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Philosophy Incommensurability in Science
by
Eric Oberheim, Paul Hoyningen-Huene

Introduction

In 1962 in independent, influential publications, Thomas S. Kuhn and Paul Feyerabend suggested the provocative idea that some scientific theories (concepts, paradigms, worldviews) separated by a scientific revolution are incommensurable. They have “no common measure.” The idea of incommensurability became central to both Kuhn’s historical philosophy and Feyerabend’s philosophical pluralism. In The Structure of Scientific Revolutions (1962), Kuhn 1996, cited in Thomas S. Kuhn on Incommensurability dramatically claims that the history of science reveals proponents of competing paradigms failing to make complete contact with each other’s views, so that they are always talking at least slightly at cross-purposes. Kuhn calls the collective causes of such miscommunication the incommensurability between pre- and postrevolutionary scientific traditions, claiming that the Newtonian paradigm is incommensurable with its Cartesian and Aristotelian predecessors in physics, just as Antoine-Laurent Lavoisier’s paradigm is incommensurable with that of Joseph Priestley’s in chemistry. These competing paradigms lack a common measure, because they use different concepts and methods to address different problems, limiting communication across the revolutionary divide. Incommensurability is also central to the aims and methods of Kuhn’s hermeneutic “new historiography of science,” which attempts to transform our image of science. Instead of the traditional image of continuous progress toward truth, Kuhn argues that scientific development is an evolutionary process away from anomalies. Kuhn’s The Structure of Scientific Revolutions is unprecedentedly popular across the human and social sciences, widely touted as among the most influential academic books of the 20th century. Feyerabend first used the term “incommensurable” in 1962 to characterize the relationship between the concepts of universal scientific theories interpreted realistically, claiming that they have no common measure. The idea of incommensurability remained central to his pluralistic approach to philosophy from his early work to his infamous Against Method (1975; Feyerabend 2010, cited in Paul Feyerabend on Incommensurability) through to his late, postmodern phase. For example, two main themes of The Tyranny of Science (Feyerabend 2011, cited in Feyerabend, Reality, and Incommensurability) are the disunity of science and the abundance of nature, which are lessons he learned directly through his experience with incommensurability. With incommensurability, Kuhn and Feyerabend appeared to be challenging the idea that science is rational, and they were called the “worst enemies of science” in the journal Nature. By now incommensurability has become a well-worn catchphrase of 20th-century philosophy, used across a range of interrelated disciplines to mean many different things in any number of controversial discussions.

General Overviews

Incommensurability and its implications have been controversially discussed ever since the inception of Western science as we know it. Incommensurability has played a starring role in a variety of controversial discussions about the nature of knowledge, from Plato, Aristotle, and Euclid to Albert Einstein, Thomas S. Kuhn, and Paul Feyerabend. Even just a comprehensive overview of the idea of incommensurability in science as it is typically used in the early 21st century is contentious, as incommensurability in science is a controversial, interdisciplinary idea that plays a wide range of roles across a broad array of interrelated discussions in contemporary history, philosophy, and sociology of science (sometimes collectively called science studies). Comparing attempted general overviews is particularly instructive with respect to the range of reconstructions, reactions, issues, and approaches that there are. Sankey 2006 attempts a concise introduction of the idea of incommensurability in science, highlighting some major developments in its reception in analytic philosophy and general philosophy of science. Oberheim and Hoyningen-Huene 2009 also attempts a general overview that distinguishes, develops, and compares Kuhn’s and Feyerabend’s evolving views on incommensurability in science. For a concise, general introduction specifically on Kuhn’s conception, see Bird 2011. For a concise general introduction specifically on Feyerabend’s conception, see Preston 2009. Incommensurability is also often a topic in general introductions to philosophy of science; for example, Chalmers 1999 has a discussion of incommensurability designed for an introductory course on philosophy of science, as does Ladyman 2002.

Bibliographies

Khalidi 2001 introduces the idea and provides an introductory selection of literature. Philpapers: Online Research in Philosophy is a free searchable database for research in philosophy on incommensurability, and the specific subsection Incommensurability in Science lists relevant materials, such as abstracts, exportable citations, and links to journal providers. For a list of publications before 2000, see Sankey and Hoyningen-Huene 2001. A similar list, Incommensurabilität, is also available from the Institute of Philosophy, Leibniz Universität Hannover.

Thomas S. Kuhn and Incommensurability

This section is divided into two subsections. The first subsection is primary literature by Thomas S. Kuhn on incommensurability. The second subsection is secondary literature on Kuhn’s conception of incommensurability.

Thomas S. Kuhn on Incommensurability

Thomas S. Kuhn was an influential 20th-century philosopher of science who took incommensurability to be the key concept of his historical approach to understanding what science is and how it develops. The original source is the popular The Structure of Scientific Revolutions (Kuhn 1996, first published in 1962), which continues to fuel controversial interdisciplinary discussions in history, philosophy, and sociology of science on a wide range of interrelated topics. Kuhn 1970 attempts to clarify his views, explicitly addressing a number of (persistent) popular misunderstandings of his historical philosophy in general and incommensurability and its implications in particular. For example, Kuhn never meant to imply that science is irrational, or that incommensurable theories are rationally incomparable, or that there is total translation (and/or communication) failure between incommensurable theories. Kuhn 1977 autobiographically recounts Kuhn’s discovery of incommensurability in science in the mid- to late 1940s while struggling to understand Aristotelian physics and how incommensurability developed into the central idea driving his historical philosophy with respect to both his punctuated account of scientific development and the hermeneutic historiographical method on which it is based. After making some significant breakthroughs in the late 1980s, Kuhn redeveloped incommensurability on the basis of “lexical taxonomy” and the “no-overlap principle.” A lexical taxonomy is a mental module that stores and structures the kinds used to state scientific laws and theories. The no-overlap principle precludes cross-classification of objects into different kinds within a theory’s lexical taxonomy, so that no two kind terms within a theory may overlap in their referents unless they are related as species to genus. For example, while there are many kinds of animals, some of which are dogs and some of which are cats, there are no dogs that are also cats, just as while there are many kinds of chemical elements (such as gold and silver), there is no gold that is also silver. Exactly such mutual exclusivity with respect to the basic kinds related by a set of general laws and theories is a necessary prerequisite for successful description and explanation of those kinds of things. By contrast, if two theories about the same individual objects do not share the same taxonomic structure with respect to kinds, then they are incommensurable. For Kuhn’s late development of incommensurability, see Kuhn 1990, Kuhn 2000, Kuhn 1991, and Kuhn 1993.

  • Kuhn, Thomas S. “Reflections on My Critics.” In Criticism and the Growth of Knowledge: Proceedings of the International Colloquium The Philosophy of Science, London, 1965. Edited by Imre Lakatos and Alan Musgrave, 231–278. Cambridge, UK: Cambridge University Press, 1970.

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    Reprinted in Kuhn 2000, pp. 123–175. See especially pp. 124, 159, 162–164. Kuhn responds directly to the 1965 conference contributions from John Watkins, Stephen Toulmin, Leslie Pearce Williams, and Karl Popper as well as Margaret Masterman from 1966 and papers by Imre Lakatos and Feyerabend from 1969.

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  • Kuhn, Thomas S. The Essential Tension: Selected Studies in Scientific Tradition and Change. Chicago: University of Chicago Press, 1977.

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    Although many of the papers collected here predate Kuhn’s 1962 use of “incommensurable,” in the preface (pp. x–xxiii) Kuhn recounts his discovery of incommensurability to explain why he chose to structure this collection into two parts: “Historiographical Studies” and “Metahistorical Studies.” See especially pp. ix–xii.

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  • Kuhn, Thomas S. “Dubbing and Redubbing: The Vulnerability of Rigid Designation.” In Scientific Theories. Edited by C. Wade Savage, 298–318. Minnesota Studies in the Philosophy of Science 14. Minneapolis: University of Minnesota Press, 1990.

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    Detailed discussion of the no-overlap principle, incommensurability, and the causal theory of reference.

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  • Kuhn, Thomas S. “The Road since Structure.” In PSA 1990: Proceedings of the 1990 Biennial Meeting of the Philosophy of Science Association. Vol. 2. Edited by Arthur Fine, Micky Forbes, and Linda Wessels, 3–13. East Lansing, MI: Philosophy of Science Association, 1991.

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    Presidential address. Reprinted in Kuhn 2000, chapter 4, pp. 90–104. On incommensurability, see especially pp. 91, 93–94, 99.

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  • Kuhn, Thomas S. “Afterwards.” In World Changes: Thomas Kuhn and the Nature of Science. Edited by Paul Horwich, 311–341. Cambridge, MA: MIT Press, 1993.

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    Kuhn clarifies his position on incommensurability in response to papers collected in the volume (Horwich 1993, cited in On Thomas S. Kuhn’s Incommensurability). Reprinted in Kuhn 2000, chapter 6, pp. 123–175. On incommensurability, see especially pp. 124, 159, 162–164.

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  • Kuhn, Thomas S. The Structure of Scientific Revolutions. 3d ed. Chicago: University of Chicago Press, 1996.

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    Originally published in 1962 (two first editions). Part of the series International Encyclopedia of Unified Science, edited by Otto Neurath, and collected in Otto Neurath, Rudolf Carnap, and Charles Morris, eds., Foundations of the Unity of Science, Vol. 2, no. 2. Second enlarged edition published in 1970. International best seller in philosophy. On incommensurability, see pp. 4, 103, 112, 148–150, 157, 165, 175, 198–204.

