the incommensurability thesis: has it lost its bite

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Journal of Indian Council ofPhilosophical Research ISSN 0970-7794 J. Indian Counc. Philos. Res.DOI 10.1007/s40961-015-0007-9

The Incommensurability Thesis: Has It LostIts Bite?

Amitabha Gupta

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The Incommensurability Thesis: Has It Lost Its Bite?

Amitabha Gupta1

# ICPR 2015

Abstract Incommensurability constitutes the focal point of Kuhn’s departure from theprevailing traditions in Philosophy of Science. The paper traces the mathematical originof the concept of “incommensurability” and philosophical environment that constrainedthe introduction of the idea in the literature. It then discusses the stages through whichthe concept of “incommensurability” evolved in Kuhn’s thought. The final account of“incommensurability,” viz., Kinds Theory of Incommensurability or TaxonomicIncommensurability, is also expounded, and some associated philosophical problemsare discussed. We analyze two case studies, provide textual and historical evidence, andcite the work of scholars supporting the conceptual continuity across the revolutionarydivide in both the case studies. Kuhn acknowledges the rigidity of his earlier positionand softens his stand on incommensurability in his last formulation of the thesis,justifying the title of the paper that Kuhn’s thesis lost its bite. At the end of the paper,we discuss some of the philosophical problems arising out of it and make certaincritical remarks on the final account.

Keywords Incommensurability.Kuhn’s“AristotleExperience” .Kuhn’s linguistic turn .

Untranslatability andmeaning change . Local incommensurability . Scientific realism

Introduction

Incommensurability constitutes the focal point of Kuhn’s departure from the prevailingtraditions in Philosophy of Science. It represents Kuhn’s attack on the idea of cumu-lative scientific progress and is indicative of radical breaks as revealed in the historicalaccount of the evolution of science. It is an assault on the common idea that earliertheories are contained in their successors in terms of reduction relation, implying thatsome of the basic theoretical concepts change meaning. This shows that comparison of

J. Indian Counc. Philos. Res.DOI 10.1007/s40961-015-0007-9

* Amitabha [email protected]

1 Logic and Philosophy Science, Indian Institute of Technology Bombay, Powai, Mumbai,400076 Maharashtra State, India

Author's personal copy

theories is dependent on holistic elements in the theory choice situations guided byjudgment and epistemic values rather than by simple-minded point-by-point compar-ison of the single predicates of the theories involved or use of algorithmic purelyrational procedures governing theory choice. The collective impact of these ideas ofKuhn represented a contrasting image of science which amounted to distancing itselffrom scientific realism by highlighting the subject-sided constitutive reality constrainedby accepted “paradigm” of the scientific community.

I

Since 1962, Kuhn’s provocative image of science roused much misunderstandings andinvited mistaken attribution of views. Of course, Kuhn provided clarifications to some.However, as Paul Hoyningen-Huene says in Kuhn’s obituary

“in its basic conception, his position remained unchanged although he came torealize that the concept of incommensurability needed much more work than hehad anticipated. More specifically, it became clear that within the framework ofthe current theories of meaning, incommensurability could not be articulated. Inhis later years, Kuhn thus concentrated more and more on a theory of meaning,especially for empirical kind terms which allowed for the sort of conceptualchange and notion of incommensurability he had in mind.”1

The paper is divided into three sections. After the introductory section, we havesection “I” in two parts: In “Kuhn’s Encounter with the Idea of “Incommensurability,”we trace the mathematical origin of the concept of “incommensurability” and philo-sophical environment that constrained the introduction of the idea in the literature. In“The Stages of the Evolution of the Concept of “Incommensurability” in Kuhn’sWork,” we identify the four stages through which the concept of “incommensurability”evolved in Kuhn’s thought and discuss the final account of “incommensurability”, viz.,Kinds Theory of Incommensurability or Taxonomic Incommensurability. Section “II”takes up two case studies: one on the concept of “mass”—Newtonian andRelativistic—and the other on the phlogiston-oxygen controversy. We try to providetextual and historical evidence in the two case studies and cite the work of scholarssupporting the conceptual continuity in both the case studies across the revolutionarydivide, repudiating the lack of communication across them as claimed by Kuhn. Wealso try to show that Kuhn acknowledges the rigidity of his earlier position and softenshis stand on incommensurability in the last formulation. In section “III”, we makecertain critical remarks on Kuhn’s Kinds Theory of Incommensurability or TaxonomicIncommensurability and some of the philosophical problems it gives rise to.

Keeping the final formulation of the incommensurability thesis (IT) in Kuhn’s workin mind, the main thrust of the paper is that incommensurability of concepts asirreconcilable and immune to rational resolution of revolutions appears to be muchless problematic than it has often been taken to be. An analysis based of two casestudies show that it is possible to revert to full communication across the revolutionary

1 Erkenntnis 45: v–viii, 1997.

J. Indian Counc. Philos. Res.


divide and that rival claimants can appeal to a shared body of evidence, experimental orotherwise, justifying the title of the paper that Kuhn’s IT has lost its bite.

