Imitation of Rigor

Mark Wilson’s “alternative history,” highly original, deeply informed, cogently argued, and elegantly written, aims to do more than chronicle the mistakes of the past. It presents a manifesto for the future, charting more profitable paths along which analytic philosophers might pursue their inquiries. Unlike some other reformers, Wilson does not take the rot to have set in fairly recently, with the ever more minute scrutiny of ever less significant questions. From his perspective, the trouble began early, with false steps made by the giants of logical empiricism, by philosophers of the stature of Carnap and Hempel and Quine. While these seminal philosophers were rightly inspired by insights of late nineteenth-century physicists, by Heinrich Hertz and Ernst Mach in particular, they misread the lessons offered by these eminent scientists. The result is a misguided picture of how to practice philosophy, although Wilson correctly acknowledges some particular insights achieved by the giants, despite the missteps of their methods.Hertz is at the heart of Wilson’s lucid and impressively researched history. In his classic Principles of Mechanics, Hertz diagnosed a recurrent problem, residing in the unclarity of some of the central concepts of Newtonian mechanics. Newton’s first law declares how “every body” will behave when it is not affected by any force. But how should we think of a “body”? Are bodies extended in space? If so, at which point (or points) are we to identify their velocity? If not, how are we supposed to derive an account of the motions of real bodies from a theory about dimensionless mass points?The Principles excavates several species of problems of this kind, affecting large parts of the physics the nineteenth century had erected on the Newtonian foundation. Wilson cites with approval Hertz’s diagnosis of the generic confusion: “We have accumulated around the terms ‘force’ and ‘electricity’ more relations than can be completely reconciled among themselves.” Hertz had recognized, he claims, an important feature of scientific practice. As theoretical proposals are developed to resolve concrete problems about different types of phenomena, the central concepts are stretched to generate recognizably successful strategies for finding solutions. In the process, those concepts “accumulate” an ever more inclusive set of “relations.” When someone as perceptive as Hertz stands back to survey the whole, the conflicts become evident. This “family” doesn’t get along.So far, Hertz has done brilliantly. Now, however, Wilson thinks, his discussion takes a wrong turn. Hertz suggests a solution to the generic problem. What is required is axiomatization. If the branch of physics in question—Newtonian mechanics, say, or Maxwellian electromagnetism—could be presented in rigorous axiomatic form, all the unclarities would be dissolved. Unsurprisingly, the pioneering logical positivists, brought up on the mathematical logic of Frege, Russell, and Hilbert, responded to this suggestion like warhorses to a bugle. “Axiomatization,” you can hear them saying excitedly to one another, “that’s something we now know how to do!” Thus philosophy of science (first) and analytic philosophy (soon after) absorbed what Wilson views as a bacillus, “theory T thinking.” The fetish for a particular style of conceptual clarification, based on finding axioms (in a first-order language with terms properly linked to experience) for a body of statements in a scientific—or nonscientific—domain took hold, surviving the midcentury transition to logical empiricism (where it was enshrined in the standard account of scientific theories), infected Quine’s influential approach to ontology, and flourishes today in the more liberated but dubious “a priori” conjectures of analytic metaphysicians, epistemologists, and metaethicists. “We do things rigorously these days,” they proudly declare, “Just like scientists, we axiomatize.”Like Carnap, Wilson has great admiration for Hertz’s classic treatise on mechanics. In his view, however, Carnap and his allies misidentified that work’s achievement. Hertz’s proposed solution was wrong—and (charitable speculation) perhaps if he had lived to see the forms in which axiomatization was later cast, he might have recognized the error. For axiomatic systems, though they might force their constructors to draw precise lines around blurry shapes, can’t respond to the predicament he diagnosed. That predicament arises from the need to reconcile claims that demonstrably work when a concept is applied to different kinds of problems. As Wilson explains, “Hertz himself is not to blame for these later abuses; his own diagnostic work was truly exemplary. It is merely that he suggested the wrong solution to the tensions that he had correctly noted” (179). Writing before the tools for formal axiomatization were at hand, Hertz can be excused for not seeing the mismatch between the difficulties he saw—the overabundance of conceptual connections—and the solution he proposed.The central chapters of Wilson’s book are devoted to showing how those kinds of conceptual difficulties can be addressed, at least in the particular form in which they arose for Hertz. My own formulation of the Hertzian predicament, derived from the passage about “accumulating relations,” is more abstract—and vaguer—than the versions arising for Newtonian mechanics. I have identified the generic problem as consisting in the existence of successful strategies for using a concept in different contexts. Wilson concentrates on the subgenus studied by Hertz: cases in which a Newtonian concept is successfully deployed, in apparently inconsistent ways, to resolve problems at different scales. As a