R. A. Fisher, Scientific Method, and the Tower of Babel, Pt. 1 February 2, 2013Posted by Will Thomas in Uncategorized.
Tags: Abraham Wald, David Howie, Harold Jeffreys, Harry Marks, Jerzy Neyman, Nancy Hall, R. A. Fisher, Stephen Jay Gould
For a paper Chris Donohue and I have been working on, I have been delving into the historiography on statistician and genetic theorist R. A. Fisher (1890-1962). The main thing I was trying to do was to make sense of the last third of Fisher’s touchstone book The Genetical Theory of Natural Selection (1930), which is a protracted eugenic explanation for why civilizations decline. When I first got onto this topic, I consulted Greg Radick about it, and he directed me to Stephen Jay Gould’s 1991 essay, “The Smoking Gun of Eugenics” (reprinted in Gould’s Dinosaur in a Haystack collection), in which Gould takes apart both Fisher’s civilizational theory as well as his 1950s-era arguments against claims that smoking leads to cancer.
If you’re interested in the specifics of Fisher’s arguments, do read Gould’s essay, or, better still, read the original. Suffice it here to say that Gould claims Fisher made bogus arguments on account of his commitment to eugenics (with a similar story for smoking). This is true, as far as it goes, but I wanted to find a “higher-order” explanation for Fisher’s civilizational theory, which would account for why he thought his arguments made sense. Fisher, after all, was a famous proponent of methodological rigor, and even prima facie his arguments about civilizational decline were, shall we say, less than rigorous.
If you’re interested in my take, you’ll have to wait until 2014 for the edited volume our essay will be in to come out (hooray for academic publishing; if you’re really interested, please do contact me for a draft copy). But the general approach I took was to delve into Fisher’s ideas about scientific methodology. Below the fold I take a meandering tour through these ideas, and the scattered historiography on them.
The main reason I wanted to do some research on Fisher was because of his manuals Statistical Methods for Research Workers (1925), and The Design of Experiments (1935). These are pertinent to my work on operations research and decision theory, as well as to my more recent work on agricultural expertise (Fisher wrote both books partially from his experiences helping design agricultural experiments at the Rothamsted Experimental Station, where he worked from 1919 to 1933). What is interesting is that neither of these works, nor his later Statistical Methods and Scientific Inference (1956), is a full treatise of scientific methodology.
All of these works were, essentially, devoted to inductive reasoning and hypothesis testing. For Fisher, the sine qua non of scientific knowledge was experience. The security of that knowledge could be ascertained through the statistical analysis of experimental tests where pertinent variables were controlled either physically or statistically. For a recent discussion of Fisher’s commitment to randomization and statistical control of experimental bias, see Nancy S. Hall, “R. A. Fisher and His Advocacy of Randomization,” Journal of the History of Biology 40 (2007): 295-325.
Of course, Fisher was aware that there was more to scientific practice than empiricism. For him, though, there had to be a definable distinction between speculation and experience, because mistaking mere speculation for scientific knowledge opened the door to dogmatism. On this point, I found Harry M. Marks, “Rigorous Uncertainty: Why RA Fisher is Important,” International Journal of Epidemiology 32 (2003): 932-937 helpful. The piece has some very interesting discussion of the ideological significance that Fisher attached to inductivism, particularly its importance to intellectual freedom—a concern that only grew more pronounced in the postwar era (Lysenko and all that).
Marks observes that similar issues were at the core of Fisher’s postwar methodological disputes with statistical theoreticians Jerzy Neyman (1894-1981) and Abraham Wald (1902-1950). Fisher made the ideological resonance he saw in this issue very explicit in his 1955 paper, “Statistical Methods and Scientific Induction,” Journal of the Royal Statistical Society B 17: 69-78, in which he linked his rivals’ theories to the technologized pragmatism of the Soviet Union and the United States, which privileged “speeding production, or saving money” rather than “drawing correct conclusions”.*
Backing up a bit: these postwar methodological disputes were basically extensions of Fisher’s lifelong campaign against “inverse probability,” or, as it is now generally known, Bayesian probability. Briefly: in Bayesian probability, an a priori probability distribution (say if there are three possible outcomes to an experiment, one might suppose that each has an equal probability of being the result) is modified following trials. For Fisher, whose position is often referred to as “frequentist”, any a priori distribution was an arbitrary imposition on an experimental interpretation, and could not therefore count as scientific knowledge—in trials, any valid conclusions had to follow purely from experience.
Now, this conflict is one of the most celebrated and contentious episodes in the history of statistics. In case Fisher’s position seems obviously correct from my brief description, here’s xkcd.com‘s fine take on the subject:
Unsurprisingly, there is a lot of scattered material on this issue, but your best one-stop-shop is probably David Howie’s Interpreting Probability (2002), which concentrates especially on Fisher’s 1930s-era disputes with Harold Jeffreys (1891-1989).
Now, despite the fact that Fisher was a champion of inductivism, he was also a great deductive statistician. For Fisher’s thoughts on deductive reasoning, Marks points us to Fisher’s 1932 lecture, “The Bearing of Genetics on Theories of Evolution,” in which Fisher extolled his mathematical accomplishments in The Genetical Theory of Natural Selection reconciling Darwin’s natural selection mechanism with Mendelian genetics.
In his lecture, Fisher offered a strikingly different portrait of scientific method from that found in his manuals. Invoking the Biblical legend of the Tower of Babel, he observed that a “common metaphor represents the labours of men of science as the construction of a gigantic edifice, upon the wings and annexes of which workers in different branches of natural knowledge are engaged. The various methods and techniques in which we have been trained correspond to the crafts of the different classes of artisans, the stone-cutters, masons, plasterers, sculptors, and painters, whose co-operation is needed to produce a finished and habitable building.”
Fisher went on to compare the disaster God inflicted at Babel to the fragmentation of scientific methodology, offering an unusually naturalistic take on how the division of language came to be:
We are not told exactly in what manner the confusion of tongues originated ; whether by a sudden and miraculous transmutation in the word-centre of each individual, he began forthwith and, all unconscious of the change, to express his ideas in a babbling jargon, meaningless to his fellows ; or whether, as the work progressed, groups of workers so concentrated their attention upon special parts of the building, and on the particular technical problems of their crafts, that they gradually came to use words unintelligible outside their own little circle ; or, still worse, to use the old words with meanings quite unknown to the workers on the floor above, until their old common language had been lost irrevocably.
Typically, Fisher cast himself as something of a hero in his lecture, bridging the “unnatural separation of mathematics from biology,” both in his work at Rothamsted, and in his work reconciling genetics with evolution. And, importantly, his accomplishment represented a reconciliation of mathematical deduction with inductive science:
Deductive and inductive reasoning … are the means by which alone we can ascertain whether or not a new slab of observational fact will fit into its place in our edifice; and the mathematical expression of such reasoning is the only effective cement which we possess, by which such new facts can be held fast as parts of a coherent structure.
Ultimately, though, Fisher’s ideas about the reassembly of the deductive and the inductive into a more unified methodology were never so clearly articulated as his ideas about statistical inference. In Pt. 2, we look at some scholars’ views of Fisher’s deductivism.
*For more on the relationship between “scientific” knowledge and the problem of limited testing opportunity from an anti-Fisherian perspective, see my post “Decision, Risk, and Values: The Philosophy of Churchman and Ackoff,” which is a brief excerpt from my book manuscript.