Kuhn’s Encounter with the Idea of “Incommensurability”

Kuhn in his autobiographical interview in 1999 (published in The Road SinceStructure, 2000 (Kuhn 1991a)) reports that he took the idea of “incommensurability”from mathematics. In mathematics, “incommensurability” means that there is nocommon measure (in=no+com=together/common+mensura=measure), and for math-ematicians, incommensurable magnitudes have no common integer divisor except thenumber 1.

Kuhn carried over this idea and extended it in the discussion of the problemof rational choice between alternative scientific theories and scientific progress.Kuhn made a metaphorical use of the term “incommensurability” in his TheStructure of Scientific Revolutions (SSR 1962) and initially developed his thesisof “incommensurability” substituting it to mean “no common language” for “nocommon measure.”

The prevailing philosophical climate of the late 1950s and early 1060s during whichincommensurability thesis (IT) emerged overlapped with the decline of Vienna CircleLogical Positivism, the influence of the later Wittgenstein, Quine’s attack on analytic-synthetic distinction, the rise of the discipline of History of Science, its sway overphilosophy of science, and the influence of Gestalt psychology on the philosophy ofperception.

Thomas S. Kuhn in his SSR (1962) introduced the notion of “paradigm shift” whilereferring to radical theory changes in his detailed historical analysis of Aristotelian toGalilean and Ptolemaic to Copernican. In addition to this, his other historical studiesinvolving the eighteenth century Matter Theory, early history of Thermodynamics,Priestley (Phlogiston Theory) to Lavoisier (Oxygen Theory), and Black BodyRadiation had several important philosophical implications.

Some of the issues raised by Kuhn that stirred the philosophical communityof his time are the following: that scientists in rival paradigm perceive theworld/phenomena differently: teleological vs. mechanical, methodological prob-lems of employing diverse standards of evaluation of theories and henceabsence of common standards of theory appraisal: qualitative vs. quantitativeand semantic or meaning variance: vocabulary employed by the scientistschanges meaning in the transition from one paradigm to another, rejecting theLogical Positivistic idea of an independently meaningful, theory-neutral obser-vation language, and supplanting it by a contextual theory of meaning claimingthat the meaning of the terms employed by scientific theories depends on thetheoretical context in which the vocabulary is employed and is subject tovariation with the theory in which they occur. Thus, IT provided characteristicfeatures of the New Movement in Philosophy of Science (the post-positivist orhistorical Philosophy of Science) that began to emerge in the late 1050s andearly 1960s.

While Kuhn espoused the notion of incommensurability largely involvingnon-semantic factors (such as perception, absence of common standards oftheory appraisal), Paul K. Feyerabend, the other main advocate of the



incommensurability thesis, always restricted his use of the notion to the seman-tical sphere. Feyerabend in his “Explanation, Reduction and Empiricism” (1962)2 developed his notion of incommensurability more than a decade earlier, drewdirectly from Duhem, who had introduced a notion of incommensurability in1906. For Feyerabend, incommensurability resulted from the absence of deduc-tive logical relation and in failure of “theory reduction.” Incommensurabilityconsisted in semantic variance of terms occurring in the competing theories.This, according to Feyerabend, rules out the possibility of any direct compar-ison of the content of the theories. The views of Feyerabend will not be themain focus of the paper

Subsequent literature on IT tends to be framed in terms of a whole range ofinterpretation of what “incommensurability”meant as applied to the problem of rationalchoice among competing scientific theories couched in such terms as

& Unintelligibility of alternative conceptual schemes,& Incomparability of the contents of scientific theories, i.e., incommensurability=

incomparability,& The discontinuity of reference of theoretical terms and, in general, variation in the

meaning of scientific terms,& Translation failure between the vocabulary of theories,& Absence of common objective standards of theory appraisal.

These alternative interpretations as to what “incommensurability” means whenapplied to the problem of choice between competing scientific theories have given riseto the questions as to

& Whether there indeed exists a “common measure,” construing “incommensurabil-ity” to be a relation that obtains in its own right while choosing between alternativetheories or

& Whether the various factors mentioned above are manifestations/aspects/compo-nents/constitutive parts/sources of incommensurability,

& Are there alternative forms of incommensurability?

Considerations of these questions led Kuhn to modify, revise, and clarify his notionof incommensurability.

The Stages of the Evolution of the Concept of “Incommensurability” in Kuhn’sWork

Kuhn developed his notion of incommensurability primarily under the influence ofFleck, Polanyi, and Köhler (Oberheim 2005) emphasizing the non-cumulative nature inthe revolutionary change in scientific knowledge. The idea is that in the course offundamental changes in scientific theories, leading to changes in meanings of the keyconcepts, it may not be possible to directly compare the contents of one scientific

2 In Feigl and Maxwell (1962).



theory with the contents of an alternative. Such revolutionary changes may result in anew conception of the nature of reality.

The Four Phases of Evolution of the Concept

Kuhn modified, revised, and clarified his notion of incommensurability3 such that thenotion underwent four major transformations, which exhibit considerable disparitybetween his original and popular articulation of the notion and the notion he embracedlast, intervened by two intermediate phases.

