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).

the formal theories

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 subjective and 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 gave 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 20^th 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?

firm fits function

The way to go beyond explanations that only describe moving things from one place to another place is to see a bigger picture of how a situation is fitting together. And as I have been arguing in previous essays, the easiest way to include how things fit together in the descriptions of change is with structures and functions. The structures are understood to be made as per how things are organized to make them (as opposed to being pure Platonic Forms), and they move as per their functions enable them to move (as opposed to moving from being pushed along from one event to the next) again with that type of movement being possible because of how situations fit together.

Biology has invented form fits function because it is a way of dealing with complex scenarios, as occur in biology.

 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, the generalizations or the particulars. 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).

The explanations are made in terms of describing these bigger pictures, the castle, not just the bricks. For instance, the problem with a hole in the roof letting in rain can be explained in terms of the function of the roof and in terms of how the structure of the roof (how it fits with the walls) supports that function.

The explanation goes beyond just describing one event leading to another.

And further, to deduce from a generality only finds you the trait that the particulars have in common. For example, if you made the generality that all the bricks are red, then you can deduce from that that a particular brick will be red. But if you talk about how you made a castle out of the bricks, and how the castle has a form and a function that mutually support one another, then you can expand the explanation to cover much more than you otherwise could.

So the more complex the subject matter, the better off we are using form fits function for an explanation.

This essay is the third in a series on Form Fits Function, beginning with Form Fits Function as a General Theory of Knowledge and also Form Fits Function in Evolution.