In my teaching and coaching, I am always looking for the repeatable, trainable activity of writing. This, I believe, should be the focus of instruction: the thing you can safely tell the student to do with an expectation of seeing improvement. To this end, I’ve been telling scholars and students to write paragraphs, the units of prose composition. I will go on doing this, of course, but I have decided to open another front. I will tell them also to think seriously about what they know. In fact, I want to suggest that the exercise of imagination is a repeatable, trainable activity. It’s something we should be encouraging students to do because it will make them better prose writers.

If paragraphs are the unit of composition, let’s say that images are the units of composure. In imagination, we bring our beliefs and desires, our concepts and emotions, our senses and motives together. “We make ourselves pictures of the facts,” as Wittgenstein put it. But how, exactly, do we do this? And how do we become better at it?

I already suggest you take a moment at the end of the day to plan a paragraph to write tomorrow. This moment can also be used to train your imagination. It should last no longer than 10 minutes, during which you call to mind some fact you know to be the case. Now, a fact is always an arrangement of things, so you do well to imagine those things and give them names. You should also give the arrangement itself a name, and once something has a name it can be a “thing” in its own right, which is to say you can imagine it as part of another, larger fact.

If I’m not mistaken, you’d like an example about now. Here’s one:

Microsoft is a hierarchical organization.

As an arrangement of things, this fact consists of organizational roles that are filled by people called “members”. To imagine this fact is to imagine that some of these members are at the “top” and others are at the “bottom” — usually there will be more people at the bottom than at the top. This arrangement is called a “hierarchy” and I will ask you to notice that this word doesn’t name the fact; it names the arrangement of these particular things, but that name could also be used to name the arrangement of the members of another organization. The fact is here named by the entire sentence, “Microsoft is a hierarchical organization,” not just the word “hierarchy”. (It takes a proposition to state a fact, not merely a word, which can only name a thing.)

So we’ve just noticed something important about imagining a fact. If something is a fact about one set of particular things it can also be a fact about another. “Microsoft is a hierarchical organization,” says something about Microsoft that could just as well be true of Google. To imagine that Microsoft is is a hierarchical organization requires the same sort of effort as imagining that Google is a hierarchical organization. And this brings us immediately to the most important thing about imagining facts: to imagine that something is the case is always to imagine a bunch of things that are not the case. That is, a fact is always contingent on other things not being the case.

There is no one, simple image of Microsoft’s hierarchy, or Google’s. A triangle with Satya Nadella at the apex would be as true as an elaborate tree diagram that reached down to the lowliest coder — the difference is a question of detail, not truth. What is important is that any particular image always suggests things that could be arranged differently. Every element could be replaced by another element. Nadella could be someone else and Microsoft wouldn’t be any less a hierarchy. On the other hand, though it is difficult, it is not impossible to imagine a significant “flattening” of the organization to destroy its hierarchical structure. The ability to imagine such a cataclysm is actually an important part of the ability to meaningfully imagine that an organization is a hierarchy.

This brings us to a final and crucial point. The “things” in the arrangement become “objects” by virtue of imagining the possible arrangements that aren’t actually the case. Objectivity is the perception of things in terms of their possible relations with other things rather than the merely subjective impression they leave on us. A fact is “objective” in that it has to co-exist with every other fact. It’s not just that in imagining a fact you have to picture where one fact ends and another begins; rather, you have to imagine where one fact must end if another is to begin. It is necessary that the actual be possible, and what makes one fact possible is that other facts don’t exclude it. (Wittgenstein originally argued that “atomic facts” are facts that can be otherwise without consideration of other facts; but one way of reading his later work is as a rejection of the existence of such factual atoms.)

So, to sum up, here’s how to imagine a fact. First, give it a name by composing a sentence. Next, imagine the things that the fact comprises. Name them. Now, consider them from an objective point view, in terms of their possible combination with other things, i.e., other objects that can be meaningfully combined with them. All of this should take no more than 10 minutes in the case of facts you know well. There should be many facts you know well enough to meaningfully imagine for ten minutes. The next day, compose the paragraph. Render the composition of pictures in your mind as a composition of words on your page. Perform your composure.