Wednesday, April 05, 2006

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) [1].

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."


[1] 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.

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At 4/07/2006 03:20:00 PM, Anonymous Robert Skipper said...

An old stand-by definition of "truth" in philosophy is that truth is correspondence to states of affairs that obtain. In other words, some statement S is true if and only if S corresponds to some state of affairs that obtains. Else, S is false. For example, the truth of the statement "Snow is white" is true if only if the state of affairs of snow's being white obtains.

Notice that the question of whether we can know that S is true is independent of whether S is true. In other words, some statement S is true or false independent of whether we believe that it is true or false. I think, from this, it follows that your archer analogy breaks down. The truth does exist independent of our pursuit of it because truth is not an epistemological notion, it's a metaphysical one. That is, truth doesn't exist only relative to the knower; it exists independently of the knower.

There is, of course, a problem about the limits of knowledge such that one wonders whether we can know that some statement is true. Skeptics argue that we can't know that "Snow is white" is true because we can't be certain of it, where certainty requires deductive proof. Some in philosophy have argued that certainty need not require deductive proof. In that case, it's possible to know "Snow is white" is true on some or other theory of knowledge. By the same token, it's possible to know that some hypothesis is true on some or other theory of knowledge, where a hypothesis is an empirical claim made about a model.

At 4/07/2006 09:03:00 PM, Blogger scott blumenthal said...

Species, or whatever we choose to call the biological division between organismal units, exist. How are those "trees, bushes, grasses, and crows" different if not by some biological division we happen to call "species?"

Morphological and behavioral variation within these units exist outside of our recognition. Not from some ideal form - simply variation. This variation indeed is the basis for descent with modification, which is not directional; only in hindsight does it seem so.

As Robert Skipper said, "truth doesn't exist only relative to the knower; it exists independently of the knower." Evolutionary biology is, then, the pursuit of the independent truth of life, not merely the satisfaction of own desire for classification.

We may never, or perhaps will never, approach full understanding of the indepedant truth, but science, at least, provides a key to attempt to at least orient ourselves toward it.

At 4/09/2006 04:20:00 PM, Blogger Allen MacNeill said...

Thanks for the comment, Robert, although I must continue to disagree. The real problem, IMO, is encapsulated in this sentence:

"...truth doesn't exist only relative to the knower; it exists independently of the knower."

I must humbly disagree. While I accept a priori the assumption that physical reality exists independently of a "knower" (i.e. an entity capable of perceiving the existence of said reality), to assert that truth exists independently of a knower is merely that; an assertion. It carries no metaphysical weight whatsoever, and is simply a reflection of the state of mind of the knower as perceived by that knower, who is, of course, capable of being deceived by her perceptions, her cognitive interpretation of those perceptions, and by the actions and statements of other "knowers".

To me, "truth" is a purely epistemological construct, based ultimately on inductive inference and having no necessary connection with physical reality beyond what we are capable of perceiving. This is, I believe, still separate from a purely solipsistic view, in which the a priori assumption is that physical reality is a pure construct of the "knower's" mind, bearing no relationship to actual reality whatsoever.

You skate close to this interpretation of "truth" in your last paragraph: " wonders whether we can know that some statement is true. Skeptics argue that we can't know that "Snow is white" is true because we can't be certain of it, where certainty requires deductive proof." I would go further: since the "truth" of any deduction is necessarily a function of the premises upon which such deduction is based, and since (as the foregoing implies) I believe that all such premises are either axiomatic (as in the assumption that physical reality exists independent of our knowledge of it) or ultimately derived by inductive inference (which is necessarily incapable of yielding certainty), I believe that the archer analogy still holds.

That is, I believe that physical reality exists without proof beyond my own perceptual and cognitive processes, and I believe (as the result of experience, i.e. induction) that induction itself is the only valid route to an understanding of said reality (excepting certain mathematical relationships such as exist in geometry, for example). Therefore, while I may hope that by increasing my precision in obtaining information about physical reality I am also becoming more accurate in my descriptions of said reality, there is in the end no way to certainty about the relationship between my perceived precision and my hoped-for concommitant accuracy.

Therefore, as a person coming from a field that is ultimately both based on and validated by induction (i.e. biology), I would have to disagree with your closing assertion: "'s possible to know that some hypothesis is true on some or other theory of knowledge, where a hypothesis is an empirical claim made about a model." [emphasis added] On the contrary, I would assert that all we can say is that some hypothesis and/or theory is merely likely (i.e. not "true"), such "likeliness" necessarily being entirely based on our confidence in our perceptual abilities, our ability to infer from such perceptions, and the statistical methods used to calculate such confidence.

In other words (as I tell my students every semester), science isn't about truth at all, it's about being relatively confident about our descriptions and explanations of what we have been able to perceive about reality up until now.

At 4/09/2006 05:04:00 PM, Blogger Allen MacNeill said...

Greetings, Scott:

Rather than report bits and pieces of your comment, I would like to respond to it as a whole:

Once again, what we call a "species" is really just a group of organisms that shares some (but not all) of the same genetic information in their individual genomes. The overlap between the actual genomes of individuals within what we refer to as a species can be (and often is) quite variable. In very diverse "species", this overlap can be surprisingly small, compared with the overlap that exists within "species" with little genetic diversity (such as cheetahs), and, of course, in asexually reproducing organisms in which virtually all the genetic diversity is attributable to either mutation or lateral gene transfer.

The underlying point here is that in nature it is almost impossible to find two organisms that have exactly the same genomes. Therefore, what actually exists is a continuum from very closely related to very distantly related organisms, with the term "species" being inserted at some relatively arbitrary point in that continuum.

That this continuum is essentially arbitrary is illustrated by the problem of prokaryotes (i.e. the most ubiquitous and numerous organisms on Earth). As Lynn Margulis and others have recently asserted, there is no non-arbitrary definition of "species" that can be applied to organisms that are simultaneously asexually reproducing and subject to relatively high levels of lateral gene transfer. To apply a term originally developed for multicellular sexually reproducing eukaryotes distorts reality to a degree that exceeds its usefulness for understanding the evolution of genomes in diverging (and converging) groups of organisms.

Furthermore, the quest for a "true" definition of "species" (as opposed to one that is merely useful for everyday taxonomy and systematics) is essentially an exercise in Platonic typology. As Darwin suggested (but did not boldly assert), all that really exists in nature is individual organisms with more or less similar (i.e. overlapping) genomes. The similarities between such genomes are related to the ability of sexually reproducing organisms to successfully reproduce, but as Darwin pointed out the degree of reproductive incompatibility between individuals within "species" are similar in both kind and degree to the reproductive incompatibility between species.

IMO, what is "real" (and therefore "true") in nature is that there are only individual organisms, more or less related to each other and more or less capable of interbreeding with each other. Sometimes we may be able to "map" such capabilities using various semantic definitions of "species," but as this description implies, "the map is not the territory."


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