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  • Kuhn, Thomas S. The Road since Structure: Philosophical Essays, 1970–1993, with an Autobiographical Interview. Edited by James Conant and John Haugeland. Chicago: University of Chicago Press, 2000.

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    Collects many of Kuhn’s major papers portraying how Kuhn’s ideas developed. On incommensurability, see pp. 33–37, 39–41, 47, 49, 53, 56, 60, 91, 93–94, 97, 99, 106, 119, 120, 124, 159, 162–164, 188–190, 204, 221, 228–229, 237, 240, 244, 297–298, 309–310, 314. Part 3 contains an interview with some biographical details related to Kuhn’s development of the idea of incommensurability.

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On Thomas S. Kuhn’s Incommensurability

There have been many attempts to reconstruct Kuhn’s philosophy that critically develop his views on incommensurability in science with respect to a wide range of issues. This section is, for that reason, highly selective. Hoyningen-Huene 1993 is a standard secondary source on Kuhn’s philosophy and the role that incommensurability plays within it. It was developed directly through discussions with Kuhn and is recommended by Kuhn in the preface. Bird 2000 reassesses Kuhn’s philosophy, particularly in light of the naturalist turn in philosophy of science. Marcum 2005 offers an extremely detailed historical reconstruction of Kuhn’s development of The Structure of Scientific Revolutions (Kuhn 1996, cited in Thomas S. Kuhn on Incommensurability), particularly useful for situating the idea of incommensurability as it first appeared in 1962. Horwich 1993 collects a wide range of approaches, including applications, critical discussions, and reconstructions of Kuhn’s views on incommensurability. For example, Hacking 1993, cited in Taxonomic Incommensurability, attempts a transcendental nominalist reconstruction of Kuhn’s conception of incommensurability. Sankey 1994 attempts to recast incommensurability as meaning change within a scientific realist framework (see also Thomas S. Kuhn, Reality, and Incommensurability and Incommensurability and Reference). Irzik and Grünberg 1998 reconstructs Kuhn on incommensurability and scientific revolution with a Whorfian conception of language set in a neo-Kantian metaphysics. Agassi 1985 is a more general discussion of Kuhn, Paul Feyerabend, and incommensurability in the context of social philosophy and its implications for technology. Demir 2008 emphasizes the distinction between actors’ and analysts’ incommensurability, the former arising in science and the latter arising in the study of science.

Paul Feyerabend and Incommensurability

This section is divided into two subsections. The first subsection is primary literature by Paul Feyerabend on incommensurability. The second subsection is secondary literature on Feyerabend’s conception of incommensurability.

Paul Feyerabend on Incommensurability

Feyerabend 1962 (collected in substantially revised form in Feyerabend 1981b) is the standard source for Paul Feyerabend’s controversial idea of incommensurability, his first paper using the term “incommensurable.” Traces of the idea are, however, readily apparent in some of his earlier publications, for example, collected in revised form in Feyerabend 1957–1958, where an early version of the idea of incommensurability in science is discussed under the rubric of “thesis I.” Feyerabend used and developed the idea in many subsequent publications, even if sometimes in somewhat different terms and with different emphasis, for example, in his discussion of “irreducibility” in Feyerabend 1999 (originally published in 1963), which (like Feyerabend 1962) criticizes contemporary empiricism for promoting dogmatic metaphysics. Feyerabend 1962 investigates the methodological structure of crucial (not definitive, just retrospectively decisive) experiments between competing universal physical theories, realistically interpreted. Feyerabend uses the example of Albert Einstein’s predictions of Brownian motion to illustrate the methodological structure of crucial experiments between such incommensurable rivals. Feyerabend concludes that while incommensurability precludes direct crucial experiments (as there is no neutral evidence base shared by both theories with which to confirm one and refute the other), indirect crucial experiments are still possible (on the basis of pragmatic or causal theories of observation). Incommensurability is intended to capture the idea of conceptual incompatibility due to changes of meaning that occur in theoretical transitions that affect our ontological beliefs. Two fundamental theories are incommensurable, because the meanings of their terms are determined by the theoretical principles that govern their use, and these principles are qualitatively incompatible. Feyerabend 1962 draws two main consequences for logical empiricism. First, logical empiricist models of reduction and explanation based on deductive relations need to be modified, as incommensurable scientific theories are stated with categories that have no logical relations. Second, a revision in the logical empiricist conception of scientific advance is required. Former theories, and the concepts used to state them, are not corrected and absorbed and thereby legitimized. They are rather rejected and replaced, having been falsified. In later publications Feyerabend often responds to a wide range of (persisting) misinterpretations of incommensurability, insisting that incommensurability implies neither that theories are incomparable nor that theory choice is irrational. See, for example, Feyerabend 1965a and Feyerabend 1965b. These and many of his early papers related to incommensurability are collected in substantially revised form in Feyerabend 1981a and Feyerabend 1981b, which do not always identify where and how many significant changes were made with respect to the originals. Feyerabend also discusses incommensurability in Against Method (Feyerabend 2010, original monograph published in 1975), which argues against the unity of science on the basis that there are no universally valid methodological rules (infamously self-sloganeered as “anything goes”). Although Feyerabend’s shifting and provocative views on incommensurability remain controversial, the resulting image of the disunity of science continued as a major theme in his late postmodern philosophy, readily apparent in Feyerabend 1991, Feyerabend 1999, and Feyerabend 2011, all cited in Paul Feyerabend, Reality, and Incommensurability.

  • Feyerabend, Paul. “An Attempt at a Realistic Interpretation of Experience.” Proceedings of the Aristotelian Society, n.s., 58 (1957–1958): 143–170.

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    Reprinted in significantly revised form in Feyerabend 1981b, pp. 17–36. Compare “thesis I”: The result of an experiment is an interpretation of observation language partly determined by those theories used to explain what is observed, and consequently it changes together with those theories.

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  • Feyerabend, Paul. “Explanation, Reduction, and Empiricism.” In Scientific Explanation, Space, and Time. Edited by Herbert Feigl and Grover Maxwell, 28–97. Minnesota Studies in the Philosophy of Science 3. Minneapolis: University of Minnesota Press, 1962.

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    Reprinted in significantly revised form in Feyerabend 1981b, pp. 33–96. Incommensurability as conceptual incompatibility due to meaning change that affects ontology.

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  • Feyerabend, Paul. “On the ‘Meaning’ of Scientific Terms.” Journal of Philosophy 62 (1965a): 266–274.

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    Response to some critical discussions of incommensurability. Reprinted in significantly revised form in Feyerabend 1981b, pp. 97–103.

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  • Feyerabend, Paul. “Reply to Criticism: Comments on Smart, Sellars, and Putnam.” In Proceedings of the Boston Colloquium for the Philosophy of Science 1962–64: In Honor of Philipp Frank. Edited by Robert Cohen and Mark Wartofsky, 223–261. Boston Studies in the Philosophy of Science 2. New York: Humanities, 1965b.

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    Response to some critical discussions of incommensurability. Reprinted in significantly revised form in Feyerabend 1981b, pp. 104–131.

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  • Feyerabend, Paul. Problems of Empiricism. Philosophical Papers 2. Cambridge, UK: Cambridge University Press, 1981a.

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    Collects many major early publications but often in substantially modified form. On incommensurability, see pp. x–xi, 23, 73, 136, 144, 152, 154, 157, 167, 238–239. “Lakatos’ analysis, I think, can be further improved . . . by allowing for incommensurability (jumps from quantity to quality in the language of dialectical materialism)” (p. 144).

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  • Feyerabend, Paul. Realism, Rationalism, and Scientific Method. Philosophical Papers 1. Cambridge, UK: Cambridge University Press, 1981b.

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    Collects many major early publications but often in substantially modified form. The introduction is particularly instructive with regard to the role of incommensurability in Feyerabend’s philosophical development.

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  • Feyerabend, Paul. “How to Be a Good Empiricist: A Plea for Tolerance in Matters Epistemological.” In Knowledge, Science, and Relativism. Edited by John Preston, 78–103. Philosophical Papers 3. Cambridge, UK: Cambridge University Press, 1999.

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    Reprinted as originally published in 1963. Argues that just as totalitarian political measures are sometimes implemented in the name of democracy, some methods of modern empiricism that were developed in the spirit of antidogmatism and progress actually lead to new dogmas about “well-confirmed theories.” See also, for example, pp. 162–163.

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  • Feyerabend, Paul. Against Method. 4th ed. New York: Verso, 2010.

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    First edition 1975. Second substantially revised and enlarged English edition 1988. Third substantially revised and enlarged English edition 1993. There are also two German editions (1976, 1983) revised independently by Feyerabend that do not correspond exactly to any English edition. Against Method continues to be characterized as an international best seller in philosophy.

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On Paul Feyerabend’s Incommensurability

There has been a wide range of controversial critical discussions of Feyerabend on incommensurability. A good place to start is Couvalis 1989, which offers an excellent reconstruction of Feyerabend’s views. Preston 1997 has also become a standard source as the first general monograph on Feyerabend’s philosophy. For a detailed reconstruction based on a historical approach that lists many further references to Feyerabend on incommensurability, see Oberheim 2005. For another extended attempt to reconstruct incommensurability in the context of Feyerabend’s controversial philosophy, see Farrell 2003, which focuses primarily on Feyerabend’s late philosophy. Sankey 1994 is mainly focused on incommensurability as a semantic thesis and attempts to incorporate incommensurability into a scientific realist framework. Perovich 1991 disentangles Feyerabend’s different presentations of incommensurability and focuses on his conception of the relationship between meaning and reference. For early detailed critical discussions, see, for example, McEvoy 1975 and Giedymin 1970.

