Razoring Ockham’s razor

by Massimo Pigliucci

Scientists, philosophers and skeptics alike are familiar with the idea of Ockham’s razor, an epistemological principle formulated in a number of ways by the English Franciscan friar and scholastic philosopher William of Ockham (1288-1348). Here is one version of it, from the pen of its originator:

Frustra fit per plura quod potest fieri per pauciora. [It is futile to do with more things that which can be done with fewer] (Summa Totius Logicae)

Philosophers often refer to this as the principle of economy, while scientists tend to call it parsimony. Skeptics invoke it every time they wish to dismiss out of hand claims of unusual phenomena (after all, to invoke the “unusual” is by definition unparsimonious, so there).

There is a problem with all of this, however, of which I was reminded recently while reading an old paper by my colleague Elliot Sober, one of the most prominent contemporary philosophers of biology. Sober’s article is provocatively entitled “Let’s razor Ockham’s razor” and it is available for download from his web site.

Let me begin by reassuring you that Sober didn’t throw the razor in the trash. However, he cut it down to size, so to speak. The obvious question to ask about Ockham’s razor is: why? On what basis are we justified to think that, as a matter of general practice, the simplest hypothesis is the most likely one to be true? Setting aside the surprisingly difficult task of operationally defining “simpler” in the context of scientific hypotheses (it can be done, but only in certain domains, and it ain’t straightforward), there doesn’t seem to be any particular logical or metaphysical reason to believe that the universe is a simple as it could be.

Indeed, we know it’s not. The history of science is replete with examples of simpler (“more elegant,” if you are aesthetically inclined) hypotheses that had to yield to more clumsy and complicated ones. The Keplerian idea of elliptical planetary orbits is demonstrably more complicated than the Copernican one of circular orbits (because it takes more parameters to define an ellipse than a circle), and yet, planets do in fact run around the gravitational center of the solar system in ellipses, not circles.

Lee Smolin (in his delightful The Trouble with Physics) gives us a good history of 20th century physics, replete with a veritable cemetery of hypotheses that people thought “must” have been right because they were so simple and beautiful, and yet turned out to be wrong because the data stubbornly contradicted them.

In Sober’s paper you will find a discussion of two uses of Ockham’s razor in biology, George Williams’ famous critique of group selection, and “cladistic” phylogenetic analyses. In the first case, Williams argued that individual- or gene-level selective explanations are preferable to group-selective explanations because they are more parsimonious. In the second case, modern systematists use parsimony to reconstruct the most likely phylogenetic relationships among species, assuming that a smaller number of independent evolutionary changes is more likely than a larger number.

Part of the problem is that we do have examples of both group selection (not many, but they are there), and of non-parsimonious evolutionary paths, which means that at best Ockham’s razor can be used as a first approximation heuristic, not as a sound principle of scientific inference.

And it gets worse before it gets better. Sober cites Aristotle, who chided Plato for hypostatizing The Good. You see, Plato was always running around asking what makes for a Good Musician, or a Good General. By using the word Good in all these inquiries, he came to believe that all these activities have something fundamental in common, that there is a general concept of Good that gets instantiated in being a good musician, general, etc. But that, of course, is nonsense on stilts, since what makes for a good musician has nothing whatsoever to do with what makes for a good general.

Analogously, suggests Sober, the various uses of Ockham’s razor have no metaphysical or logical universal principle in common — despite what many scientists, skeptics and even philosophers seem to think. Williams was correct, group selection is less likely than individual selection (though not impossible), and the cladists are correct too that parsimony is usually a good way to evaluate competitive phylogenetic hypotheses. But the two cases (and many others) do not share any universal property in common.

What’s going on, then? Sober’s solution is to invoke the famous Duhem thesis.** Pierre Duhem suggested in 1908 that, as Sober puts it: “it is wrong to think that hypothesis H makes predictions about observation O; it is the conjunction of H&A [where A is a set of auxiliary hypotheses] that issues in testable consequences.”

This means that, for instance, when astronomer Arthur Eddington “tested” Einstein’s General Theory of Relativity during a famous 1919 total eclipse of the Sun — by showing that the Sun’s gravitational mass was indeed deflecting starlight by exactly the amount predicted by Einstein — he was not, strictly speaking doing any such thing. Eddington was testing Einstein’s theory given a set of auxiliary hypotheses, a set that included independent estimates of the mass of the sun, the laws of optics that allowed the telescopes to work, the precision of measurement of stellar positions, and even the technical processing of the resulting photographs. Had Eddington failed to confirm the hypotheses this would not (necessarily) have spelled the death of Einstein’s theory (since confirmed in many other ways). The failure could have resulted from the failure of any of the auxiliary hypotheses instead.

This is both why there is no such thing as a “crucial” experiment in science (you always need to repeat them under a variety of conditions), and why naive Popperian falsificationism is wrong (you can never falsify a hypothesis directly, only the H&A complex can be falsified).

What does this have to do with Ockham’s razor? The Duhem thesis explains why Sober is right, I think, in maintaining that the razor works (when it does) given certain background assumptions that are bound to be discipline- and problem-specific. So, for instance, Williams’ reasoning about group selection isn’t correct because of some generic logical property of parsimony (as Williams himself apparently thought), but because — given the sorts of things that living organisms and populations are, how natural selection works, and a host of other biological details — it is indeed much more likely than not that individual and not group selective explanations will do the work in most specific instances. But that set of biological reasons is quite different from the set that cladists use in justifying their use of parsimony to reconstruct organismal phylogenies. And needless to say, neither of these two sets of auxiliary assumptions has anything to do with the instances of successful deployment of the razor by physicists, for example.

So, Ockham’s razor is a sharp but not universal tool, and needs to be wielded with the proper care due to the specific circumstances. For skeptics, this means that one cannot eliminate flying saucers a priori just because they are an explanation less likely to be the correct than, say, a meteor passing by (indeed, I go in some detail into precisely this sort of embarrassing armchair skepticism in Chapter 3 of Nonsense on Stilts). There is no shortcut for a serious investigation of the world, including the spelling out of our auxiliary, and often unexplored, hypotheses and assumptions.

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** Contra popular opinion even among philosophers, this is not the same as the Duhem-Quine thesis, which is a conflation of two separate but related theses, one advanced by Duhem (discussed here) and one — later on — by Quine (to be set aside for another discussion).