The evolution of Kuhn’s central thesis of incommensurability may be divided intothe following four phases keeping a more nuanced discussion of the concept ofincommensurability in mind:

First Phase—Observational—Kuhn’s “Aristotle Experience”

The notion of incommensurability was not as such clearly present in Kuhn’s earliestwork nor in The Copernican Revolution (Kuhn 1957), although in the latter case, hintsof the idea are scattered throughout the book as Kuhn sought constantly to contrastways of thinking before and after Copernicus. By the late 1950s, especially in his 1959paper entitled “Energy Conservation as an Example of Simultaneous Discovery,” Kuhnbegan to articulate a notion of “incommensurability” in terms of fundamental, holisticincompatibility between conceptual schemes:

“…to historian acquainted with the concept of energy conservation, the pioneersdo not all communicate the same thing. To each other, at the same time, theyoften communicate nothing at all.” (Kuhn 1977a)

Kuhn claimed to have relied too much on his own phenomenal experience as ahistorian attempting to understand Aristotle’s worldview. At this early stage, as aninstructor at Harvard, Kuhn prepared one of the “case studies” on mechanics fromAristotle to Galileo, leading later to his detailed work on the Copernican revolution,which became the subject of his first book. Kuhn realized that a careful study of theAristotle’s ancient texts on motion did make sense: Aristotle had not been writing badNewtonian physics but good Greek philosophy. Within his system and purposes,Aristotle was apt and reasonable. The sympathetic reading of texts, the search forapparent absurdities as clues to interpretation and tests for understanding, becameKuhn’s historical and pedagogical method. This sudden recognition, what Kuhn calledhis “Aristotle experience,” the completely holistic gestalt switch, the passing from oneframe of mind or world picture to another, marked in Structure the origin of a newparadigm based on his idea of theory-dependent observation.

However, incommensurable paradigms present scientists not only with differ-ent “visual gestalts” of the same world, but have, as some claimed, certain

3 Buchwald and Smith (1997), Buchwald (1992), Heilbron (1998), Sankey (1993), Paul Hoyningen-Huene’saccount of the development of Kuhn’s incommensurability thesis from the 1970s to the early 1980s inReconstructing Scientific Revolutions: Thomas S. Kuhn’s Philosophy of Science. University of Chicago Press,Chicago, 1993 and Chen (1997).



philosophical implications as can be derived from statements made by Kuhn:(a) “although the world does not change with the change of paradigm thescientist afterward …works and lives in a different world” 4 implying thatKuhn was espousing a much stronger thesis leading to the metaphysical viewof “non-realism” discarding the existence of a mind-independent reality, (b) aphilosophically dubious theory of reference, (c) Kuhn’s paradigm shiftamounting to a “conversion experience”5 signifying, as many indicted him of,“irrationalism”, and (d) others concluded that Kuhn’s thesis of incomparabilitybetween paradigms implies relativism, claiming that relativism is a thesis aboutreference (Scheffler 1967).

Many saw the problematic implications of Kuhn’s analysis in scientificpractices, e.g., he needed to explain how science is empirical and objectiveand what difference observations make.6 Some argued that Kuhn’s characteri-zation of radical shifts in scientific theorizing is better regarded less as anargument for incommensurability than as his attempt to analyze and to explainwhat lies behind the discontinuity in ways of thinking before and after majorconceptual readjustments that he had observed in the history of science.

Soon after the publication of SSR, Kuhn realized that the gestalt switchmetaphor would amount to committing a category mistake since he had appliedit to a community whereas the notion rightly applies to an individual. Basedupon this understanding, Kuhn notes that the metaphor of gestalt switch is notonly inappropriate but damaging in describing the development of science(Kuhn 1989a). Consequently, Kuhn backed away from the gestalt switch met-aphor abandoning the perceptual observational interpretation of the thesis.

The other difficulty Kuhn faced was with the “multiple definitions” of in theconcept of “paradigm.” Margaret Masterman (1970) identified 21 possiblemeanings. The main tenets were clear: from the concept of canonical orexemplary problems and solutions (the word “exemplars” for the exemplaryproblem solutions) to “disciplinary matrix” for the shared commitments of thecommunity—the scientists learn to practice their discipline through exemplars,and that in the process, they assimilate a way of thinking that forms the core ofa disciplinary matrix. Kuhn himself clarifies his preference for the meaning of“paradigm”:

“That more global use of the term is the only one most readers of the book haverecognized, and the inevitable result has been confusion: many of the things theresaid about paradigms apply only to the original sense of the term. Though bothsenses seem to me important, they do need to be distinguished, and the word“paradigm” is appropriate only to the first.” (Kuhn 1977b)

4 Ibid. p. 121.5 Ibid. p. 151.6 This is what Mary Hesse told Kuhn as he reported in his autobiographical discussion published in The RoadSince Structure (2000) shortly after writing his The Structure of Scientific Revolutions, which he agreed he hadnot previously seen it that way.



