Monday, June 9, 2014

The explanatory reductio

“It ain’t what you don’t know that gets you into trouble. It’s what you know for sure that just ain’t so.”

                                                                                                                                     ~ Mark Twain

One simple way of identifying the defining characteristic of an explanation is to distinguish it from an argument. Whereas an argument provides reasons we should believe something, an explanation provides reasons why something we already believe, actually occurs.  In rhyme:
  • An argument says how we know. 
  • An explanation says why it is so.
This is an excellent general purpose way to think about the nature of explanation (and argument) and I recommend tattooing it somewhere special. 

But it isn't the whole story. To appreciate why, let's begin with Twain's lovely remark: Sometimes what we know just ain't so.  Of course, if you are accustomed to philosophical usage, you'll see that this is paradoxical: knowledge implies truth. So, in more quotidian terms, Twain is observing that we are often utterly convinced of things that turn out to be false.

I doubt any reader of this blog will need to be convinced of Twain's fundamental point, that passionate commitment to falsehoods can cause far greater harm than simple ignorance.  My point is that what we know that ain't so is also a nice way to  appreciate the fact that explanation has a larger role than simply accounting for the facts.

Consider an everyday example.  I get a check in the mail saying that I have just won 10 million dollars. Do I even bother to open it?  Nope.  I can partly defend this by appeal to probability and expected value: It is so fantastically unlikely that 10 million dollars would simply drop out of the sky that the time it would take to inquire is far more trouble than its worth. But the other, equally important way of accounting for it is explanatory in nature: Why the hell would anyone just give me 10 million dollars? If there is no plausible explanation, maybe that's because they didn't.

Now, what exactly am I doing when I put the matter this way?  Am I accepting it as actual fact that I won 10 million dollars and proceeding to explain said fact?  No, rather, I am engaging in what I will call an explanatory reductio ad absurdum.  

You are familiar with the standard reductio:  We accept a claim for the sake of argument, and show that it implies an absurdity.  In the explanatory reductio we accept something for the sake of explanation, and show that it rests on an absurd understanding of the world.

Here is one of my favorite New Yorker cartoons, which makes the point beautifully.

So our powers of explanation do not, as our initial definition suggests, exist simply to help us understand independently established facts. Rather, we often engage in explanation in order to determine whether we've got hold of the right ones. 

Some other examples:

Did you see the movie A Beautiful Mind?  There is a poignant moment in which John Nash, a (real life) brilliant mathematician and game-theoretician suffering from schizophrenia uses the power of pure reason to break the grip of his mental illness and convince himself that a young girl appearing to him over a long period of time is not real. 

Nash uses an explanatory reductio:  If she is real, why doesn't she get older?

Another.  I recently read Philip Roth's book American Pastoral.  It is predicated on a sensationally unlikely event: A teenage girl raised in an affluent New York family by two devoted and loving parents (allegedly) bombs a local post office, killing a local man, an (apparently) loco act of protest against the Vietnam War, and then (unquestionably) disappears. Almost the entire book is an act of excruciating soul searching in which the girl's father attempts to understand how a child he raised could have performed such an abominable act. There is just no explanation for it compatible with his understanding of the world. Consequently- he often confidently concludes, only to reverse himself a moment later- she simply could not have done it.

Or consider an example from science.  You are probably familiar with the Alvarez hypothesis (named after Walter Alvarez and his famous dad Luis) which claims that the massive extinction at the end of the Cretaceous period  (think dinosaurs) was caused by a massive asteroid. Although widely accepted today, it was initially met with scorn by the scientific community, especially by biologists who were deeply committed to the view that evolution necessarily occurs gradually. The gradualists employed an explanatory reductio: The very fact, Professors Alvarez, that you must appeal to Biblical scenarios like this one to explain this sudden massive extinction of the dinosaurs is a very good reason for thinking that no such extinction event ever occurred (i.e., that it is just an illusion created by an incomplete fossil record.)

The famous theoretical physicist Richard Feynman characterized the explanatory reductio about as elegantly as one can in this brief clip:


Ok, enough, now you are coming up with examples of your own. They're everywhere. So what is the subtler account of explanation that emerges here?

Try this: Explanation is fundamentally an attempt to improve our understanding of the world. Sometimes accepted facts will challenge our limited understanding and we are forced to develop better theories to account for them. Other times a better understanding of the world will challenge our 'facts', and we are forced to consider the possibility that what we know just ain't so. On those occasions, our understanding will be improved by explaining how we came to be convinced of a falsehood.  As I'll explain in a future post, a very large number of pivotal explanatory episodes in the history of science can be understood in this way, not as the explanation of accepted facts, but as the explanation of universal illusions.

G. Randolph Mayes
Department of Philosophy
Sacramento State


  1. Randy, your presentation is very clear. Is there is a camp of people out there who disagree with the points you are making?

    Let’s consider the clever, but crude idea of paradigm change that was presented by Thomas Kuhn in his book Structure of Scientific Revolutions. A paradigm is, among other things, a standard way of creating explanations, and a collection of “what is so.” Would you agree that the revolutionary change from the pre-Darwin paradigm to the post-Darwin paradigm was caused by scientists eventually realizing that what we supposedly knew within the old paradigm just ain’t so?

    1. Brad, absolutely. You've anticipated the sequel to this post. And, as to your question, I can't imagine any thoughtful person disagreeing with me on this :). My hope is that this is the sort of thing that might strike some readers as "Oh, yes, well that's obviously true isn't it, but I never quite noticed it before."

  2. Randy, Would I be saying the same thing if I described our reasoning process as a simple use of modus tollens? e.g.: If I've won ten million dollars, then someone is handing out vast sums of money to strangers. People don't hand out vast sums of money to strangers. Therefore I haven't won a million dollars. I'm not sure whether this is different reasoning or just a different description of the same reasoning.

  3. Em, a preference for modus tollens over modus ponens in this case would signal greater confidence in the claim that people do not give vast sums of money to strangers than the claim that you have won ten million dollars. I think explanatory reasoning kicks in when we are conflicted. We have the testimony of the senses (normally quite reliable) that a particular event is in fact occurring, and the wisdom of experience (also normally quite reliable) that it probably is not. To dramatize the situation, imagine that you are in WalMart and just as you get rung up the cashier says: Congratulations you are our 10 billionth customer and you have just won 10 million dollars! after which balloons are flying, sirens are going off, confetti is falling from from the ceiling and an NBC camera crew shows up out of nowhere. Now you are forced to say: How can I explain all this, if I have NOT in fact won 10 million dollars?

    In general, unlikely things are happening all of the time, and when experience informs us that this is the case, we rely on our explanatory abilities to determine whether to trust our current experience, or our reservoir of knowledge about how the world works. I think explanation may actually be a heuristic we use in lieu of Bayesian updating, however, and it often delivers the wrong answer. For example, if a very reliable blood test indicates that you have an extremely rare condition, the chances are still overwhelming that you do not. But this is something that can only be appreciated in probabilistic terms, not in explanatory terms. Our explanatory impulse will be to say: If I do not have this condition, then how am I to explain the results of this highly reliable test?