Incommensurability and the Discontinuity of Evidence

Incommensurability and the Discontinuity of Evidence Jed Z. Buchwald California Institute of Technology George E. Smith Tufts University Incommensurability between successive scientiªc theories—the impossibility of empirical evidence dictating the choice between them—was Thomas Kuhn’s most controversial proposal. Toward defending it, he directed much effort over his last 30 years into formulating precise conditions under which two theories would be undeniably incommensurable with one another. His ªrst step, in the late 1960s, was to argue that incommensurability must result when two theories involve incompatible taxonomies. The problem he then struggled with, never obtaining a solution that he found entirely satisfactory, was how to ex- tend this initial line of thought to sciences like physics in which taxonomy is not so transparently dominant as it is, for example, in chemistry. This paper reconsiders incommensurability in the light of examples in which evidence historically did and did not carry over continuously from old laws and theories to new ones. The transition from ray to wave optics early in the nineteenth century, we argue, is especially informative in this regard. The evidence for the theory of polarization within ray optics did not carry over to wave optics, so that this transition can be regarded as a prototypical case of discontinuity of evidence, and hence of incommensurability in the way Kuhn wanted. Yet the evidence for classic geometric optics did carry over to wave optics, notwithstanding the fundamental conceptual readjustment that Fresnel’s wave theory required. In the late 1970s, Kuhn remarked in reference to his 1968 lecture “The Relations between the Historyand the Philosophyof Science,” In the almost nine years since its presentation many more philoso- phers of science have conceded the relevance of historyto their con - cerns. But, though the interest in historythat has resulted is wel - come, it has so far largelymissed the central philosophical point: Perspectives on Science 2001, vol. 9, no. 4 ©2002 byThe Massachusetts Institute of Technology 463 Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/106361401760375839 by guest on 30 September 2021 464 Incommensurabilityand the Discontinuityof Evidence the fundamental conceptual readjustment required of the historian to recap- ture the past or, conversely, of the past to develop toward the present. (Kuhn 1977, p. xiv) [italics added] The question that preoccupied him for 45 years, what do such conceptual readjustments tell us about science as a kind of knowledge?, forms a large part of Kuhn’s legacy. The book he was writing when he died in 1996—“the grandchild of Structure, since the child was still-born”—was intended to answer this question, together with its correlate, what do these readjustments involve and why do they occur? Kuhn, of course, was scarcelythe ªrst to be - come preoccupied with the conceptual readjustments that have occurred in science. The revolutions marked ªrst bythe special theoryof relativity and then bygeneral relativityand quantum mechanics were as central to philosophyof science during the ªrst half of the twentieth centuryas the extraordinarysuccess of Newtonian physicswas to philosophyof science during the nineteenth century. What separated Kuhn from those preceding him was his insistence that these revolutions marked radical disconti- nuities of the same sort as the transition from Aristotelian to modern physics. 1.0 Kuhn on Incommensurability Starting with Structure and continuing to his last unªnished book, four propositions earmarked Kuhn’s thought. First, scientiªc research is a highlyspecialized social practice modeled on a set of prior achievements that function as exemplars; learning how to engage in this practice is learning how to extrapolate, so to speak, from these exemplars. Second, scientiªc revolutions involve the replacement of one set of exemplars by another set, resulting in a distinctlynew practice. Third, scientiªc revolu - tions in this sense have occurred far more often in the historyof modern science than one might have thought from taking relativityand quantum mechanics as prototypical; indeed, revolutions in this sense lie behind the continual “speciation” of scientiªc disciplines into increasinglyspecialized sub-disciplines. Fourth, (now quoting) “the normal-scientiªc tradition that emerges from a scientiªc revolution is not onlyincompatible but of - ten actuallyincommensurable with that which has gone before” (Kuhn 1970, p. 103). Kuhn originallylatched onto the term ‘paradigm’ in con - junction with the ªrst of these four propositions, but he subsequently abandoned it because his expanded use of it ended up obscuring the root-idea that made it appropriate