Methodological Incommensurability

Methodological incommensurability is the idea that there are no shared, fixed, objective standards of scientific theory appraisal, so that there are no external or neutral standards that univocally determine the comparative evaluation of competing theories. Kuhn 1977 discusses generally accepted epistemic values that guide but do not dictate rational theory choice, such as simplicity, scope, empirical accuracy, coherence with other beliefs, and fruitfulness. Such epistemic values vary among individuals within any actual scientific community. Moreover, they shift and develop as science advances. What was once accepted as legitimate science may later turn out to look unscientific, while ideas once banned as unscientific may later look legitimate. Kuhn argues that although there is often wide agreement with respect to theory choice (for example, in a normal science phase), in a crisis phase differences between interpretations, applications, and relative weightings of these values, which may even pull in different directions, allow for the possibility of rational disagreement with respect to theory choice. For an introduction to the distinction between taxonomic and methodological incommensurability, see Sankey and Hoyningen-Huene 2001 and compare Oberheim and Hoyningen-Huene 2009. For a brief introduction to Thomas S. Kuhn on methodological incommensurability, see Bird 2011. Carrier 2008 offers an illustration of methodological incommensurability and how rational disagreements with respect to the relative merits of competing theories were due to differences in interpretation and application of epistemic values (such as simplicity and scope) in the Copernican revolution. Farrell 2003 develops Feyerabend’s later philosophy on the basis of such epistemic values. Some defenders of cultural variations in legitimate scientific practice, such as Lacey 2001, draw on Kuhn’s views about incommensurability and incompatible paradigms to defend multicultural science. While Kuhn’s account of rational disagreement and the roles of epistemic values in theory choice has been very influential to the development of historical philosophy, it also unwittingly fostered an extreme externalism in sociology of science, from which Kuhn was eager to distance himself. For an introduction and some general background, see Godfrey-Smith 2003.

  • Bird, Alexander. “Thomas Kuhn.” In The Stanford Encyclopedia of Philosophy. Edited by Edward Zalta. 2011.

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    On methodological incommensurability, see section 4.1.

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  • Carrier, Martin. “The Aim and Structure of Methodological Theory.” In Rethinking Scientific Change and Theory Comparison. Edited by Léna Soler, Howard Sankey, and Paul Hoyningen-Huene, 273–290. Dordrecht, The Netherlands: Springer, 2008.

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    Carrier calls methodological incommensurability “methodological underdetermination.” Revision of a paper originally presented at an international colloquium at the University of Nancy, France, June 2004.

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  • Farrell, Robert. Feyerabend and Scientific Values: Tightrope-Walking Rationality. Dordrecht, The Netherlands: Kluwer, 2003.

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    See especially section 8.5, “Values-Based Rationality,” pp. 202–213.

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  • Godfrey-Smith, Peter. Theory and Reality: An Introduction to the Philosophy of Science. Chicago: University of Chicago Press, 2003.

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    On the impact of Kuhn’s incommensurability and the rise of the “strong program,” see chapter 8, “The Challenge from Sociology of Science,” especially section 8.3, “Rise of the Strong Program,” pp. 126–128. See the bibliography for a selection of references relevant to the roles played by incommensurability in sociology of science.

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  • Kuhn, Thomas S. The Essential Tension: Selected Studies in Scientific Tradition and Change. Chicago: University of Chicago Press, 1977.

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    On epistemic values, see “Objectivity, Value Judgment, and Theory Choice,” pp. 320–339, especially pp. 321–322. See also Kuhn 1996, cited in Thomas S. Kuhn on Incommensurability, p. 155.

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  • Lacey, Hugh. “Incommensurability and ‘Multicultural Science.’” In Incommensurability and Related Matters. Edited by Paul Hoyningen-Huene and Howard Sankey, 225–239. Boston Studies in the Philosophy of Science 216. Dordrecht, The Netherlands: Kluwer, 2001.

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    Shows how different cultural values underlie the salience of empirical questions sometimes sidelined by mainstream science, for example, with “seeds.”

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  • Oberheim, Eric, and Paul Hoyningen-Huene. “The Incommensurability of Scientific Theories.” In The Stanford Encyclopedia of Philosophy. Edited by Edward Zalta. 2009.

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    On the distinction between methodological and taxonomic incommensurability, see especially sections 2.3.1 and 2.3.2.

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  • Sankey, Howard, and Paul Hoyningen-Huene. “Introduction.” In Incommensurability and Related Matters. Edited by Paul Hoyningen-Huene and Howard Sankey, vii–xxxiv. Boston Studies in the Philosophy of Science 216. Dordrecht, The Netherlands: Kluwer, 2001.

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    On taxonomic and methodological incommensurability, see pp. vii–xv. Book collects eleven contributions to a 1999 conference in five sections: “Meaning and Reference” (Richard N. Boyd, Martin Carrier, Fred Kroon, Robert Nola), “Realism” (Harold I. Brown, Michael Devitt), “Rationality and Relativism” (Gerald Doppelt, Dudley Shapere), “Multiculturalism and Science Education” (Harvey Siegel, Hugh Lacey), and “Cognition and Conceptual Change” (Peter Barker, Nancy J. Nersessian). See also Sankey and Hoyningen-Huene 2001, cited under Bibliographies.

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Taxonomic Incommensurability

From the late 1980s Thomas S. Kuhn developed incommensurability as a form of conceptual incompatibility in terms of differences in lexical taxonomy underlying classification. A lexical taxonomy stores and structures the vocabulary used to state laws and theories. Competing theories are incommensurable if their lexical taxonomies break the no-overlap principle, which precludes cross-classification of objects into different kinds within a theory’s taxonomy. Many of Kuhn’s major papers on this topic are collected in Kuhn 2000. Hacking 1993 attempts a precise critical reconstruction, to which Kuhn directly responded. Sankey 1998 offers a critical reconstruction in the context of Kuhn’s developing philosophy and attempts to counter Kuhn’s suggestions that taxonomic incommensurability undermines the scientific realist characterization of scientific advance as progress toward truth and so should be replaced by an evolutionary account that emphasizes progress away from anomalies. Chen 1995 is a historical case study of taxonomic incommensurability on the basis of optical theory in the 1830s. Buchwald and Smith 2001 develops the idea with a case study from early to late-19th-century optics. For a more general critical discussion of the idea of hierarchical, natural categories, see Khalidi 1998. Fu 1995 (cited in Incommensurability and Historiography of Science) attempts to extend the application of the idea of taxonomic incommensurability from the classifications used in science to classifications of the sciences themselves. See also Incommensurability, Cognition, and Categorization.

Incommensurability, Cognition, and Categorization

In some of his late papers, many collected in Kuhn 2000, Thomas S. Kuhn uses the term “lexicon” to refer to mental modules in which members of a speech community store the community’s kind terms. Such mental modules result from the evolution of neural mechanisms for identifying something being the same thing from origin to demise, something that traces a lifeline through space over time. Kuhn suggests seeing Wiggins 1980 on sameness and substance. The resulting mental modules allow human beings to learn to recognize kinds of physical objects, such as elements, field, and forces and more broadly furniture, government, personality, and so on. There are many attempts to bring cognitive and developmental psychology to bear on Kuhn’s late conception of incommensurability and scientific development. A popular tool for depicting shifting conceptual relations, such as incommensurability, is the frame model developed in cognitive psychology. See, for example, Chen, et al. 1998, which provides background and further references, and Andersen and Nersessian 2000, Barker 2001, and Chen 2003. Khalidi 1998 and Tsou 2006 attempt to develop Kuhn’s ideas about revolutionary developments on the basis of analogies to developmental psychology. See also the papers collected in Part 4 of Favretti, et al. 1999, cited in Incommensurability, Translation, and Communication.

Revolutions and Reality

This section is divided into two subsections. The first subsection concerns Thomas S. Kuhn’s conception of the relations between incommensurability and reality. The second subsection concerns Paul Feyerabend’s conceptions of the relations between incommensurability and reality.

Thomas S. Kuhn, Reality, and Incommensurability

Thomas S. Kuhn’s conception of realism and its relation to incommensurability is complex and continues to be controversial. From Kuhn 1996 to Kuhn 2000, he uses incommensurability to challenge the scientific realist conception of scientific advance as progress toward truth and to challenge the scientific realist conception of the ontological independence of empirical reality as the subject and object of scientific study. Moreover, Kuhn 2000 uses incommensurability to develop an alternative to scientific realism as a form of evolutionary epistemology. See also Incommensurability and Evolutionary Epistemology. Hoyningen-Huene 1993 reconstructs Kuhn on incommensurability and reality as developing a form of (nonscientific realist) neo-Kantian metaphysics, according to which empirical reality is coconstituted by subject- and object-sided moments (in the Hegelian sense, that is, inseparably bound) and consequently is not fixed but changes in the course of revolutionary scientific advance. Compare Hacking 1993, cited in Taxonomic Incommensurability, which develops Kuhn as a form of revolutionary transcendental nominalism. Boyd 1984, Devitt 2001, and Sankey 2009 attempt to defend scientific realism from the purported threat posed by incommensurability. Weinberg 1998 is a high-profile critical discussion of Kuhn’s influential views on incommensurability, revolutions, and normal science from a physicist’s perspective. Brown 2005 develops Kuhn’s revised account of incommensurability as a challenge to realism, attempting to avoid Kuhn’s antirealist conclusions.

  • Boyd, Richard N. “The Current Status of Scientific Realism.” In Scientific Realism. Edited by Jarrett Leplin, 41–82. Berkeley: University of California Press, 1984.

