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How To Explain

We go to a training session or meet with a boss, but no one comes out understanding what they were attempting to explain. Why is that?

We explain something to others, but they don’t get it. How could we do better?

Why does that happen? Why are those explanations ineffective? How can we explain well and effectively?

An Example

Let’s start by studying an example of how to explain and how not to explain, from an essay by the Nobel Prize winning physicist Richard Feynman.

First, an introduction to the article that I will excerpt: “In 1964 the eminent physicist Richard Feynman served on the State of California’s Curriculum Commission and saw how the Commission chose math textbooks for use in California’s public schools. In his acerbic memoir of that experience, titled “Judging Books by Their Covers,“ Feynman analyzed the Commission’s idiotic method of evaluating books, and he described some of the tactics employed by schoolbook salesmen who wanted the Commission to adopt their shoddy products. ‘Judging Books by Their Covers’ appeared as a chapter in ‘Surely You’re Joking, Mr. Feynman!’ — Feynman’s autobiographical book that was published in 1985 by W.W. Norton & Company.”

And now the excerpt:

It was a pretty big job, and I worked all the time at it down in the basement. My wife says that during this period it was like living over a volcano. It would be quiet for a while, but then all of a sudden, “BLLLLLOOOOOOWWWWW!!!!’”— there would be a big explosion from the “volcano” below. The reason was that the books were so lousy. They were false. They were hurried. They would try to be rigorous, but they would use examples (like automobiles in the street for “sets”) which were almost OK, but in which there were always some subtleties. The definitions weren’t accurate. Everything was a little bit ambiguous — they weren’t smart enough to understand what was meant by “rigor.” They were faking it. They were teaching something they didn’t understand, and which was, in fact, useless, at that time, for the child.

It’s vaguely right — but already, trouble! That’s the way everything was: Everything was written by somebody who didn’t know what the hell he was talking about, so it was a little bit wrong, always! And how we are going to teach well by using books written by people who don’t quite understand what they’re talking about, I cannot understand. I don’t know why, but the books are lousy; UNIVERSALLY LOUSY!

What finally clinched it, and made me ultimately resign, was that the following year we were going to discuss science books. I thought maybe the science would be different, so I looked at a few of them.

The same thing happened: something would look good at first and then turn out to be horrifying. For example, there was a book that started out with four pictures: first there was a wind-up toy; then there was an automobile; then there was a boy riding a bicycle; then there was something else. And underneath each picture it said, “What makes it go?”

I thought, “I know what it is: They’re going to talk about mechanics, how the springs work inside the toy; about chemistry, how the engine of the automobile works; and biology, about how the muscles work.”

It was the kind of thing my father would have talked about: ”What makes it go? Everything goes because the sun is shining.” And then we would have fun discussing it:

No, the toy goes because the spring is wound up,” I would say.
“How did the spring get wound up?” he would ask.
“I wound it up.”
“And how did you get moving?”
“From eating.”
“And food grows only because the sun is shining. So it’s because the sun is shining that all these things are moving.” That would get the concept across that motion is simply the transformation of the sun’s power.

I turned the page. The answer was, for the wind-up toy, “Energy makes it go.” And for the boy on the bicycle, “Energy makes it go.” For everything, “Energy makes it go.”

Now that doesn’t mean anything. Suppose it’s “Wakalixes.” That’s the general principle: “Wakalixes makes it go.” There’s no knowledge coming in. The child doesn’t learn anything; it’s just a word!

What they should have done is to look at the wind-up toy, see that there are springs inside, learn about springs, learn about wheels, and never mind “energy.” Later on, when the children know something about how the toy actually works, they can discuss the more general principles of energy.

It’s also not even true that “energy makes it go,” because if it stops, you could say, “energy makes it stop” just as well. What they’re talking about is concentrated energy being transformed into more dilute forms, which is a very subtle aspect of energy. Energy is neither increased nor decreased in these examples; it’s just changed from one form to another. And when the things stop, the energy is changed into heat, into general chaos.

But that’s the way all the books were: They said things that were useless, mixed-up, ambiguous, confusing, and partially incorrect. How anybody can learn science from these books, I don’t know, because it’s not science.

(The article is also available at (1) “Judging Books By Their Covers” and (2) “Judging Books By Their Covers.”)

Lessons From Feynman

And what can we learn from Feynman? What are some logical and cognitive principles we can abstract from that excerpt?

  • consider the audience’s context of knowledge, not just your own
  • know at least some of the basic cognitive steps that take you from the evidence of the senses to the explanation (to figure that out, think “what did I have to learn from when I was a baby till now to get this?” or “what did scientists/experts have to learn through history to understand an idea?”)
  • pick out what cognitive step you can start at with your audience, and build up from there
  • you need a cause, a “why,” for things happening
  • you need a nice, tight chain of reasoning laid out for the audience, a “how do you know?”