Second Phase—Kuhn’s Linguistic Turn—The Thesis of Untranslatability and MeaningChange

It began with Logic of Discovery or Psychology of Research (1970).7 In this phase,Kuhn started using the metaphor of alien language to develop his notion of incom-mensurability. In a paper that belongs this phase, Kuhn writes:

“Concerned to reconstruct past ideas, historians must approach the gener-ation that held them as the anthropologist approaches an alien culture.They must, that is, be prepared at the start to find that the natives speak adifferent language and map experience into different categories from thosethey themselves bring from home. And they must take as their object thediscovery of those categories and the assimilation of the correspondinglanguage.” (Kuhn 1984)

Kuhn’s linguistic turn was a shift of focus and not an abandonment of thestruggle to construct a viable perceptual theory. Kuhn, however, maintains thatduring scientific revolutions, scientists experience translation difficulties whenthey discuss concepts from a different paradigm, as if they were dealing with aforeign language. Incommensurability thus is confined to meaning change ofconcepts due to the lack of common semantic content resulting in a form ofuntranslatability. By espousing the absence of any neutral observational lan-guage, denying the role of crucial observation and experiment for falsifying atheory, and assimilating Quinean indeterminacy of translation, Kuhn claims thatthere is no objective basis and logic and no neutral algorithm or decisionprocedure for theory choice that can adjudicate between theories.

In this, Kuhn had to face many critics (Popper 1970, 1976; Shapere 1964, 1966;Achinstein 1968; Davidson 1973–4; Kordig 1971): most notably, Popper, who accusedKuhn for irrationalism, and Dudley Shapere (1966) and others complained that Kuhnoffered no clear analysis of meaning to explain meaning change.

There was also talk of the “the sociological turn” in the history and philosophy ofscience, “emphasized and developed by people who often called themselves‘Kuhnians’.” Kuhn reacted by saying: “I think their viewpoint damagingly mistaken,have been pained to be associated with it, and have for years attributed that associationto misunderstanding.”8

Towards the end of his career, Kuhn became particularly uncomfortable withhis apparent links with the so-called “strong programme” in the sociology ofscience, with its combination of sociological allusions and methodologicalrelativism. About this movement, Kuhn remarked: “I am among those whohave found the claims of the strong program absurd, an example of decon-struction gone mad.” 9

7 In Lakatos and Musgrave (1970).8 Cited in Matthews (2000).9 Kuhn (1992). Also, see Kuhn “Discussion” (1997), T. S. Kuhn, foreword to Hoyningen-Huene,Reconstructing Scientific Revolutions, p. xi (quotation); and Hoyningen-Huene, Reconstructing ScientificRevolutions, pp. 240, 254, Keith (1986), Nola (1990), and Bloor (1991).



Third Phase—Local Incommensurability, Methodological, and Conceptual Disparity

In this phase of Kuhn chooses to narrow the scope affected by revolutions. In the early1980s, he introduced a notion of “local incommensurability,” claiming that during ascientific revolution,

“…most of the terms common to the two theories function the same way in both;their translation is simply homophonic. Only for a small subgroup of (usuallyinter-defined) terms and for sentences containing them do problems of translat-ability arise.” (Kuhn 1983a)

Incommensurability thus becomes untranslatability caused by the meaning changeof a small group of terms. With this revision, Kuhn hopes that his thesis no longerimplies incomparability of rival paradigms, because there always exist unchangedconcepts between rival paradigms during revolutions.

Kuhn repeatedly claims that these charges of incomparability and relativism repre-sent misunderstandings of his thesis, which in effect allows rational comparisons ofsuccessive theories or paradigms and does not imply relativism.10

Kuhn continued to believe that an understanding of how the scientist’s experience ofthe world changes in a revolution needs to be figured into the account of incommen-surability. He states:

“though the world does not change with the change of paradigm, the scientistafterwards works in a different world…I am convinced that we must make senseof statements that at least resemble these”.11

Kuhn’s “Commensurability, Comparability, and Communicability” sums up histhinking in this phase by making three claims. Theory change (i) exhibits localcommensurability (i.e., meaning and reference of most terms and many truth-valuesof sentences in the competing theories remain invariant leading to the possibility oftheory comparison, but opening up the question of what constitutes this invariance andwhether this would lead to making a tacit assumption of observationally neutral termsor neutral observation language between two theories being compared), (ii) demon-strates local incommensurability (i.e., some key theoretical terms are immune totranslation in the rival scientific theory, although it is common phenomena that archaictheories and alien languages are rendered into modern language), and (iii) stresses theneed for making a distinction between ideal translation and real translation orinterpretation.

Distinction Between “Translation” and “Interpretation” At the heart of Kuhn’spaper “Commensurability, Comparability, Communicability” (Kuhn 1983c) is a dis-tinction between translation and interpretation.

Kuhn replaces the notion of ideal translation (i.e., the concept of translationof current analytic philosophers which assumes that most terms in a scientific

10 See Kuhn (1983b, 1989b, 1991b).11 Kuhn, T.S. Structure, ibid, p. 121.



theory retain their meanings through theory change) presupposed in standardtheories of meaning, by a notion of “real translation” which actually goes onbetween languages both natural and scientific and which he calls interpretation.

Translation of a passage of an alien tongue occurs when one “tells the samestory” in sentences of the home language. In constructing the translation, thehome language remains unmodified: its stock of expressions is unaltered, andthe semantic features of old expressions (in particular the ways in which thereferents of those expressions are determined) persist unchanged. Kuhn suggeststhat translation does not alter “the way in which … referents … are deter-mined.” By contrast, in interpretation, one gains access to the content ofstatements in the alien language by extending the resources of the homelanguage, so that parts of the alien discourse are accommodated within thehome language. We can comprehend the meaning of an alien term through aprocess of interpretation, by directly identifying its referents in its linguisticcontext without referring to our native language.