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    Informative overview of realist responses to various purported threats posed by incommensurability. Scientific Realism collects influential papers by Boyd, Arthur Fine, Clark Glymour, Ian Hacking, Larry Laudan, Ronald Laymon, Jarrett Leplin, Michael Levin, Ernan McMullin, Hilary Putnam, and Bas C. van Fraassen. Excellent starting point for scientific realism in the early 1980s. On incommensurability, see pp. 52–56, 99, 144, 156–157, 194, 204.

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  • Brown, Harold. “Incommensurability Reconsidered.” Studies in History and Philosophy of Science A 36 (2005): 149–169.

    DOI: 10.1016/j.shpsa.2004.12.008Save Citation »Export Citation »E-mail Citation »

    Brown turns the standard conception of the relation between realism and incommensurability on its head, arguing that scientific realism requires recognizing incommensurability as an important component of searching for truth. Compare Harold Brown, “Incommensurability and Reality,” in Paul Hoyningen-Huene and Howard Sankey, eds., Incommensurability and Related Matters (Dordrecht, The Netherlands: Kluwer, 2001), pp. 123–142.

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  • Devitt, Michael. “Incommensurability and the Priority of Metaphysics.” In Incommensurability and Related Matters. Edited by Paul Hoyningen-Huene and Howard Sankey, 143–157. Boston Studies in the Philosophy of Science 216. Dordrecht, The Netherlands: Kluwer, 2001.

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    Reprinted in Devitt 2010, cited in Against Incommensurability. Devitt treats incommensurability as a semantic thesis and argues that scientific realist metaphysics is more securely grounded in common sense experience than the speculative semantic and epistemological ideas motivating the challenge to realism posed by incommensurability.

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  • Hoyningen-Huene, Paul. Reconstructing Scientific Revolutions: Thomas S. Kuhn’s Philosophy of Science. Translated by Alexander T. Levine. Chicago: University of Chicago Press, 1993.

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    With a foreword by Thomas S. Kuhn. An English translation of a slightly expanded Die Wissenschaftsphilosophie Thomas S. Kuhns: Rekonstruktion und Grundlagenprobleme (Brunswick, Germany: Vieweg, 1989). On Kuhn on reality, see “Part II. Scientific Knowledge and Its Object,” pp. 29–164.

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  • Kuhn, Thomas S. The Structure of Scientific Revolutions. 3d ed. Chicago: University of Chicago Press, 1996.

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    Originally published in 1962 (two first editions). Part of the series International Encyclopedia of Unified Science, edited by Otto Neurath, and collected in Otto Neurath, Rudolf Carnap, and Charles Morris, Foundations of the Unity of Science, Vol. 2, no. 2. Second enlarged edition 1970. On incommensurability, world change, and reality, see, for example, chapter 10, “Revolutions as Changes of World View,” pp. 111–135; p. 150; and “Postscipt-1969.”

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  • Kuhn, Thomas S. The Road since Structure: Philosophical Essays, 1970–1993, with an Autobiographical Interview. Edited by James Conant and John Haugeland. Chicago: University of Chicago Press, 2000.

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    On reality, see, for example, pp. 203, 228–234, 244–247.

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  • Sankey, Howard. “Scientific Realism and the Semantic Incommensurability Thesis.” Studies in History and Philosophy of Science A 40 (2009): 196–202.

    DOI: 10.1016/j.shpsa.2009.03.007Save Citation »Export Citation »E-mail Citation »

    Sankey attempts to incorporate incommensurability as a semantic thesis about meaning change into a scientific realist metaphysical perspective. See also the papers collected in Howard Sankey, Scientific Realism and the Rationality of Science (Aldershot, UK: Ashgate, 2008), which contain discussions on a range of directly related topics, including incommensurability and its (controversial) relationship to scientific realism.

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  • Weinberg, Steven. “The Revolution That Didn’t Happen.” New York Review of Books, 8 October 1998, 48–52.

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    Examines Kuhn on incommensurability and scientific revolutions from a practicing physicist’s scientific realist perspective. Available online for purchase or by subscription.

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Paul Feyerabend, Reality, and Incommensurability

Paul Feyerabend’s views on scientific realism and its relation to incommensurability are complex and contentious. For primary literature, the introduction of Feyerabend 1981, which is the first of three volumes of Feyerabend’s collected papers, is a good place to start. For a general introduction to the topic, see Sankey and Hoyningen-Huene 2001. Preston 1997 presents a controversial account of Feyerabend as initially a scientific realist who gradually reversed his position. Oberheim 2006 challenges Preston’s account, arguing that Feyerabend was not initially a scientific realist on the basis of a distinction between normative realism (science should aim for truth), which Feyerabend accepted, and scientific realism (science succeeds in that aim), which Feyerabend rejected. Incommensurability and reality were also major interrelated themes in Feyerabend’s late philosophy, as is readily apparent in his Three Dialogues on Knowledge (Feyerabend 1991), Conquest of Abundance (Feyerabend 1999), and The Tyranny of Science (Feyerabend 2011). Farrell 2003 is primarily focused on Feyerabend’s later philosophy with a chapter critically discussing Feyerabend’s conception of worldviews.

  • Farrell, Robert. Feyerabend and Scientific Values: Tightrope-Walking Rationality. Dordrecht, The Netherlands: Kluwer, 2003.

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    On incommensurability and realism, see especially chapters 3 and 9.

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  • Feyerabend, Paul. Realism, Rationalism, and Scientific Method. Philosophical Papers 1. Cambridge, UK: Cambridge University Press, 1981.

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    Collects many of Feyerabend’s early papers, often in significantly (but unidentified) modified form so is therefore somewhat unreliable as a historical source with respect to his original views. On realism and incommensurability, see especially the introduction.

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  • Feyerabend, Paul. Three Dialogues on Knowledge. Oxford: Blackwell, 1991.

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    On incommensurability in Feyerabend’s late philosophy, see pp. 154–159.

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  • Feyerabend, Paul. Conquest of Abundance: A Tale of Abstraction versus the Richness of Being. Edited by Bert Terpstra. Chicago: University of Chicago Press, 1999.

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    Posthumously edited into two parts: “The Unfinished Manuscript” (pp. 3–128, four chapters with an interlude) and “Essays on the Manuscript’s Themes” (pp. 131–273, collects a dozen previously published pieces from the late 1980s to the mid-1990s). On incommensurability in Feyerabend’s late philosophy, see pp. 26–27, 252–264, 267–268.

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  • Feyerabend, Paul. The Tyranny of Science. Edited by Eric Oberheim. Cambridge, UK: Polity Press, 2011.

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    Although Feyerabend does not use the term “incommensurability,” one main consequence of incommensurability for Feyerabend was the disunity of science, which became a major theme in his later philosophy. See especially chapter 2. Introduction by Eric Oberheim.

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  • Oberheim, Eric. Feyerabend’s Philosophy. New York: de Gruyter, 2006.

    DOI: 10.1515/9783110891768Save Citation »Export Citation »E-mail Citation »

    See especially chapter 6, “Incommensurability and Scientific Realism,” for Feyerabend’s controversial relation of realism.

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  • Preston, John. “Feyerabend’s Retreat from Realism.” Philosophy of Science 64 (1997): 421–431.

    DOI: 10.1086/392619Save Citation »Export Citation »E-mail Citation »

    Compare Preston 1997, cited under On Paul Feyerabend’s Incommensurability.

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  • Sankey, Howard, and Paul Hoyningen-Huene. “Introduction.” In Incommensurability and Related Matters. Edited by Paul Hoyningen-Huene and Howard Sankey, vii–xxxiv. Boston Studies in the Philosophy of Science 216. Dordrecht, The Netherlands: Kluwer, 2001.

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    See especially sections 6 and 7.2. Book collects eleven contributions to a 1999 conference in five sections: “Meaning and Reference” (Richard N. Boyd, Martin Carrier, Fred Kroon, Robert Nola), “Realism” (Harold I. Brown, Michael Devitt), “Rationality and Relativism” (Gerald Doppelt, Dudley Shapere), “Multiculturalism and Science Education” (Harvey Siegel, Hugh Lacey), and “Cognition and Conceptual Change” (Peter Barker, Nancy J. Nersessian).

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Incommensurability, Progress, and Rationality

Laudan 1977 develops a normative theory of rationality and an explicit meta-methodology that criticizes Thomas S. Kuhn’s approach to incommensurability. Pearce 1984 challenges Larry Laudan’s claim that there are no incommensurable pairs of theories or research traditions and argues against Laudan’s claim that his problem-solving model of scientific progress provides the basis for comparing pairs of incommensurable theories. Sankey 1997 is a critical discussion of Kuhn’s views on scientific progress and rationality. Newton-Smith 1981 provides an extensive critical development of Kuhn’s and Paul Feyerabend’s views on progress and rationality. Dilworth 2007 is an excellent source that clarifies many aspects of Feyerabend’s views on incommensurability and progress. Zheng 1988 attempts to illustrate incommensurability through a comparison of Western and Chinese medicine. Soler, et al. 2008 collects papers and commentaries discussing a range of consequences of incommensurability with respect to the nature of scientific progress, rationality, and realism. Stanford 2006 breathes new life into discussions of scientific progress and rationality that are critical of contemporary scientific realism based on a more hermeneutic historiographical approach.

  • Dilworth, Craig. Scientific Progress: A Study Concerning the Relation between Successive Scientific Theories. 4th ed. Dordrecht, The Netherlands: Reidel, 2007.

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    Originally published in 1981. Includes a detailed discussion of Gestalt metaphor.