We need to think of the audience, and what they know, and not explain on our own terms using our own context of knowledge. To get better at explanation, we need to practice looking at things from other points of view, we need to think back to all the steps (and frustrations and failures) we had to go through to get to some point in knowledge, and we need to have other people sometimes drill us with questions about our explanations.

The people who wrote the book (that Feynman discussed) should have asked themselves: do the readers of the book know what energy is? Do I know? What did I have to learn through life so that talking “energy” makes sense to me as an explanation now? What steps should I take the readers through so they get “energy” like I get “energy?” What concepts of physics help us build up to “energy?” What observations do those concepts require? How can I lay it all out logically for students?

And there we have lots of cognitive and logical ideas to help us explain well. Plenty there to practice with, on our own, with friends, or with coworkers.

But is there also some useful technical information that we can learn from good thinkers?

The Logic of Explanation

Logicians and philosophers have a lot to say about how to explain well. Explanation will be part of a good text on logic. But please make sure the text is more Aristotelian, and is not influenced, as much as possible, by the ideas of Plato, Hume, Popper, etc. (Assess “does it have real examples?,” “does it make sense, or is it abstruse?,” “is it about the real world, or is it lost in a world of symbols or ideas?,” “does it help me think better, or is it confusing?,” “would a reasonable person really use this stuff in everyday life?”.)

Studying argument analysis can help understand how to put together a good explanation, but argument is to show “that” and explanation is to show “why.”

As David Kelley says in The Art of Reasoning (p. 548, 3 ed.):

The theoretical relationship between arguments and explanations is complex and controversial. But it seems clear that there is at least a difference in emphasis. The primary goal of an argument is to show that some proposition is true, while the primary goal of an explanation is to show why it is true. In an argument, we reason forward from the premises to the conclusion; in an explanation we reason backwards from a fact to the cause or reason for that fact. Why does ice float in water? How do salmon find their way back to the streams they were spawned in? Why did the Industrial Revolution occur when it did? Why do human beings so often make war on each other? In all these cases, we know that a certain proposition is true: ice floats, salmon find their way, etc. This proposition is the explanandum (plural: explananda) a Latin word meaning “that which is to be explained.” What we want to know is the cause or the reason for the explanandum. We’re looking for a hypothesis that will make the explanandum intelligible to us by explaining why it is true. Ordinarily, the word “hypothesis” suggests something tentative, an idea that hasn’t been proven yet. But we’re going to use the term in a broader sense, to mean any explanatory idea, no matter how well confirmed. In this sense, for example, Newton’s law of gravitation is a hypothesis when it is used to explain the motion of physical objects.

With that said, Kelley provides some standards for assessing your own or others’ explanations (ibid, p. 548):

Every branch of knowledge has its own specific guidelines for evaluating the adequacy of explanations in that area, but there are also some general standards that apply across the board.

1. The inference from hypothesis to explanandum should have a high degree of logical strength.

2. The explanation should be complete: It should explain all significant aspects of the explanandum.

3. The explanation should be informative: The hypothesis should state the fundamental cause or reason for the explanandum.

Strength refers to the degree of certainty of a causal connection we have identified. We are trying to tell “why,” after all.

Strength estimates where in the possible-probable-certain continuum our knowledge is: how much evidence and proof we have for something.

“Certain” here does not refer to a feeling. It is not to be confused with “confidence,” a confusion I have seen a number of people make. And “probable” does not refer to probability theory and all that math stuff. The certainty continuum refers to how much evidence, cognitive context, and reasoning we have for a conclusion.

A “gold standard” of strength can be found in geometric proof, in the two-column proofs many of us studied in school.

“Certainty” is a logical, cognitive assessment that, in our context of knowledge, all evidence we need for a conclusion is known and true, and all essential steps in a reasoning process from the evidence of the senses to the conclusion have been performed. There is no doubt to an informed person. This is a high degree of strength for an explanation.

Atomic theory is certain, it is a strong explanation, now that it is evidenced and proven in all aspects of matter: the ideal gas laws, chemical reactions, electrical conduction, electromagnetism, the production of light, the nature of heat, etc.

“Probable” is a lower degree of strength. “Probable” is a logical, cognitive assessment that, in our context of knowledge, some but not all the evidence we need for a conclusion is known and true, and some but not all the essential steps in a reasoning process from the evidence of the senses to the conclusion have been performed. An informed person could have some doubt. Based on how much evidence and reasoning we have, an explanation will be somewhere on the scale of strength, from weakish to strongish.

