being the case”. None of these words are especially technical — we all knew what they meant before we read the sentence — but he commits us to a certain relationship between them. They don’t represent a fact; they show us the logic of language. Interestingly, he will go on to claim (just as meaninglessly, he would argue) that the logic of language is the same thing as the logic of facts, the logic of the world.

His mentor, Bertrand Russell, has summarized this idea in a sentence that has never left me since I read it many years ago. “The essential business of language,” he said in his introduction to Wittgenstein’s treatise, “is to assert or deny facts.” On the face of it, this claim seems less certain than Wittgenstein’s opening statement, though he presents it with the same assured feeling of logical truth. We can push back against it a little by asking, What about the “business” of demanding and denouncing acts? I.e., surely the normative functions of language are as “essential” as its empirical functions? And Wittgenstein himself would indeed eventually abandon any reduction of language to any particular “essence”; language is used for so many different things that it seems odd to give statements of fact some sort of priority. What about asking questions, for example? What about expressing feelings?

In his notebooks, Wittgenstein once remarked that beginning the Tractuatus by invoking “the world” was a kind of conjuring act, a magic trick, an attempt to get us to imagine something that can’t actually (or in fact!) be imagined. He should perhaps have started, he went on, with “this tree” or “this table”, i.e., things that actually exist and can be seen and talked about meaningfully. “We make ourselves pictures of the facts,” Wittgenstein had said elsewhere in the Tractatus, and we can certainly imagine a tree, we can picture it, much more clearly than we can imagine “the world”. If we stuck to simple imagery — trees, rain, birds — perhaps philosophical problems would never arise? That is one way of putting Wittgenstein’s philosophy.

Will you allow a little poetry? Here’s a poem that Jonathan Mayhew recently drew to my attention.

The trees--being trees
thrash and scream
guffaw and curse--
wholly abandoned
damning the race of men--

Christ, the bastards
haven't even sense enough
to stay out in the rain--

That’s William Carlos Williams. He’s the one who also pointed out how “much depends upon” red wheelbarrows glazed with rainwater. His friend, Ezra Pound, believed that “the arts provide data for ethics,” the materials out of which to construct a worldview, a moral universe. Can they also provide data for epistemology? Can they help us to understand the logic of representation, the rules by which we make pictures of the facts? Can they help to imagine the structure of the world? These days, after all, we poor bastards hardly even go outside, let alone to stand in the rain. I’m going to devote a few posts to this subject, if you’ll bear with me.