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  • Laudan, Larry. Progress and Its Problems: Toward a Theory of Scientific Growth. Berkeley: University of California Press, 1977.

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    Develops provocative views on a range of related topics, including scientific revolutions, incommensurability, scientific progress, and the interrelated roles of philosophy and sociology of science. On incommensurability, see especially chapter 4, pp. 121–154.

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  • Newton-Smith, William Herbert. The Rationality of Science. London: Routledge and Kegan, 1981.

    DOI: 10.4324/9780203317211Save Citation »Export Citation »E-mail Citation »

    Introduction to the philosophy of science from a moderate rationalist perspective. Examines Karl Popper, Kuhn, Imre Lakatos, and Feyerabend. On incommensurability, see especially chapter 7, “Theories Are Incommensurable?” pp. 148–182.

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  • Pearce, David. “Research Traditions, Incommensurability, and Scientific Progress.” Journal for General Philosophy of Science 15 (1984): 261–271.

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    Argues against Larry Laudan, who rejects the problem of incommensurability in science.

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  • Sankey, Howard. Rationality, Relativism, and Incommensurability. Avebury Series in Philosophy. Aldershot, UK: Ashgate, 1997.

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    See especially “Part II: Incommensurability,” pp. 19–80, and “Part IV: Rationality,” pp. 123–146.

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  • Soler, Léna, Howard Sankey, and Paul Hoyningen-Huene, eds. Rethinking Scientific Change and Theory Comparison: Stabilities, Ruptures, Incommensurabilities? Boston Studies in the Philosophy of Science 255. Dordrecht, The Netherlands: Springer, 2008.

    DOI: 10.1007/978-1-4020-6279-7Save Citation »Export Citation »E-mail Citation »

    Collection of essays analyzing scientific change and stability, focusing on history and philosophy of science. Contributors include Alexander Bird, Aristides Baltas, Eric Oberheim, Anouk Barberousse, Igor Ly, Stephan Hartmann, Edward Jurkowitz, Bernard D’Espagnat, Marcel Weber, Robert Nola, Steve Clarke, Hervé Twirn, Soazig Le Bihan, Rom Harré, Mauricio Suárez, Paul Teller, Ronald N. Giere, Martin Carrier, Michel Bitbol, Thomas Nickles, Emiliano Trizio, and the editors.

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  • Stanford, P. Kyle. Exceeding Our Grasp: Science, History, and the Problem of Unconceived Alternatives. Oxford: Oxford University Press, 2006.

    DOI: 10.1093/0195174089.001.0001Save Citation »Export Citation »E-mail Citation »

    On incommensurability, see p. 22. Critical of scientific realism in light of transient underdetermination as evidenced by the historical record.

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  • Zheng, Lan. “Incommensurability and Scientific Rationality.” International Studies in the Philosophy of Science 2 (1988): 227–236.

    DOI: 10.1080/02698598808573316Save Citation »Export Citation »E-mail Citation »

    Discusses the reception of Kuhn and Feyerabend on incommensurability in China.

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Incommensurability and Reference

Thomas S. Kuhn’s and Paul Feyerabend’s claims about incommensurable theories were widely misunderstood as suggesting that incommensurable theories cannot be rationally compared (see also Incommensurability and Relativism and Against Incommensurability). For example, according to Putnam 1981, incommensurability is the thesis that terms used in another culture, for instance, “temperature” as used by a 17th-century scientist, cannot be equated in meaning and reference with any terms or expressions that we now possess. On this basis, Hilary Putnam concludes that the incommensurability thesis is “self-refuting,” as to claim that Galileo has concepts incommensurable with ours and then to describe those concepts at length is “totally incoherent.” In response to Kuhn’s and Feyerabend’s claims about incommensurability in science, one popular strategy is to admit that theory change does indeed involve meaning change while attempting to undermine undesirable antirealist implications of incommensurability on the basis of casual theories of reference. The basic idea is that even when there is radical meaning change in the course of revolutionary scientific advance, reference to the same objects suffices to secure the possibility of objective theory comparison based on empirical evidence. In this way meaning change can be remedied with scientific realist conceptions of progress as improved approximation to truth. See, for example, Scheffler 1982 (originally published in 1967), which concludes that meaning variance is insufficient to prevent rational theory comparison. Martin 1971 defends and develops Israel Scheffler’s views, concluding that even reference variance can be compatible with objective theory choice. Kitcher 1982 also reconstructs incommensurability on the basis of meaning and reference and argues that reference to the same objects suffices for rational theory comparison. Sankey 1994 (also cited under On Thomas S. Kuhn’s Incommensurability) develops a casual-descriptivist theory of reference designed to meet the challenges incommensurability poses for scientific realism. Nola and Kroon 2001 reviews developments in a range of approaches to reference and theoretical terms in light of incommensurability. Wolf 2007 argues that the causal theory of reference does not alleviate the challenges posed by incommensurability.

Incommensurability and Reductionism

Feyerabend 1962 (also cited in Paul Feyerabend on Incommensurability) uses incommensurability to attack logical empiricist models of theory reduction, according to which reduction is accomplished by deduction. According to such conceptions of scientific progress, the superseded theory is thereby shown to be a special case of the newer, improved version of it, which explains why it was empirically successful while less approximately true than its successor. Paradigmatic examples of such progress purportedly include the transitions from classical mechanics and phenomenological thermodynamics to relativity theory and statistical thermodynamics, respectively. Paul Feyerabend, in contrast, repeatedly emphasizes that the concepts (such as mass, time, space) of universal theories (such as Newtonian mechanics) have “no logical relations” to their corresponding “incommensurable” counterparts in the general theory of relativity, which replaced (not improved on) Newtonian concepts (not instrumentally but realistically interpreted, that is, with respect to the conception of reality that they suggest). But even incommensurable theories can be tested against their own predictions, which can serve as an indirect crucial experiment between them. Feyerabend’s paradigmatic example was Albert Einstein’s calculations of the statistical properties of Brownian motion, which when confirmed served as the basis for an “indirect crucial experiment” between energeticist and atomistic worldviews. The standard source for logical empiricist models of reduction is Nagel 1979. Teller 1980 reviews major issues related to incommensurability and theory reduction. Pearce 1986 is on Wolfgang Stegmüller and the structuralist view of theories. More specifically, David Pearce discusses Stegmüller’s challenge to the orthodox view of theory reduction as logical derivation, according to which reduction is impossible for incommensurable theories.

  • Feyerabend, Paul. “Explanation, Reduction, and Empiricism.” In Scientific Explanation, Space, and Time. Edited by Herbert Feigl and Grover Maxwell, 28–97. Minnesota Studies in the Philosophy of Science 3. Minneapolis: University of Minnesota Press, 1962.

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    Reprinted in significantly revised form in Feyerabend 1981b, pp. 33–96 (cited under Paul Feyerabend on Incommensurability). The theory of meaning underwriting Feyerabend’s use of incommensurability in this paper is explicitly part of an immanent criticism of logical empiricism, as Ernest Nagel accepts that the meanings of theoretical terms are determined by the theories to which they belong.

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  • Nagel, Ernest. The Structure of Science: Problems in the Logic of Scientific Explanation. 2d ed. Indianapolis: Hackett, 1979.

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    Classic source for a logical empiricist conception of reduction and explanation against which Feyerabend argued in Feyerabend 1962 on the basis of incommensurability. Originally published in 1961. Second edition 1966.

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  • Pearce, David. “Incommensurability and Reduction Reconsidered.” Erkenntnis 24 (1986): 293–308.

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    Discusses Stegmüller’s attempt to modify customary usage of “reduction” and “incommensurability,” attempting to provide a rationalist account of scientific progress through scientific revolutions. Shows how Stegmüller defends Thomas S. Kuhn against charges of subjectivity and irrationality.

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  • Teller, Paul. “Yoshida’s Reduction in the Sciences.” Nous 14 (1980): 136–140.

    DOI: 10.2307/2214904Save Citation »Export Citation »E-mail Citation »

    Bibliography offers a concise selection of reliable resources.

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Incommensurability, Translation, and Communication

Thomas S. Kuhn’s views on incommensurability and translation changed. Kuhn initially took translation as a potential way to resolve incommensurability (for example, in Kuhn 1996, cited in Thomas S. Kuhn on Incommensurability) before later deciding that translation is exactly what cannot bridge the gap between incommensurable theories; see Kuhn 1999. Carrier 2001 reconstructs Kuhn’s conception of incommensurability and translation, illustrating why incommensurable theories are untranslatable on the basis of well-explained examples. Davidson 2001 (also cited in Against Incommensurability) is an influential paper on translation and comprehensibility critical of the idea of incommensurability. Sankey 1991 offers a critical discussion of Kuhn on incommensurability and untranslatability. Favretti, et al. 1999 collects a range of papers on many interrelated topics, providing a rich source of interesting discussions and further references. Murthi and Sarukkai 2009 investigates the concept of a scientific language and the process of symbolization in the context of Kuhn’s incommensurability as based on meaning variance and lexical cross-classification resulting in the impossibility of translation of terms from incommensurable theories. Harris 2005 develops incommensurability as a problem concerning argumentation and dialogue, highlighting many uses of “incommensurable” while discussing the implications of incommensurability as a rhetorical phenomenon.

  • Carrier, Martin. “Changing Laws and Shifting Concepts: On the Nature and Impact of Incommensurability.” In Incommensurability and Related Matters. Edited by Paul Hoyningen-Huene and Howard Sankey, 65–90. Boston Studies in the Philosophy of Science 216. Dordrecht, The Netherlands: Kluwer Academic, 2001.

