Theories of Explanation

As a desert dweller, I have faced down a mountain lion on three separate occasions, and I can attest that solving problems in daily life really is different from, say, solving differential equations.

But I should back up and explain what I mean.

In philosophy there are six formal theories of what it means to make an explanation, all based on a Newtonian outlook. But must all explanation really be in terms of mechanics? Could making that assumption actually be a hindrance to progress in such fields as AI, mind, big-picture physics, and biology?

In this post, I will first examine the six formal theories of explanation, and then I will introduce how biology has come up with an alternative that goes beyond mechanics.

In doing so, I begin by making two definitions. To “explain” means to tell why one event occurs and not another. And by being premised on a “Newtonian outlook,” I mean that a theory depends on describing one action “leading to” the next and the next as it happens in the Newtonian theory of motion (there are other theories of motion).

Accordingly, the six formal theories of explanation are as follows (garnered from Boyd, Gasper, and Trout, editors, [1991] The Philosophy of Science, a collection of papers which includes representative articles advocating each theory mentioned here).

A “causal explanation” is when an event is understood by tracing the history of one cause giving rise to the next and the next until the event in question is arrived at. In that way, the reason for an event happening is explained by supplying the list of causes which led to it. Again, my point here is not to discuss the pros and cons of causality but to point out that a causal explanation does fit the format of one event “leading to” another and another, as I suggested, above, characterizes all six theories. As for the efficaciousness of causal explanation, I will simply summarize Bertrand Russell’s objections as an example of that debate. Russell argued that there is nothing really in a differential equation which can be called a cause or an effect, and if we insist on finding one, it is difficult not to let error and bias enter into how the causes and effects are delineated. So a causal explanation can end up being unreliable.

Russell suggested that we are better off just using the equations to explain what happened and to predict how things will be at other times. That has come to be known as making a “mathematical explanation.” Yet even Russell eventually give up on mathematical explanation as impractical for addressing problems in daily life. Many daily life problems (why did John propose to Mary?) simply do not lend themselves to differential equations. And even if they did, most of us do not go around solving differential equations in our heads.

So a third theory is that in daily life we do not actually solve the equations but rather we just cite the law as being applicable. Called “deductive-nomological explanation” (“nomological” means pertaining to a law), it is to explain an event by saying, “Yeah, that occurred because of such-and-such a law” (without actually doing the math). And for much of the second half of the 20th Century, that was the dominant theory. But this theory, associated with Hempel, is now out of favor for the same reasons as the mathematical explanations. It has become recognized that to apply equations made for physics to situations outside of physics is not germane. It does not work in practice (even if at first blush it sounds as if it ought to work).

So it is important to elaborate what that means. It means that simply to cite an equation lacks the detail (about John and Mary) to “really explain.” And not being able to “really explain” means that just citing an equation is unable to tell why one event happens and not another. Even if we posit some kind of determinism wherein the molecules of our body, by following physical laws, are determining our daily-life decisions, that still is of no use in telling us why one event happens and not another. (Two possible outcomes are both following Newton’s laws, for instance, so that merely citing the law does not distinguish between them). Or in Mendelian genetics, the “laws” do not describe one event automatically leading to another but only tell us how, say, one in four offspring will have a certain trait. Again, it does not tell why in a specific case one event ended up one way and not another. (To say it lacks the “depth” to “really explain” are Gasper’s words).

So an obvious fourth theory of explanation is to make a “probabilistic explanation” where people are said to go through life judging the odds of events happening. But even if so, to simply give the odds is not the same as to explain why one event happens and not another. That approach has all the problems of citing laws except that now, when we talk about one event leading to another, we have to stipulate that the explanation only “might” happen. And in any case, there are many examples in science where it does make very specific predictions, not just give the odds of an event happening. So there must be more to knowledge and to explanation than just to guess at the odds.

For brevity, I will only mention the last two formal theories of explanation. They are pragmatism and explaining in terms of the unification of science (how a tenet of one science can be used in another science). But these theories, too, are usually just about one thing moving another thing, so that one action leads to another and another, either as described in a practical manner or by relying on equations about motion.

In order to use any of these theories, it turns out that the hard part is to show why the general statement applies to the specific situation at hand. Knowing about force and acceleration does not really tell us if the flowers will be pink or yellow. There is more to it (more depth) than can be deduced just from knowing about force and acceleration.

So how does biology make explanations differently, in order to have depth?

The way to go beyond explanations that only describe moving things from one place to another place is to include a role for arrangement—how things fit together—in the descriptions of that movement. And as I have been arguing in previous essays, the easiest and most succinct way to include how things fit together in descriptions of change is with structures and functions.

 To illustrate, consider the old Mediaeval problem of Universals versus particulars. Universals are basically generalizations about the particulars, and the controversy in philosophy was over which is more real. In comparison, a structure in biology is more like putting bricks together to make a castle. Instead of making generalizations about the bricks, the bricks are assembled into some different object. There is a fundamental difference in approach regarding what to do with the particulars (fit them together to make things versus generalize about their qualities).

And that difference is extended by how the castle also comes to have functions (shelter, defense, storage) because of how it fits in combination with still other things (rain, attackers, foodstuffs).