friendly amendment to his specification, I offer my imprecise abstraction as characterizing the general problem, requiring the kind of precise specification Wilson provides if significant clusters of special cases (e.g., conceptual difficulties in classical mechanics) are to be fruitfully addressed.Troubles arise in the practice of mechanics because physicists need to address situations in which forces of different types interact to generate the dynamics of the bodies involved, and the routinely used specifications of those types of forces and those kinds of bodies clash with one another. The would-be axiomatizer seeks general notions capable of resolving the inconsistencies, while remaining rich enough to yield a solution. In practice, the ingenious physicist adjusts the specifications and the inferential connections so that “the parts no longer grind against one another inconsistently” (70). Wilson views the physicists’ successes as depending on “multiscalar tactics” and turns to applied mathematics and computer science for the general concepts underlying such tactics.We understand the workings of actual practices through articulating the multiscalar architectures that structure them. Models at different scales are linked by using feedback loops for connecting the scales, so that trial proposals for modeling are adjusted to one another. Wilson’s explanation of his central concept (multiscalar architecture) proceeds through detailed discussion of particular examples. Thus a physicist, concerned to understand the potential stresses within a rock begins by drawing from a general mathematical apparatus for representing stress, offering a trial model, then adjusting it in light of physical characterizations of the rock’s interior, refining further by taking into account of features at a finer grain. Techniques for averaging and approximating eventually bring the scales into harmony, enabling successful prediction of whether (for example) the rock will support a proposed building.The concluding chapters draw some morals for philosophy. Wilson begins by showing how, in everyday usage as in scientific discussion, causation figures in various guises. Some philosophers (he singles out Judea Pearl and James Woodward) have provided a “wonderfully detailed exploration” of some patterns of causal explanation (131). Practitioners devoted to analytic metaphysics sometimes complain of the inadequacy of this work, accusing it of failing to attend to the underlying causal processes. Wilson sees nothing but confusion in this charge. To be sure, there are types of causation (e.g., in the propagation of waves) where an appeal to causal processes is valuable (well studied in the tradition that runs from Hans Reichenbach to Wesley Salmon and Phil Dowe) but the general hankering after a “metaphysics of causation” is, he suggests, a blunder, born of “theory T thinking” together with a focus on misleading examples and an utter neglect both of science and of half a century’s work in the philosophy of science. Like many philosophers of science, Wilson seems to have heard the talks frequently given about the “metaphysics of causation” with the same pain generated when fingernails scratch a blackboard.Wilson is not opposed to metaphysics. Indeed, he laments the positivist efforts to ban metaphysics as, once again, drawing the wrong lesson from the great late nineteenth-century philosopher-scientists. The aim of metaphysics is not a grand overarching axiomatized theory (“grounding fundamental physics”) but the disclosure of places in our attempts to make sense of the world where concepts are overstretched. Hertz, the great diagnostician, pioneered a “small metaphysics,” and philosophers should emulate his efforts.This is a salutary challenge, one the priests of “high analytic philosophy” and their many acolytes should take seriously. During the last half century, philosophy of science has engaged deeply with the practices of the sciences. In consequence, many of the old tenets of logical empiricist philosophy of science have been refined or overthrown. The vast majority of analytic philosophers—devoted to metaphysics or epistemology or philosophy of mind or metaethics—don’t seem to have attended to the news. They write as if the unity of the sciences isn’t simply a “working hypothesis” but an item of scriptural dogma. They tacitly treat science (total science?) as a collection of universal laws gathered together in a tidy hierarchy of axiomatic systems. This not only limits their philosophical options but inspires them to undertake quixotic quests in fantasy land.Wilson’s admirable book should be required reading not only for the analytic faithful but for all those entering the novitiate, hoping one day to contribute something to analytic metaphysics, epistemology, philosophy of mind, or metaethics. It demonstrates, clearly and decisively, the limits of the logical empiricist assumptions entrenched early in the history of analytic philosophy—while also recognizing the achievements of some of the founders in their own detailed philosophical work. Wilson has diagnosed one of the maladies of much Anglophone philosophy in our day, and simultaneously enriched the “turn to practice” in the philosophy of science.Books, we are often told, shouldn’t be judged by their covers. This one is an exception. Wilson’s hijacking of the poster for the movie Imitation of Life advertises the wit and insight with which his monograph overflows. Perhaps philosophers will be inspired by the picture to forsake imitations and return to the real thing

Analytic philosophy · Contemporary philosophy · Epistemology · Imitation · Rigour · Philosophy · Philosophy, Science, and History · Psychology · Social Psychology