Before atomic theory had been evidenced and proven in the study of heat or electrical conduction, but after it was evidenced and proven in the stuf of the gas laws and chemical reactions, it’d be assessed as “probable.” Atomic theory as an explanation of matter would be less strong.

“Possible” means something cannot be dismissed, it might be true, but we just don’t know. If all we have is evidence and reasoning that something is possible, an explantion is weak.

Atomic theory as Leucippus wrote about it would be assessed “possible.” As an explanation, it would be weak — maybe even, in context of what they knew at the time, the idea of atoms would have to be dismissed out of hand.

Same, at the time, with the idea that the earth goes around the sun: in context of what they knew, any explanation for heliocentrism would be very weak. (It took the work of Copernicus, Kepler, Galileo, and Newton to make the explanation strong and certain.)

The other concepts, “complete” and “informative,” should be fairly clear on their own: “complete,” of course, means to explain everything that needs to be explained, to account for all the essentials; “informative” means to tell why, to tell them something they didn’t already know.


My recommendation is to work on mastering the logical and cognitive principles in “Lessons From Feynman” first, then work on mastering the standards of explanation in “The Logic of Explanation.”

Study and practice some on your own. Ask others to assess your explanations, both written and verbal. Ask to assess other’s explanations, both written and verbal. Have business meetings where everyone works on explanations and on assessing them; they’ll help everyone understand their jobs better, understand their field better, communicate better and more efficiently, write better, speak better, and understand each other better.

If you’d like to dig into explanation more, the 4th edition of The Art of Reasoning is available on The Internet Archive. You could also buy a copy on Amazon, of course. In the 3rd edition, explanation is discussed in Chapter 18, pp. 547–582. (Other helpful chapters are Basic Argument Analysis, Advanced Argument Analysis, Inductive Generalizations, and Argument by Analogy.)

If you want more information on explanation, HWB Joseph discusses it in his logic text An Introduction to Logic in Chapter 23, “Of Explanation,” which is on pp. 502–527 of my edition. It was first published in 1918, so the language will be a bit different than that of today. Note also that some people I know have said that An Introduction to Logic is an advanced text on logic. It is also available on Amazon.

So go out and explain well. Remember, it starts with “why” — what gives a “why” for the audience, not us.


To really dig into how knowledge develops step by step, so we can explain well, we should study how some field of knowledge has developed step by step through history.

One thing to study in that regard is Part Two: Astronomy of the physics text Physics for the Inquiring Mind by Eric Rogers. Please ignore his mistaken philosophy of science, and focus only on the science and its historical development. He is, after all, a physicist, not a logician, epistemologist, philosopher of physics, or philosopher of science — Galileo and Newton, in contrast, were each part logician, epistemologist, and philosopher; they were more united in theory and practice.

You can, of course, skip some of the math and science in Part Two; just get enough detail, evidence, and reasoning to grasp the step-by-step reasoning process occurring.

Introductory Physics by Herbert Priestley goes through most all of basic physics and how it developed historically. Again, please study the historical development of science, but ignore what Priestley says about how science works. (Better to study the practice of Galileo and Newton to see how science really works, to get the method and logic of it.) And, again, you can skip some of the math and science; just get enough detail, evidence, and reasoning to grasp the step-by-step reasoning process occurring.

The Montessori Method might also help us see how knowledge develops from the least abstract to the more abstract.

Michael helps students, teachers, and business professionals in academic subjects and professional fields, and in critical thinking, logic, and root-cause analysis. He has a B.S. in Mathematics, a B.A. in Philosophy, and a Texas Teacher Certificate (Secondary Mathematics), and is a MovNat Certified Level 2 Fitness Trainer. He studies the history and philosophy of physics, tracing out its logical development step by step from ancient times to modern, and has studied some history and philosophy of chemistry and mathematics. He has decades of experience with students in public schools, homeschools, elite private schools; decades of experience studying philosophy and logic; and decades of successful experience teaching logic and thinking skills. He teaches and tutors physics, chemistry, math, SAT/ACT prep, sentence diagramming, philosophy, fitness, logic, critical thinking, root-cause analysis, and epistemology. You may find him at Gold AcademyTotal Human FitnessLinkedIn, and Outschool, and on YouTube @GoldAcademy and @TotalHumanFitness. He also posts nature videos @TrueToNature and nature pictures on Flickr.

(Image of Richard Feynman from https://commons.wikimedia.org/wiki/File:RichardFeynman-PaineMansionWoods1984_copyrightTamikoThiel_bw.jpg)

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