Kuhn argues that the languages used by the rival protagonists in revolution-ary debates are not intertranslatable, even though the user of one language caninterpret the remarks made by the rival. He attempts to show that the proposalsthat have been offered for constructing translation manuals between suchlanguages as the language of phlogistic chemistry and the language ofLavoisier’s chemistry do not yield translations. Although Lavoisier can interpretPriestley, he cannot translate Priestley’s claims into his own idiom. Kuhn claimsthat those who have tried to show how the translation might proceed have beenguilty of confusing interpretation with translation.

However, the main issue in this phase is the standards, values, and criteria ofevaluation revealing the conceptual disparity engendered by the successive or compet-ing theories. Kuhn’s list of values for appraising theories, sometimes designated as“The Big Five,” include “accuracy,” “consistency,” “broad scope”/“breadth of applica-bility,” “simplicity,” and “fruitfulness” (Kuhn 1977c).

Final phase—Kuhn’s Kinds Theory of Incommensurability or TaxonomicIncommensurability

In the chapter titled “Afterwords” (Kuhn 1993a), Kuhn states that his efforts tounderstand and refine the incommensurability thesis has been his primary and increas-ingly obsessive concern for 30 years.

By further limiting the scope of the incommensurability thesis in Road SinceStructure (1991), Kuhn had already focused his attention on what may be called thescientific “lexicon.”

“[b]y now, however, the language metaphor seems to me far too inclusive.To the extent that I’m concerned with language and with meanings at all,. . . it is with the meanings of a restricted class of terms. Roughlyspeaking, they are taxonomic terms or kind terms, a widespread categorythat includes natural kinds, artificial kinds, social kinds, and probablyothers” (Kuhn 1991c)



In this phase, Kuhn presents the non-cumulative nature of scientific revolu-tions in terms of his characterization of radical paradigm shifts as changes inthe taxonomic structure which scientific theories impose upon the world. 12

Incommensurability arises because it is impossible to transfer the natural cate-gories employed within one taxonomic structure into the categorial system ofanother such structure.

For example, the term “planet” in the Aristotelian lexicon cannot be trans-lated by the term “planet” in the Copernican-Galilean structure because theyrefer to different kinds. The same is true of the chemical categories of “com-pound” and “mixture.” Scientific theories typically classify their domains into anumber of distinct categories; such theoretical classification requires a taxo-nomic system with multiple categories. The kind terms support the categoriesnecessary for describing and generalizing about the world, and different kindsprovide for different descriptions and generalizations and thereby, experientially,different worlds.

In Shearman Memorial Lectures, Kuhn gives a canonical set of historical examplesto illustrate the incommensurability thesis in terms of natural kind terms and thetaxonomic distinctions they express. These examples are concerned with Aristotelianmotion, the Voltaic pile, and Planck’s Black-Body Theory. With reference to thesecanonical historical examples, Kuhn goes on to say:

“In each of these examples, I have described a set of past beliefs about someaspect of nature. To do that, however, I have needed also in each case to describethe meanings of a few of the terms in which these beliefs were stated. Theseterms, furthermore, have been of a special sort. Generally, they are among thenames of taxonomic categories available to members of the speech communitythat uses them. They carry the community’s ontology, supplying names for thingswhich its world can and cannot contain. They are very like the terms that Milldescribed as the names of natural kinds . . .” 13

Apart from developing a Theory of Kinds, Kuhn dwells on other related issues, suchas a cognitive exploration of how language of a scientific community is acquired,language learning process (in the analogy of bilingualism), the epistemological issue ofthe rationality of scientific development (the evolutionary epistemology), and howchange in the network of scientific kind in different theories relates toincommensurability.

In spite of narrowing down and refining the scope of IT in successivephases, the opposition to Kuhn’s thesis has not diminished. In what follows,we cite two historical examples to show the possibility of communicationacross revolutionary divide.

12 Shearman Memorial Lectures at University College London in 1987 and in “The plurality of worlds: anevolutionary theory of scientific discovery,” a book two-thirds completed at the time of his death. Also, seeHoyningen-Huene, “Thomas S. Kuhn” (cit. n. I), p. 241. Kuhn, “Afterwords” (cit. n. 18), pp. 314–319, 330,Hacking, Ian “Working in a new world” (cit. n. 18), pp. 283–297 and Chien (1997).13 Kuhn (1987a); italics mine.



II

Two Case Studies Rebutting Kuhn’s Claim that CommunicationAcross the Revolutionary Divide Is Not Possible

The case studies (and many similar ones) and the conclusions drawn based on in-depthand meticulous historical analysis perhaps reveal why Kuhn had to soften his positionin the final phase (mentioned above) regarding lack of communication across therevolutionary divide.

Case Study 1: Alleged Incommensurability of the Concept of “Mass”in the Revolutionary Divide: Newton and Special Theory of Relativity

Classification of Concepts

1. Undoubtedly, many analyses in science are limited to taxonomic conceptsThese concepts constitute a class of scientific concepts, which refer to things

that can be picked out individually. They refer to contrast sets (family resemblanceon the superordinate level) such as “planet,” “comet,” etc. However, things getcomplicated by the fact that such concepts are not the only ones which scientistsuse.