Then explanations can be made in terms of describing these new structural features and functions (of the castle) which do not even exist in the bricks all by themselves. Such explanations are not the same as the traditional approach of deducing the qualities of one particular brick by knowing a generalization about all of the bricks. And further, such explanations are not about describing one event “leading to” another and another since, instead, they are about telling “what gets made” and about what can happen because of the way that a situation has become arranged.

So the bottom line is that the explanations are made in terms of telling “how it works.”—how it functions—given how things are fitting together.

Instead of deducing from a generality, with structures and functions we tell how it works.

That is the way to explain why there is one outcome and not a different outcome. For instance, showing how the rain and wind cannot enter the castle explains how it provides a comfortable and sage place to be during a storm. And an aspect of telling “how it works” is to include “how it is put together,” so that a castle having rooms with walls and ceilings is an aspect of showing how the castle has the function of providing shelter. Form fits function. So, for example, getting wet can be explained by telling how a hole in the roof interferes with “how it works” regarding how a castle provides shelter.

The fitting together occurs both internally to make the structure (the castle), and also it includes what happens when various structures fit together (the castle and the rain) to make the functions (providing shelter). In other words, the fitting together makes something more complicated than what was started with.

Another way of saying it is that the explanation occurs in terms of describing the formation of complexity (the castle, not just the bricks). And that suggests why explaining with structures and functions is so good at dealing with complex scenarios, as occurs, for instance, in biology.

That also explains why it fails simply to cite a law or generality and expecting it to apply to the situation at hand. Descriptions of “how it works” cannot be deduced just from knowing a general statement about particulars because knowing a function requires knowing how it all fits together. There is more to a castle (more depth) than just describing the qualities of the bricks.

To deduce from a generality only finds you a trait that the particulars have in common (to have been inductively made into the generality). But to explain a specific individual instance—to tell why an event is one way and different from another way—you have to go beyond commonalities and tell the story of how it works.

That also shows how chemistry and biology do not simply “reduce” to physics. The properties of atoms are well-described by physics, but “how it works” once the atoms fit together cannot be automatically derived just from knowing the common properties of its constituent parts. There is a “depth” to chemistry and biology than cannot be fully explained with physics alone. (That also explains so-called emergence, but the point is different. Instead of saying that—abracadabra!–the whole is greater than the sum of its parts, the point here is that it is productive to explain in terms of “how it works,” which among other things also explains why the whole is greater than the sum of its parts)

In other words, to have functions (from how things fit together) is a characteristic of what it means in the first place to be complex. To have functions is a telltale sign of being non-simple rather than simple (assuming there is such a thing as being simple or unassembled). So it makes sense that a productive way of dealing with complexity is with structures and functions.

And that is what biology does when it describes the structure of a wing and how it works, or of DNA and how it functions. If we want to explain why there is a hole in your tooth, we do so by telling the story of tooth decay and how it works because of the structure of the teeth and mouth.

And telling “how it works” does indeed occur in the other sciences, such as telling how it works regarding gismos, atoms, planetary motion, or chemical reactions.

The argument against functions has historically been that functions are just concepts made by our minds, and so they are not really in nature, since what is actually real is only particles following laws (even though our brains might interpret the overall activity as appearing like things acting with purposes). Furthermore, the word “functions,” by being similar to the word “purposes,” can imply teleology or the belief that actions occur as per a goal or a design. But once we recognize that functions exist in how situations fit together, then we can consider how nature is capable of fitting together on its own, without minds needing to be present. So it is understandable that all of the sciences incorporate descriptions of “how it works.” into their studies because fitting together occurs throughout nature.

And once recognized, there is great utility in describing functions because we can manipulate how a situation is fitting together to improve or diminish the function. Instead of merely moving things around, we can move things around in a way that factors in “how it works.” For instance, we can brush our teeth once we understand how it works regarding tooth decay.

The apparent difference (between biology and physics) has to do with equations. But equations, too, can be seen as a shorthand way of showing how it works. They are a way of showing “how it works” when multiple changes are occurring together or in a pattern so that the equations show how the multiple changes are related (a relationship that exists because of how it works). And of course the equations are not used all by themselves but in conjunction with verbal descriptions of “how it works.”

And functions are also used in daily life (not just in science). If you are hiking in a mountainous desert and come across a mountain lion, you realize that you are in danger by knowing “how it works.” Maybe you also know that you should face down a lion, and perhaps raise your arms to appear bigger, but not to run away since that could elicit a chase instinct in the lion. You might know about that from a memory of being told how it works. But you do not know it from doing it 1000 times to find a pattern (as in artificial intelligence) or act as per being passively pushed into doing it by a law or by the immediately prior event.

And yes, I have faced down a mountain lion on three different occasions, and I can attest that it is not really about solving physics problems.

Understanding “how it works” is a key aspect to knowledge and to navigating life, and certainly it is a seventh manner of making explanations.

And that makes sense on a fundamental physical level because the world is made of energy, and energy can move, but also it can fit together to make arrangements of itself.

Form fits function is yet another way in which energy builds complexity because of its capacity to arrange itself.

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