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    Discusses cross-classification of scientific kinds as the basis of the untranslatability of scientific theories.

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  • Davidson, Donald. “On the Very Idea of a Conceptual Scheme.” In Inquiries into Truth and Interpretation. 2d ed. By Donald Davidson, 183–198. Oxford: Clarendon, 2001.

    DOI: 10.1093/0199246297.003.0013Save Citation »Export Citation »E-mail Citation »

    Presidential address, Seventieth Annual Eastern Meeting of the American Philosophical Association in Atlanta, 28 December 28, 1973. Originally published in Proceedings and Addresses of the American Philosophical Association 47 (1973–1974): 5–20. Argues that the distinction between conceptual scheme and content is a third dogma of empiricism.

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  • Favretti, Rema Rossini, Giorgio Sandri, and Roberto Scazzieri, eds. Incommensurability and Translation: Kuhnian Perspectives on Scientific Communication and Theory Change. Cheltenham, UK: Edward Elgar, 1999.

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    See Part 1, “Incommensurability, Translation, and Theory Change.” Parts 2, 3, and 4 are “Communicating Science,” “Cognition and Formal Reconstruction,” and “Lexicon and Semantics,” respectively. Contributors include Kuhn, Maria Luisa Altieri Biagi, Eva Picardi, Timothy S. McDermott, Michael A. K. Halliday, Enrico Arcaini, Vivenza, Vilks, Pera, Raccah, Petroni, Viale, Boudon, Maki, Festa, Galavotti, Gambetta, Vercelli, Zamagni, Sinclair, Scalise, Casadio, Weinberger, and Giorgio Sandri.

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  • Harris, Randy Allen, ed. Rhetoric and Incommensurability. West Lafayette, IN: Parlor Press, 2005.

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    Contributions on rhetoric, history, and philosophy of science by eleven authors: Paul Hoyningen-Huene, Alan G. Gross, Thomas M. Lessl, Herbert W. Simons, Leah Ceccarelli, Lawrence J. Prelli, John Angus Campbell, Jeanne Fahnestock, Charles Bazerman, Rene Agustin De los Santos, and Carolyn R. Miller.

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  • Kuhn, Thomas S. “Remarks on Incommensurability and Translation.” In Incommensurability and Translation: Kuhnian Perspectives on Scientific Communication and Theory Change. Edited by Rema Rossini Favretti, Giorgio Sandri, and Roberto Scazzieri, 33–37. Cheltenham, UK: Edward Elgar, 1999.

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    Explains how Kuhn initially took translation as a potential way to resolve incommensurability (for example, in Kuhn 1996, cited in Thomas S. Kuhn on Incommensurability, originally published 1962) before deciding that translation cannot bridge the gap between incommensurable theories in later publications.

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  • Murthi, S. K. Arun, and Sundar Sarukkai. “Multisemiosis and Incommensurability.” International Studies in the Philosophy of Science 23 (2009): 297–311.

    DOI: 10.1080/02698590903197773Save Citation »Export Citation »E-mail Citation »

    Argues that there are interesting overlaps concerning incommensurability and the problem of meaning associated with multisemiosis.

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  • Sankey, Howard. “Incommensurability, Translation, and Understanding.” Philosophical Quarterly 41 (1991): 414–426.

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    Provides relevant references on the referential response to incommensurability, including Michael Devitt, Field, Philip Kitcher, Michael Martin, Hilary Putnam, and Israel Scheffler.

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Incommensurability and Relativism

Incommensurability is often taken to imply some form of relativism as it challenges the total objectivity of truth, allowing for different truths from different worldviews. For example, Barnes 1982 develops Thomas S. Kuhn as endorsing a form of relativism. For some general background on relativism, see Goodman 1978 and for more recent developments the papers collected in Mazzotti 2008. Siegel 1980 is a review article that walks the reader through several different facets of the early reception of Kuhn and Paul Feyerabend, who are often understood as promoting some form of epistemic relativism based on the misconception that incommensurability implies either incomparability or incommunicability (see also Against Incommensurability). Goldberg and Rellihan 2008 responds to challenges to the coherence of the idea of incommensurability in science as delineated, for example, by Donald Davidson and Richard Rorty. Sankey 1997 is focused on Kuhn’s conception of incommensurability and its implications for rationality and relativism. Malone 1993 develops Kuhn on incommensurability while attempting to avoid the pitfalls of relativism.

Incommensurability and Evolutionary Epistemology

Incommensurability is directly connected to evolutionary epistemology in Thomas S. Kuhn’s historical philosophy. Kuhn uses incommensurability to argue against scientific realist conceptions of progress in science in favor of an evolutionary epistemology, itself partly explicated in terms of incommensurability. Kuhn 1996, pp. 172–173 (cited in Thomas S. Kuhn on Incommensurability) draws analogies between scientific advance and biological evolution. In “Postscript-1969,” added to the enlarged 1970 edition of Kuhn 1996, Kuhn insists that the evolutionary analogy fits perfectly with respect to the adaptive, punctuating process he describes in chapter 12 (the resolution of scientific revolutions) as a process of selection (through conflict within the scientific community) of the fittest way to practice science in which what counts as legitimate science evolves together with current scientific theories, methods, and standards. (See also Methodological Incommensurability.) Scientific progress is explained as adaptation away from anomaly, in contrast to teleological scientific realist conceptions of scientific progress as a process directed toward some preset truth (see also Incommensurability and Historiography of Science). The basic idea is that the entire process may have occurred like biological evolution––that is, without a preset or fixed goal (such as truth) that each new phase in the development of science purportedly (retrospectively) better approximates. Moreover, in later publications, such as Kuhn 2000, pp. 94–99 (cited in Thomas S. Kuhn on Incommensurability), Kuhn reaffirms his evolutionary approach and expands specifically on the functional analogy between the role of incommensurability in scientific evolution through revolutions that result in splitting into contemporaneous incommensurable subdisciplines and the role of isolating mechanisms (such as reproductive barriers) in evolution through speciation. Biagioli 1990 critically discusses Kuhn’s evolutionary analogy on the basis of a historical case study on Galileo and the Copernican hypothesis. Renzi 2009 attempts to criticize Kuhn’s evolutionary approach, and Reydon and Hoyningen-Huene 2010 responds to Renzi 2009, arguing that it attacks a straw man. Barrett 2010 considers the evolution of incommensurable languages in the context of signaling games, illustrating how meaningful language may evolve from initially meaningless random signals and then into incommensurable languages. For some general background on evolutionary epistemology, see Bradie and Harms 2008. For some historical setting concerning the evolutionary analogy, see, for example, Popper 1979. See also Einstein and Infeld 1938, aptly named The Evolution of Physics, which claims that nearly every great advance in science has arisen out of a crisis in the older theory through an endeavor to find a way out of difficulties and that suggests world change through revolution as an evolution driven by such crisis. Cziko and Campell 1997 provides a range of references on evolutionary epistemology in an online bibliography that helpfully links sources directly to some quotes contained in them about scientific advance as an evolutionary process.

Against Incommensurability

For a number of reasons, incommensurability is often taken to imply incomparability, incommunicability, and even some form of irrationality (see also Incommensurability and Relativism and Incommensurability, Translation, and Communication). For example, the idea that different theories (worldviews, paradigms, languages) are incommensurable may seem to imply incomparability on the assumption that rational comparison is possible only on the basis of a shared common measure. A number of critical discussions have suggested that the idea of incommensurability is incoherent, self-refuting, or otherwise untenable. Davidson 2001, for example, is often taken to provide an argument against the very idea of incommensurability; see for example, Douven and De Regt 2002. Putnam 1981 infamously challenged the coherence of both Thomas S. Kuhn and Paul Feyerabend on the idea of incommensurability in science, asserting that they had proposed a self-refuting thesis. Devitt 2010 also argues directly against incommensurability as implying incomparability (see also Devitt 1979). Musgrave 1979 argues that incommensurability is the erroneous consequence of mistaken assumptions. Rorty 2008 reviews the reception of Kuhn on incommensurability couched in a discussion about the inherent tension between epistemology and hermeneutics.

  • Davidson, Donald. “On the Very Idea of a Conceptual Scheme.” In Inquiries into Truth and Interpretation. 2d ed. By Donald Davidson, 183–198. Oxford: Clarendon, 2001.

    DOI: 10.1093/0199246297.003.0013Save Citation »Export Citation »E-mail Citation »

    Often-cited presidential address, Seventieth Annual Eastern Meeting of the American Philosophical Association in Atlanta, 28 December 1973. Originally published in Proceedings and Addresses of the American Philosophical Association 47 (1973–1974): 5–20.

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  • Devitt, Michael. “Against Incommensurability.” Australasian Journal of Philosophy 57 (1979): 29–50.

    DOI: 10.1080/00048407912341021Save Citation »Export Citation »E-mail Citation »

    Argues that Kuhn and Feyerabend were wrong to suggest that incommensurable theories cannot be rationally compared.

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  • Devitt, Michael. “Incommensurability and the Priority of Metaphysics.” In Putting Metaphysics First: Essays on Metaphysics and Epistemology. By Michael Devitt, 99–116. New York: Oxford University Press, 2010.

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    Reprinted from Paul Hoyningen-Huene and Howard Sankey, eds., Incommensurability and Related Matters (Dordrecht, The Netherlands: Kluwer Academic, 2001), pp. 143–158. Argues that scientific realist metaphysics is more secure than the semantic speculations and epistemic skepticism purportedly underlying the idea of incommensurability (understood as implying rational incomparability of scientific theories). Responds to the meta-incommensurability thesis.