2. There are many nontaxonomic concepts, such as “force” and “mass.” Mostscientific concepts, such as “force” and “electromagnetic field,” refer to entitiesand processes that are learned by apprehending complex problem situations towhich given law applies and in which several laws are used. For example, what areusually learned are instances of the application of a natural law, such as Newton’ssecond law, F=ma, in which the concepts “force,” “mass,” and “acceleration” areinvolved simultaneously.

Kuhn noted this problem on two occasions. In the early work SSR, he distinguishedbetween taxonomic scientific concepts, called “basic,” and “nontaxonomic” concepts,called “theoretical.” Elsewhere, he referred to these as “normic” and “nomic” concepts,respectively (Kuhn 1993a).

Concept of “Mass” in the Revolutionary Divide: Newton and Special Theory ofRelativity In SSR, Kuhn claims that Einsteinian concepts, e.g., “mass,” are by nomeans identical with those of the Newtonian concepts that bear the same name. InKuhn’s view, the reason for radical difference of “mass” in the two paradigms is asfollows: the definition of Newtonian mass involves the law of conservation of masswhich is central to the Newtonian paradigm, and the definition of Einsteinian massinvolves laws central to the Einsteinian paradigm; hence, the Kuhnian thesis that themeaning of scientific terms is, in some manner, dependent on the theoretical context (orparadigm) in which the terms occur.

Newton’s Concept of “Mass” At the beginning of the Principia, Newton gives twodefinitions of “mass.” In the first definition, mass is the quantity of matter in a body, themagnitude of which is given by the product of the density and volume. In another



definition, he introduces the notion of an innate force of matter, the vis insita or visinertiae, i.e., the inertial mass of a body, which “is a power of resisting, by whicheverybody continues in its present state, whether it be of rest, or of moving uniformlyforwards in a right line” (Newton 1971).

In commenting on these definitions, Newton adds that there is always a constantproportionality between mass as quantity of matter in an object and the inertial mass ofthat object; given appropriate units, the magnitude of each is the same. A power ofresisting, a property of all bodies, is picked out and named as “inertial mass” by virtueof its causing bodies to remain in their state of rest or uniform velocity, or causing themto resist any change in their state of motion. Thus, the definition of inertial mass isgiven in Kripke fashion. This power also has a magnitude given by the magnitude ofthe mass in virtue of the above constant proportionality.

The definition given by Newton in the Principia is not the one usually found inbooks on Newtonian mechanics. Dissatisfaction with talk of “powers” and “innateforces” and their operation led to reformulations of the definition of “mass” from Kantto Mach and beyond.

It was Euler who introduced the formula “force equals mass times acceleration.”This is not the same as the second law of motion given by Newton in the Principia.That law states that the impressed force is proportional to the change in momentum,this being in the same direction as the force. Such a law occurs both in classicalNewtonian mechanics and in the special theory of relativity while Euler’s reformulationdoes not.

Euler then used the formula to give a definition of the magnitude of the mass, i.e., anumerical coefficient characteristic of a body given by the ratio of the force to theacceleration. Metaphysical scruples over entities such as the “quantity of matter in abody, and over realism about “powers” and “innate forces” in bodies, led to theseattempts to redefine “mass” in a way that does not offend a more positivist view ofscience.14

“Mass” in Special Theory of Relativity In his 1905 paper entitled “On theElectrodynamics of Moving Bodies” (Einstein 1905), where the Special Theory ofRelativity was enunciated, Einstein uses the same property of inertial mass, which canbe picked out by the same definition that was used by Newton. The reason for this isthat in the Special Theory of Relativity (STR), Einstein does not deny that bodies havethe property of resisting change in their uniform motion or rest with respect to a givenframe of reference. Thus, the term “mass” refers to the same property in both theories.Had STR implied that nothing could have such a property, then, it would have beenproper to conclude that Newton’s definition fixed a radically different reference or noreference at all for the concept “mass.”

Instead what STR denies is that there is one unique value for the magnitude of massfor all frames of reference and that the sum of the magnitudes is conserved. This doesinvolve introduction of concepts of “time,” “observer,” “synchronization of clocks,”“judgment of simultaneous events,” and several other complications in accounting forthe manner in which STR supplants the Newtonian theory. A close analysis of these

14 For Kant’s objection and Euler’s redefinition of mass, and other more positivist attempts at the same such asMach’s, see the history of the concept of mass in Jammer (1961), especially Chaps. 7 and 8.



differences would show that STR does not repudiate the entities, such as “mass,” of itsrival theory, viz., Newtonian mechanics, in the same way that, say, the oxygen theoryrepudiates the phlogiston. What it does repudiate is best expressed by Geoffrey Joseph:

“Are we to say that in the transition from Newtonian to Einsteinian physics suchterms as ‘the magnitude of the spatial separation of two events’, ‘the magnitude ofthe temporal separation of two events’, ‘the momentum of particles’ etc., to whichwe could add ‘the mass of particles’ changed their reference? This question is ill-formed, for it is based on an artificial dichotomy of the possible relations betweenthe domains of two theories. According to this dichotomy, a successor theoryeither acknowledges or else repudiates the objects, states, properties, etc., of itspredecessor. But special relativity did neither of these things. It showed not thatthe description of space-time from the one preferred frame erroneously thought tobe required by Maxwell’s equations was false, but that it was not the uniquelycorrect description it had been thought to be. The numerically determinate systemof referents of component expressions in classical physics was not shown to beincorrect, but was shown to be only one among many possible such systems….The classical system of numerical referents for the relevant physical magnitudeterms was not abandoned. It was maintained as one possible system among aninfinite number of equally admissible systems” (Joseph 1977)

