Accuracy, Precision, Nominalism, and Occam's Razor
AUTHOR: Allen MacNeill
SOURCE: Original essay
COMMENTARY: That's up to you...
Robert Skipper has a new blog in which he discusses (among other things) the concept of simplicity in science (also called the principle of parsimony). In it he discusses the importance of "Occam's Razor," named for the English logician (and Franciscan monk) William of Ockham. Skipper then goes on to provisionally define "simplicity" in scientific explanations as "paucity of parameters," and defends this interpretation from several different perspectives, including empiricism, Baysian inference, computationalism, and that of individual selectionism a la Coyne, Barton, and Turelli (1997) .
He concludes that the application of Ockham's razor doesn't necessarily produce "truth," but is a necessary part of an investigative procedure that does:
[Evolutionary biologists] urge us to run with the simplest model among the relevant alternatives unless we're forced to abandon that model for a more complicated one. What does the forcing is empirical evidence. Indeed, none of the biologists I quoted above said anything about the fact that simplicity is truth-indicative....So, simplicity doesn't indicate the truth of some hypothesis or model or theory. Rather, it's a strategy that directs us toward the truth....At least we can say we've eliminated some fruitless paths of inquiry.
I have a problem with this analysis, specifically with the idea that science (properly applied, and including Occam's Razor) gets us closer and closer to "truth." The problem, as I see it, has to do with the idea that "truth" exists independently of our pursuit of it, in the same way that a target exists independently of an archer who is trying to hit it. From this viewpoint, science is to "truth" what practice is to the archer; it is that method by which we get closer to hitting some independently existing "truth."
Don't get me wrong: I'm not arguing for solipsism here. Yes, indeed, I believe (without proof, BTW) that nature exists independently of our ability to describe or analyze it...that is, I'm a naturalist through and through, at least as far as grounding my thinking in non-solipsistic metaphysics is concerned. However, I make a distinction between nature and our descriptions/analyses of it; science is the latter. In the same way, I believe that there is a fundamental distinction that must be made between what actually exists in nature and what science can describe/analyze about it. And I believe that this difference can be captured in understanding the difference between "accuracy" and "precision".
Consider the example of the archer and her target once again. The name for the phenomenon that she is honing via practice is "accuracy." Accuracy is the point for an archer: as an archer practices shooting, she hits closer and closer to the gold, and consequently we would say that her accuracy improves – her shooting is becoming more accurate through practice.
By contrast, our archer could become more precise: that is, her shots could become more tightly clustered, but not necessarily in the gold. As an archer myself, I find that my precision is already pretty good - my shots all hit pretty close to the same place. Hitting the target then involves compensating for whatever is causing my precision to veer from the target. That is, I am trying to "map" my actual precision onto some theoretical "accuracy."
As the foregoing description implies, accuracy is a teleological process, whereas precision need not be. A machine that doesn't aim at all can be very precise, missing a target in exactly the same way every time. Only a goal-oriented entity can be accurate, as aiming for a target is inherently teleological.
So, is science goal-directed (i.e. is it teleological)? Of course it is; however, is our "aim" a more accurate or a more precise description/analysis of nature (or both)? I believe that, in general, we are doing pretty well if we can manage precision. After all, most statistical tests can't distinguish between the two (Bayesian inference is an exception); that's what hypothesis-spinning and experimental design is all about. We try to design our investigations so that we get precise data that we can then apply to a description/analysis of nature that we believe is accurate.
But this all leads to a problem, one that I have alluded to before: the problem of Platonic idealism. To believe that accuracy is possible is to believe that ideal forms are "real" and that we can get closer and closer to describing/analyzing them. From this viewpoint, scientists who believe (like Robert Skipper apparently does) that our descriptions of nature are coming closer and closer to some ideal "truth" are therefore Platonic idealists.
As I pointed out in an earlier post to this list ("On the Origin of the Specious"), this problem is most acute in biological taxonomy. Believing that there really are such things as "species" is a form of Platonic idealism. That this is so is easily demonstrated: simply ask any taxonomist to explain what a "type specimen" is. S/he will tell you that this is the "ideal" example of a member of that species (usually the first one classified and stored in a collection somewhere) against which all new specimens of that species are checked to determine if they are members of the same species.
Ernst Mayr railed against "typological thinking," and yet biology (including evolutionary biology) is shot through with it. And where typology lurks, teleology is close behind. Is it any wonder that the vast majority of people (including many scientists) would agree with the statement that organisms reproduce "in order to ensure the survival of the species?" A more egregious misrepresentation of the adaptiveness of reproduction would be difficult to formulate, and yet most people would simply nod their heads in agreement with such a statement.
Why? Because most people (including most scientists) are, whether they realize it or not, "idealists" in the Platonic sense. From this viewpoint, organisms do what they do "in order to ensure the survival of" the ideal form of their "species," regardless of any benefit or cost to themselves as individuals. Individuals don't matter, in other words; the "target" is the "survival of the species."
But, as I have asserted before, "species" don't really exist. They are literally a figment of the human imagination...or rather, a by-product of the human tendency toward teleological idealism. Look outside: do you see any "species?" I see trees, bushes, grasses, a couple of crows...but nowhere are there any "species" in view. I can learn that the trees and bushes and grasses and crows that look very similar to each other can be thought of as members of particular "species," but that is quite literally a thought : I infer upon these individual things imaginary categories that I refer to as "trees," "bushes," "grasses," and "crows."
As I have stated before, Darwin's most subversive idea was that the variation between individual organisms (which provides the raw material for natural selection) is real, irreducible, and the basis for (to quote Wallace) "the tendency for variations to depart indefinitely from the original type." If the "original type" were "real," then variations from it wouldn't matter. Furthermore, if we think about "species" as being "real," then descent with modification becomes a kind of "blind archery" in which the "species" is "shooting" into the future toward becoming some other "species."
This way of thinking is entirely human, and entirely without empirical foundation. And, perhaps not accidentally, William of Ockham had a solution to this problem. His solution was to break fundamentally from Platonic idealism: to adopt a viewpoint about reality known as nominalism. To a nominalist, the names we invent for objects and processes that appear similar/the same are only names: they are not real. The only real things are individual objects and processes. True, there are similarities between them that we can recognize – indeed, we "re-cognize" them - we "re-think" them in our minds. Science is that process by which we identify and systematically analyze such patterns of similarity, which we codify into "scientific theories/laws." When we do so, we somewhat unintentionally reify those similarities of appearance/behavior as "natural laws/processes" and believe that we have come closer to somehow "hitting" the "truth."
If the history of science has shown us anything, however, it is that when we think we are closest to the "truth" we are furthest from reality. Lord Kelvin infamously proclaimed that 19th century physicists had discovered virtually everything there was to know about physical reality. He did so only a few years before Einstein swept away the foundations of 19th century physics (perhaps this is why, a century later, so many neo-Platonists still can't countenance Einstein and the new physics he spawned). The real joy (and, to some, the real terror) of science is that as far as we can tell, there is no end to the game, and the more precise our descriptions become, the more absolute "truth" seems to "softly and suddenly vanish away."
 Coyne, J. A., N. H. Barton, and M. Turelli (1997), “Perspective: A Critique of Sewall Wright’s Shifting Balance Theory of Evolution”, Evolution 51: 643-671.