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  • Douven, Igor, and Henk W. De Regt. “A Davidsonian Argument against Incommensurability.” International Studies in the Philosophy of Science 16 (2002): 157–169.

    DOI: 10.1080/02698590220145098Save Citation »Export Citation »E-mail Citation »

    Discusses the Davidsonian charge that Kuhn’s and Feyerabend’s conceptions of incommensurability in science are incoherent. Defends incommensurability from Donald Davidson’s criticism.

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  • Musgrave, Alan. “How to Avoid Incommensurability.” Acta Philosophica Fennica 30 (1979): 336–346.

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    Critical discussion of incommensurability as implying incomparability.

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  • Putnam, Hilary. Reason, Truth, and History. Cambridge, UK: Cambridge University Press, 1981.

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    For Feyerabend’s response to Putnam, see the discussion in Paul Feyerabend, “Putnam on Incommensurability,” British Journal for the Philosophy of Science 38 (1987): 75–81.

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  • Rorty, Richard. Philosophy and the Mirror of Nature. Princeton, NJ: Princeton University Press, 2008.

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    Originally published in 1979. For Rorty on incommensurabilty, see especially pp. 316, pp. 322–333.

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Incommensurability, Theory, and Observation

The relation between theory and observation is a central component of contemporary empiricism, according to which science is rational because (or to the extent that) disputes are decided upon the basis of the available empirical evidence. This section is divided into two subsections. The first subsection provides references to primary literature by Thomas S. Kuhn and Paul Feyerabend on incommensurability and observation as well as detailed critical reconstructions of their respective views on observation and its relation to scientific theory. The second subsection provides a few milestones in the secondary literature specifically focused on incommensurability and the theory-ladenness of observation as well as some standard background material leading up to contentious, continuing discussions of a controversial topic.

Thomas S. Kuhn and Paul Feyerabend on Incommensurability and Observation

Kuhn 1996 and Kuhn 2000 suggest that scientific revolutions involve transitions between incommensurable paradigms that reshape observations according to conceptual categories. Kuhn 1996 compares the experience of a historian of science relearning the concepts of our Aristotelian heritage to those of individual scientists making revolutionary progress in natural sciences, suggesting that both can involve something similar to a Gestalt switch––like the geometrical figure on the cover of the second edition of Kuhn 1996 or Joseph Jastrow’s infamous duck/rabbit in Ludwig Wittgenstein’s influential Philosophical Investigations (New York: Macmillan, 1953). For general introductions to Thomas S. Kuhn on incommensurability and observation, see and compare Hoyningen-Huene 1993 and Bird 2000. Paul Feyerabend develops and defends a causal theory of observation in earlier papers, such as “An Attempt at a Realistic Interpretation of Experience” (Feyerabend 1958), which argues that the interpretation of an observation language is determined by the theories that we use to explain what we observe and it changes as soon as those theories change. Feyerabend 1981 develops incommensurability on the basis of such a causal theory of observation, according to which theories are not interpreted on the basis of independently fixed or given experiences (for example, according to classical empiricism) but rather experiences are reinterpreted on the basis of improving scientific theories. Feyerabend concludes that while observation language does not provide a neutral basis for staging crucial experiments between incommensurable rivals, no such neutral basis is required. Many of these and related issues are discussed in detail in Feyerabend 1981b, cited in Paul Feyerabend on Incommensurability, which collects some of his early papers (often in deceptively revised form). For introductions to Feyerabend on incommensurability and observation, compare Preston 1997 (also cited under On Paul Feyerabend’s Incommensurability) and Oberheim 2006.

  • Bird, Alexander. Thomas Kuhn. Princeton, NJ: Princeton University Press, 2000.

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    On observation and incommensurability, see especially chapter 3.

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  • Feyerabend, Paul. “An Attempt at a Realistic Interpretation of Experience.” Proceedings of the Aristotelian Society, n.s., 58 (1958): 143–170.

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    Feyerabend defends a causal or pragmatic theory of observation; see especially pp. 146–147.

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  • Feyerabend, Paul. “Explanation, Reduction, and Empiricism.” In Realism, Rationalism, and Scientific Method. Philosophical Papers 1. Edited by Paul Feyerabend, 44–96. Cambridge, UK: Cambridge University Press, 1981.

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    Original version published in 1962 (see Feyerabend 1962, cited under Paul Feyerabend on Incommensurability). Feyerabend developed a causal or pragmatic theory of observation across a wide range of early papers, explicitly following René Descartes, John Locke, Bertrand Russell, Rudolf Carnap, and Otto Neurath.

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  • Hoyningen-Huene, Paul. Reconstructing Scientific Revolutions: Thomas S. Kuhn’s Philosophy of Science. Translated by Alexander T. Levine. Chicago: University of Chicago Press, 1993.

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    With a foreword by Thomas S. Kuhn. An English translation of a slightly expanded Die Wissenschaftsphilosophie Thomas S. Kuhns: Rekonstruktion und Grundlagenprobleme (Brunswick, Germany: Vieweg, 1989). On Kuhn on perception, see pp. 83–89. For a discussion and further references to Kuhn’s use of the Gestalt metaphor, see pp. 38–63.

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  • Kuhn, Thomas S. The Structure of Scientific Revolutions. 3d ed. Chicago: University of Chicago Press, 1996.

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    Originally published in 1962 (two first editions). Part of the series International Encyclopedia of Unified Science, edited by Otto Neurath, and collected in Otto Neurath, Rudolf Carnap, and Charles Morris, eds., Foundations of the Unity of Science, Vol. 2, no. 2. Second enlarged edition published in 1970. On incommensurability and observation, see, for example, pp. 102, 111, 118, 150. For the analogy to a Gestalt switch, see p. 204.

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  • Kuhn, Thomas. S. The Road since Structure: Philosophical Essays, 1970–1993, with an Autobiographical Interview. Edited by James Conant and John Haugeland. Chicago: University of Chicago Press, 2000.

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    On Kuhn’s views on observation, kinds, and incommensurability, see, for example, chapter 8, “Metaphor in Science,” pp. 196–207, originally published in 1979. See also p. 242 for some explicit reservations about particular aspects of the Gestalt metaphor.

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  • Oberheim, Eric. Feyerabend’s Philosophy. New York: de Gruyter, 2006.

    DOI: 10.1515/9783110891768Save Citation »Export Citation »E-mail Citation »

    For Feyerabend on incommensurability and observation, see pp. 49–52 and 125–127, which provide further references to Feyerabend and critically discusses Preston 1997. For references to Feyerabend’s use of the Gestalt switch metaphor, see p. 44.

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  • Preston, John. Feyerabend: Philosophy, Science, and Society. Cambridge, UK: Polity Press, 1997.

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    On observation and incommensurability, see especially chapter 3, “Theories of Observation,” pp. 40–60, and chapter 6, “Incommensurability,” pp. 99–123.

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Incommensurability and Theory-Ladenness of Observation

Methodologically, Thomas S. Kuhn and Paul Feyerabend were following Duhem 1991, cited under Historical Background (originally published in French in 1906), which is a classic source on physical theory with respect to the roles of experiment and observation, transient underdetermination, and what has been recast as “the problem of unconceived alternatives” (Stanford 2006, cited under Incommensurability, Progress, and Rationality). Specifically on the theory-ladenness of observation, Kuhn and Feyerabend were also following Köhler 1938 (originally published in 1920), Hanson 1958, and Fleck 1986 (which collects essays originally published in 1927–1960). For some relevant philosophical background on the theory-ladenness of observation, compare Wittgenstein 2009 (originally published in 1953). Wolfgang Köhler was an influential Gestalt psychologist who suggested that the concepts of physics and psychology are “incommensurable.” Ludwik Fleck, as a forerunner of Kuhn, encouraged sociological investigation of scientific change. In a paper collected in Fleck 1986, Ludwik Fleck suggests that scientific concepts are incommensurable. His sociological comparative epistemology examines the generation and transmission of scientific observations and psychological gestalts in the process of concept formation (see also Historical Background). Kordig 1971 critically discusses Kuhn’s, Feyerabend’s, Norwood R. Hanson’s, and Stephen Toulmin’s views on the theory-ladenness of observation. Gale and Walter 1973 is an informative discussion that reviews responses to major positions and arguments about the theory-ladenness of observation. Zahar 1982 reviews Feyerabend’s early papers (1958–1977) on observation and empirical content and offers a critical comparison to Imre Lakatos. McEvoy 1975 (also cited in On Paul Feyerabend’s Incommensurability) offers a detailed critical discussion of incommensurability and the theory-ladenness of observation.

  • Cohen, Robert, and Schnelle, Thomas, eds. Cognition and Fact: Materials on Ludwik Fleck. Boston Studies in the Philosophy of Science 87. Boston: Reidel, 1986.

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    Collects many relevant papers. See, for example, “Scientific Observation and Perception in General” (1935), pp. 59–78; and “To Look, to See, to Know” (1947), pp. 129–152. See pp. 44–45 for Fleck using the term “incommensurable” applied to scientific concepts. Part 3 contains papers on Fleck by Rotenstreich, Jerzy Giedymin, Wolniewicz, Markiewicz, Thomas Schnelle, Stephen Toulmin, Heelna, Elkana, Wittich, Steven Shapin, David Bloor, Zalc, Moulin, Löwy.

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  • Gale, George, and Edward Walter. “Kordig on the Theory-Ladenness of Observation.” Philosophy of Science 40 (1973): 415–432.

    DOI: 10.1086/288544Save Citation »Export Citation »E-mail Citation »

    Discussion with an overview of main topics. Provides a good selection of further resources.