Kuhn’s Kinds Theory of Incommensurability or Taxonomic Incommensurabilityand Its Criticisms For Kuhn Taxonomic Incommensurability, his final version of in-commensurability, based on Kind-Terms, such theoretical terms as “mass” seem to bedefined in terms of theoretical laws, which link “mass” with other kind terms, “force,”“acceleration,” “velocity,” “time,” and “distance.” This interdefinability may result indeveloping dissimilar “exemplars,” leading to the introduction of novel referents or newuses of these kind terms. However, the relevant scientific community would come to learnthese new uses or referents from each other and their disagreements and lack of commu-nication would be resolved (Kuhn 1991d). Many, such as Hartry Field (1973) in his“Theory Change and Indeterminacy of Reference”, made an attempt to support the claimof variance of meaning of “mass” between Newtonian mechanics and Special Theory ofRelativity by introducing the concept of partial denotation involving “proper mass” and“relativistic mass” to show how the scientific community may settle their differences.

A strong rebuttal, however, was given by Earman and Fine (1977) in their “AgainstIndeterminacy” by providing textual and historical evidence supporting the conceptualcontinuity of the concept of “mass” between Newtonian mechanics and Special Theoryof Relativity, repudiating lack of communication across revolutionary divide.

Case Study 2: Phlogiston Example

The phlogiston-oxygen controversy between Priestley and Lavoisier has been con-strued by many (Partington 1937; Conant 1948; Priestly 1970; Schofield 1966;Cavendish 1961; Kirwan 1968) as a clear example exhibiting Kuhn’s claim of lackof communication across the revolutionary divide.



Nevertheless, Philip Kitcher’s analysis of the phlogiston example15 illustrates as tohow historical episodes which led Kuhn to talk of incommensurability as irreconcilableand immune to rational resolution of revolutions exhibiting lack of communicationacross the revolutionary divide appear to be much less problematic than it has often beentaken to be. Kuhn’s claim that scientific decisions are inevitably decrepit and inherentlylacking in rational reconstruction also, Kitcher insists, lose much of their force.

Let us consider Priestley’s key concept “dephlogisticated air.”By heating the red calx ofmercury on its own, Priestley found that he could obtain the metal mercury and a new kindof “air,” which he called “dephlogisticated air.” (According to the phlogiston theory, thecalx of mercury has been turned into the metal mercury by taking up phlogiston; since thephlogiston must have been taken from the air, the resultant air is dephlogisticated.)Dephlogisticated air supports combustion, and respiration is (in which Priestly and micecould breath) better than ordinary air, but this is only to be expected, since the removal ofphlogiston from the air leaves the air with a greater capacity for absorbing phlogiston.

Kitcher shows that many tokens of this term “dephlogisticated air” used earlier byPriestley and other phlogistonians have their referents fixed through a causal chaininitiated by the event, viz., burning mercury in charcoal in which Stahl explicitly specifiedphlogiston as the substance emitted in combustion. The view that phlogiston is a substanceemitted in combustion is central to the phlogiston theory and is the doctrine fromwhich thetheory develops. Hence, it is quite natural to assume that the reference of “phlogiston” isfixed by this view, so that “phlogiston” refers to that which is emitted in all cases ofcombustion. Stahl takes phlogiston as being, by definition, that which is emitted incombustion. The phlogistonian tradition repeats Stahl’s definition and honors his usage.Thus, this is the problem of “theory-ladenness” of key terms in the phlogiston theory.

But there is nothing—which is emitted in all cases of combustion. From this, wemust conclude that “phlogiston” does not denote anything; hence, the tokens of“dephlogisticated air” fail to refer. But, after Priestley had unknowingly isolatedoxygen, viz., the gas he actually isolated by burning mercury in non-charcoal environ-ment by using magnifying glass, he continued to call it “dephlogisticated air.” Priestley,therefore, misidentified it. Nevertheless, many subsequent tokens of “dephlogisticatedair” had their reference fixed through causal chains initiated by encounters withoxygen. Those tokens in fact referred to oxygen.

In spite of this, phlogistonians continued to engage in taxonomical practices which ledthem to produce tokens of “dephlogisticated air” initiated in these two different ways (viz.charcoaled and non-charcoaledmodes of burning) because theywere confident that the gasisolated from the red substance obtained by burning mercury was dephlogisticated air.

However, from Lavoisier’s perspective, this was quite wrong and Lavoisier’s tax-onomy contained no expression which made any allusion to the phlogistonian term“dephlogisticated air.”

Nevertheless, Priestley concludes that “dephlogisticated air” supports combustionbetter than ordinary air. This is precisely why we recognize that the basis for Priestley’sjudgment proceeds from an experiment in which a gas evolved, and his beliefs mainlyconcern about this evolved gas in that experiment. Therefore, the tokens of“dephlogisticated air” which Priestley uses in recording his beliefs actually refer towhat Lavoisier calls “oxygen.”