in the ªrst place. Still, in Kuhn’s mind this ªrst proposition remained the cornerstone. The other three derive from it. The fourth proposition, needless to say, is the one that has pro- Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/106361401760375839 by guest on 30 September 2021 Perspectives on Science 465 voked byfar the most controversy.Kuhn never abandoned it. Indeed, the announced goal of his unªnished book was to clarifyand defend it. Kuhn’s defense of incommensurabilityin Structure pivoted on his con- tention that Newton’s laws of motion cannot properlybe derived as limit - ing-case approximations of the laws of motion in relativistic mechanics. For “the physical referents of these Einsteinian concepts [of space, time, and mass] are byno means identical with those of the Newtonian concepts that bear the same name” (Kuhn 1970, p. 102). Kuhn subsequentlycon - cluded that the argument in Structure “was both uninformative and in a central respect misleading.”1 Its sweeping appeal to meaning-change failed to discriminate the speciªc, narrower kind of change in meaning that produces what he called in Structure “a displacement of the conceptual network through which scientists view the world.” The defense of incommensurabilityin Structure seems to us unfortunate in still a further way. It focused the issue too much on the transition from Newton to Ein- stein, a transition that is far too contentious to serve as a prototype of incommensurability. A central claim of the present paper is that the transition from rayto wave optics at the beginning of the eighteenth century is a much better prototype for purposes of clarifying the intricacies of incommensurability. Another shortcoming of Kuhn’s “meaning-change” defense of incommensurabilityin Structure was the failure to tie it to his claim about the role of exemplars in scientiªc practice. The approach he took to incom- mensurabilityfrom the late 1960s on alwayshad as its starting point the process of learning from examples—in particular, learning natural kind terms and the taxonomic distinctions theymark from instances. 2 Because natural kind terms are open-ended in their application, several comple- mentaryexamples or illustrative situations are required to assimilate them. Theyare acquired not individually,but as an interrelated group, for theyhave the signiªcance theydo onlyin relation to one another. The fact that different individuals have acquired them along different trajectories involving different speciªc examples normallydoes not interfere with communication. Different trajectories of acquisition, however, do affect communication when anomalous examples are encountered, and such anomalies can throw the entire set of distinctions into question. 1. This quotation is taken from the beginning of the third chapter of Kuhn’s unªnished book manuscript. 2. The development of Kuhn’s approach to incommensurabilityafter Structure is sum- marized in Buchwald and Smith (1997, p. 367–375). See also the various lectures and pa- pers now published in (Kuhn 2000). Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/106361401760375839 by guest on 30 September 2021 466 Incommensurabilityand the Discontinuityof Evidence Factors like these gave Kuhn reason to think that taxonomyprovides a wayof explicating and defending incommensurability.Two scientiªc sys - tems can be commensurate with one another—or, in the phrasing he often preferred, mutuallytranslatable—onlyif theyshare the same taxonomic structure. Scientiªc categories can be thought of as forming a taxonomic tree. Distinct branches emerge from the trunk, marking principal kinds. Each branch maydivide further, yieldingsub-kinds. Everykind, however, emerges either directlyfrom a single immediatelypreceding node on the tree or from the trunk. Because no kind descends from more than one im- mediate ancestor, there is no possibilityof partial overlap among kinds. This requirement on kinds, which is equivalent to requiring each category to be immediatelysubordinate to at most one ancestor, Kuhn concluded is crucial to taxonomic distinctions in science. Anyaddition to a tree of kinds must accordinglybe grafted onto its structure without violating its integrity: additions can be made, but multiple connections between exist- ing kinds are not permitted, nor can new kinds be added unless they emerge directlyfrom a preceding kind or from the trunk. Two taxonomies in science are then commensurable if either of two conditions is satisªed: (1) everykind in the one can be directlytranslated into a kind in the other, which means that the whole of one taxonomic structure is isomor- phic to some portion of the other; or (2) one structure can be directly grafted onto the other without otherwise disturbing

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