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  • Hanson, Norwood Russell. Patterns of Discovery: An Inquiry into the Conceptual Foundations of Science. Cambridge, UK: Cambridge University Press, 1958.

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    Norwood Russell Hanson (b. 1924–d. 1967) argued that observation is not neutral sensory input but is filtered by preconceptions and consequently that observation is theory laden. Distinguishes “seeing as” and “seeing that” in pursuit of a logic of scientific discovery based on C. S. Peirce’s conception of abduction.

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  • Köhler, Wolfgang. “Physical Gestalten.” In A Source Book of Gestalt Psychology. Edited by Willis D. Ellis, 17–54. London: Kegan, 1938.

    DOI: 10.1037/11496-000Save Citation »Export Citation »E-mail Citation »

    Translation of an excerpt originally published in German in Köhler’s Die Physischen Gestalten in Ruhe und in stationärem Zustand, Eine naturphilosophische Untersuchung (Brunswich, Germany: Vieweg, 1920). Compare Feyerabend’s discussion of incommensurability in his formulation of the mind-body problem in “Materialism and the Mind-Body Problem,” Review of Metaphysics 17 (1963): 49–66.

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  • Kordig, Carl R. “Theory-Ladenness of Observation.” Review of Metaphysics 24 (1971): 448–484.

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    Good source for detailed discussion and further references.

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  • McEvoy, John. “A ‘Revolutionary’ Philosophy of Science: Feyerabend and the Degeneration of Critical Rationalism into Sceptical Fallibilism.” Philosophy of Science 42 (1975): 49–66.

    DOI: 10.1086/288620Save Citation »Export Citation »E-mail Citation »

    Review and critical discussion of major issues, including incommensurability and theory-ladenness of observation.

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  • Wittgenstein, Ludwig. Philosophical Investigations. 4th ed. Edited by P. M. S. Hacker and Joachim Schulte. Oxford: Wiley-Blackwell, 2009.

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    Philosophical Investigations (PI) was originally published posthumously in 1953 in two parts. See PI 11 193e–214e. Part 1 has 693 numbered paragraphs prepared for printing in 1946 (rescinded by Wittgenstein). Part 2 was added by the editors of the 1953 edition, G. E. M. Anscombe and Rush Rhees.

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  • Zahar, Elie. “Feyerabend on Observation and Empirical Content.” British Journal for the Philosophy of Science 33 (1982): 397–408.

    DOI: 10.1093/bjps/33.4.397Save Citation »Export Citation »E-mail Citation »

    Detailed discussion that provides a good selection of further resources, especially concerning Feyerabend on observation and empirical content.

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Incommensurability and Historiography of Science

Kuhn 1977 explains how incommensurability became the main methodological tool of the new historiography of science. According to Kuhn 1996, pp. 137–138 (cited in Thomas S. Kuhn on Incommensurability), for obvious and highly functional reasons science textbooks (and all too many older histories of science) typically select the parts of past scientists’ work that are easily explained as contributions to the same problems solved by the current paradigm. In this way scientists of earlier ages are implicitly misrepresented as having worked upon the same fixed set of problems according to the same fixed set of canons that the most recent scientific revolution has made seem scientific. As scientific textbooks are rewritten after scientific revolutions, the history of science is rewritten from the current perspective, so that science once again seems largely cumulative. In fact, however, it is not, as changes in both scientific theory and scientific method redefine what counts as scientific. The new historiography uses a hermeneutic historiographical method in an attempt to recast scientific development as it actually transpires. Hoyningen-Huene 1993 reconstructs the historical development of “pure” (as opposed to “applied”) natural science as the topic of Thomas S. Kuhn’s philosophy of science and explains its relation to the hermeneutic methods used in the new historiography of science. Horwich 1993 collects a number of papers relevant to incommensurability and historiography of science. For some in-depth background on hermeneutic historiography and the history of historiography, see especially Collingwood 1993. Fu 1995 develops higher incommensurability on the basis of taxonomic differences between Thomas Hobbes’s (in a tradition including René Descartes, Christian Huygens, and Gottfried Wilhelm Leibniz) and Robert Boyle’s (in the Newtonian tradition) classifications of science and how these incommensurable classifications of science affected their respective interpretations of the comparative merits of a range of experimental results. Gooding 1989 offers a review of a wide range of authors’ contributions to related topics.

  • Collingwood, Robin George. The Idea of History. Rev. ed. Edited by Jan Van der Dussen. Oxford: Clarendon, 1993.

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    Classic source on the history of historiography and the philosophy of history. New introduction by the editor. Originally published in 1946.

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  • Fu, Daiwie. “Higher Taxonomy and Higher Incommensurability.” Studies in History and Philosophy of Science A 26 (1995): 273–294.

    DOI: 10.1016/0039-3681(95)00002-5Save Citation »Export Citation »E-mail Citation »

    Begins with a detailed discussion of the Hacking 1993 (cited in Taxonomic Incommensurability) reconstruction of Kuhn’s taxonomic incommensurability. On higher incommensurability, compare Kuhn 2000, for example, pp. 234–237 (cited under Thomas S. Kuhn on Incommensurability).

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  • Gooding, David. “How to Be a Good Empiricist.” British Journal for the History of Science 22 (1989): 419–427.

    DOI: 10.1017/S0007087400026364Save Citation »Export Citation »E-mail Citation »

    Reviews individual contributions to two edited volumes: Arthur L. Donovan, Larry Laudan, and Rachel Laudan, eds., Scrutinizing Science: Empirical Studies of Scientific Change (Dordrecht, The Netherlands: Kluwer Academic, 1988), and Diderik Batens and Jean Paul van Bendegem, eds., Theory and Experiment: Recent Insights and New Perspectives on Their Relation (Dordrecht, The Netherlands: Reidel, 1988).

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  • Horwich, Paul, ed. World Changes: Thomas Kuhn and the Nature of Science. Cambridge, MA: MIT Press, 1993.

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    Kuhn responds to the papers collected in this volume in “Afterwards,” pp. 311–341. Contributors include Horwich, Carl G. Hempel, John Earman, Michael Friedman, Ernan McMullin, J. L. Heilbron, N. M. Swerdlow, Ian Hacking, and Kuhn.

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  • Hoyningen-Huene, Paul. Reconstructing Scientific Revolutions: Thomas S. Kuhn’s Philosophy of Science. Translated by Alexander T. Levine. Chicago: University of Chicago Press, 1993.

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    Originally published in German in 1987. On Kuhn and the new historiography of science, see especially chapter 1, pp. 3–24.

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  • Kuhn, Thomas S. The Essential Tension: Selected Studies in Scientific Tradition and Change. Chicago: University of Chicago Press, 1977.

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    Kuhn recounts his discovery of incommensurability (pp. ix–xii) to explain why he chose to structure this collection of papers into two parts, “Historiographical Studies” and “Metahistorical Studies.” Kuhn first uses the term “paradigm” in “The Essential Tension: Tradition and Innovation in Scientific Research?” pp. 225–239 (originally published in 1959).

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Historical Background

Thomas S. Kuhn and Paul Feyerabend drew from a number of sources in developing their conceptions of incommensurability in science. This section provides sources that were influential with respect to Kuhn’s and Feyerabend’s development of the idea of incommensurability in science in an attempt to situate the idea into its historical context. Duhem 1991 (originally published in book form in French in 1906) was a major influence on both Kuhn and Feyerabend on incommensurability and is a benchmark with respect to the historical approach to scientific methodology. It is also the standard source on underdetermination of theories by evidence. While Pierre Maurice Marie Duhem clearly anticipates many central components of the idea of incommensurability in science, he does not actually use the term “incommensurable” as applied to science prior to Kuhn and Feyerabend (which is not the case with Ludwik Fleck, Wolfgang Köhler, and Albert Einstein). Kuhn explicitly acknowledges Fleck, a bacteriologist who developed the first explicit sociology of natural science and anticipated many contemporary views about the social construction of knowledge, as a major influence on the development of his ideas. Fleck 1979 calls scientific concepts “incommensurable” in the context of his sociological “comparative epistemology.” (See also Fleck 1986, cited under Incommensurability and Theory-Ladenness of Observation.) Fleck argued that the old concept of “disease” became incommensurable with the new concept, which initially was not completely adequate as a replacement for it. Babich 2003 is just one of many papers comparing Kuhn and Fleck more generally. Another precursor to Kuhn and Feyerabend on incommensurability in science is the often overlooked Polanyi 1974; on Michael Polayni’s contribution to the idea of incommensurability in science, see Jacobs 2002. Both Feyerabend and Kuhn were also directly influenced by Wolfgang Köhler, a cofounder of Gestalt psychology who had already used the term “incommensurable” to describe the relationship between the concepts of psychology and physics in Köhler 1938. Yet another major influence on Kuhn and Feyerabend was Einstein. Einstein 1951 uses “incommensurable” to describe the challenges involved in theory choice, given empirical underdetermination, in his discussion of attempting to weigh the comparative merits of quantum theory and relativity theory. More generally, see also Einstein and Infeld 1938, cited in Incommensurability and Evolutionary Epistemology, which claims that nearly every great advance in science has arisen out of a “crisis” in the older theory through an endeavor to find a way out of difficulties and suggests “world change” through “revolution” as an “evolution” driven by such crisis. Oberheim and Hoyningen-Huene 2009 is a brief introduction to a selection of some major influences on Kuhn and Feyerabend with respect to incommensurability.

LAST MODIFIED: 06/26/2012

DOI: 10.1093/OBO/9780195396577-0022

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