15 Kitcher (1978), especially pp. 529–547.



Thus, Kitcher’s context-sensitive historical explanation account of reference and theintensionlist mechanism of reference fixation ensure the possibility of reverting to fullcommunication across the revolutionary divide and show how the rival claimants canappeal to a shared body of context-sensitive account of reference fixation and obser-vational evidence.

Two Morals Drawn by Kuhn from the Phlogiston Example Nevertheless, takingthe phlogiston example, Kuhn, on the other hand, shows that a small group of termsremains for which the modern chemical vocabulary offers no equivalent. Terms such as“phlogiston,” “dephlogisticated air,” and “principle” form a cluster of conceptuallyrelated terms which cannot be defined on the basis of the lexicon of the oxygen theory.“They constitute”, Kuhn says, “an interrelated or interdefined set that must be acquiredtogether, as a whole, before any of them can be used, applied to natural phenomena”(Kuhn 1983d). Kuhn develops two lessons from this.

1. Meaning variance and “local holism”In his last published work, Kuhn characterized the “lexicon” as the mental

“module in which members of a speech community store the community’skind terms” (Kuhn 1993b). The lexicon engenders variable beliefs andexpectations, depending on an individual’s experience and learning. Whatthe community holds in common Kuhn called “lexical structure.” It is thedifference in lexical structure that creates incommensurability. Different lex-ical structure embodies different kind relations, and these constitute differentperceived realities.

As a consequence of narrowing down the scope of IT to only scientificlexicon, Kuhn had to revise his earlier position of total communicationbreakdown. Nevertheless, he continued to hold the holistic nature of thevariance of meaning with regard to subset of lexicon that led to reclassifi-cation or re-categorization of entities constituting a common domain ofobjects shared between the theories in the revolutionary divide.

“Since such redistribution always involves more than one category and sincethose categories are interdefined, this sort of alteration is necessarily holistic.”(Kuhn 1987b)

This holistic interdefinition of clusters of category terms exhibits a revision ofthe incommensurability thesis construing it as a localized phenomenon restrictedto narrow subsets of terms figuring in the alternative theories.

2. Pragmatic justification for taxonomies eschewing truth claims and realismKuhn continues to oppose the correspondence theory (Kuhn 1991e, 1993c) since

he claims that lexicons are conventional structures which lack truth-value.Nevertheless, Kuhn does suggest that his kind terms are projectibile (Kuhn 1993d)because they refer to things which display lawful behavior. Indeed, Kuhn takes thelaws which govern the behavior of kinds to be an essential part of the meaning ofkind terms.16

16 Ibid p. 317.



Kuhn’s objection is not just that no theory may be closer to truth than another. It isthat there is no basis on which to judge that theories are closer to the truth. Kuhnclaims that the inability to integrate two lexicons corresponding to two rival theoriesentails that theories are unable to be compared for closeness to truth. Moreover,lexicons cannot be true or false. Their justification is pragmatic, i.e., they are bettersuited for a given purpose.

“Each lexicon makes possible a corresponding form of life within which the truthor falsity of propositions may be both claimed and rationally justified … “lexi-cons are not … the sorts of things that can be true or false” Their “logical statuslike that of word-meanings in general, is that of convention” 17 “The justificationof lexicons or lexical change can only be pragmatic”.18

Thus, according to Kuhn, a lexicon by itself cannot have truth-value because it hasthe status of a linguistic convention which may be judged on the basis of how well itserves a particular purpose rather than how well it reflects reality.

Although this view of scientific theory has profound consequences so far as Kuhn’sviews on realism-antirealism is concerned, it clearly demonstrates softening and toningdown of his initial position on incommensurability.

III

Conclusion

I believe that taxonomic incommensurability do not rule out scientific realism. It mustbe admitted that in all Kuhn’s accounts, the tension between admission of an indepen-dent reality and rejection of it was never resolved leading to a widespread impressionthat his versions of incommensurability involves some form of idealism. Kuhn’s ownstatement gives credence to such tension:

“Some ways are better suited to some purposes, some to others. But none is to beaccepted as true or rejected as false; none gives privileged access to a real, asagainst an invented, world. The ways of being-in-the-world which a lexiconprovides are not candidates for true/false.” (Kuhn 1991)

Thus, it appears that Kuhn upholds a weaker form of idealism which contrasts thereality independent of theory with the changing and constructed reality experienced bythe scientist. Hoyningen-Huene (1993) seems to support a similar view.

However, scientific realism is uncompromised by the thesis of taxonomic incom-mensurability. There is no need whatsoever to suppose that the world does change withchange of taxonomy. Different theories may classify the world differently while theworld remains the same. Hence, variation of taxonomic scheme is fully consistent with

17 Ibid, (1993), p. 330.18 Ibid, p. 331.



the mind-independence aspect of realism. Secondly, the terms of the lexicon are naturalkind terms and the relation between natural kind terms and reality would require anexplanation as to whether the entities postulated by such terms actually exist and howthese terms hook to reality. Hence, the issue of scientific realism cannot be dismissed.

Acknowledgments I am grateful to two anonymous reviewers of the paper and the editor of the journal fortheir incisive and constructive comments.

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the incommensurability thesis: has it lost its bite

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