Chapter 11: Incommensurability

In The Structure of Scientific Revolutions, Kuhn introduced the idea of incommensurability through a series of interconnected claims about paradigm change. The term itself is borrowed from mathematics, where two quantities are incommensurable if they have no common measure (as the side and diagonal of a square are incommensurable in the sense that their ratio is irrational). By analogy, Kuhn claimed that successive paradigms lack a common measure — a neutral standard against which they can be compared.

Kuhn identified three dimensions of incommensurability in his early work:

• Standards and values: Different paradigms may differ about what problems are important, what counts as a solution, and what standards a solution must meet. The Aristotelian physicist sought teleological explanations of motion (in terms of natural places); the Newtonian physicist sought mechanical explanations (in terms of forces and accelerations). These are not just different answers to the same question but different conceptions of what the question is.
• Perception and world-view: Scientists working in different paradigms literally see the world differently. The Aristotelian sees a constrained body that gradually comes to rest; the Newtonian sees a body approaching zero velocity under the influence of friction. These are different perceptions of the same physical event, shaped by different theoretical frameworks.
• Concepts and meanings: The key terms of scientific theories change meaning from one paradigm to the next. “Mass,” “space,” “time,” “element,” “planet” — all these terms mean different things in different paradigms, making direct comparison and translation impossible.

“The proponents of competing paradigms practice their trades in different worlds. One contains constrained bodies that fall slowly, the other pendulums that repeat their motions again and again. In one, solutions are compounds, in the other mixtures. Neither is wrong; the two simply describe different situations. But their worlds are not the same.”— Thomas Kuhn, The Structure of Scientific Revolutions (1962), p. 150

Taken together, these three dimensions of incommensurability seem to imply that paradigm choice cannot be rational in the traditional sense. If the standards for evaluating theories change with the paradigm, if the observational evidence is paradigm-dependent, and if the very meanings of theoretical terms shift, then there is no neutral ground from which to compare rival paradigms. The choice between them resembles a conversion experience more than a logical deduction.

Paul Feyerabend developed the concept of incommensurability independently of Kuhn, drawing on different sources and arriving at more radical conclusions. Feyerabend's version focused on meaning variance: the claim that the meanings of theoretical terms are determined by the theories in which they are embedded, so that a change of theory entails a change in the meanings of all terms connected to that theory.

Feyerabend traced this idea to Pierre Duhem and to the later Wittgenstein's thesis that the meaning of a word is determined by its use. If the meaning of “mass” is determined by its role in physical theory, then “mass” in Newtonian mechanics (an intrinsic property of bodies, independent of their velocity) and “mass” in relativistic mechanics (a property that depends on velocity) are different concepts, not the same concept with a different value.

“Introducing a new theory involves changes of outlook both with respect to the observable and with respect to the unobservable features of the world, and corresponding changes in the meanings of even the most ‘fundamental’ terms of the language employed... What does happen is, rather, a complete replacement of the ontology (and perhaps even of the formalism) of the preceding theory by the ontology (and the formalism) of a new theory.”— Paul Feyerabend, “Explanation, Reduction, and Empiricism” (1962), p. 29

Feyerabend drew from this analysis a conclusion that Kuhn resisted: if successive theories are incommensurable, then there can be no logical derivation of one theory from another, and the standard account of scientific progress through theory reduction fails. The Newtonian theory cannot be “reduced” to the relativistic theory (or vice versa) because the terms of the two theories do not mean the same thing. What appears to be a reduction is actually a replacement of one conceptual scheme by another.

Feyerabend went further than Kuhn in two important respects. First, he applied the incommensurability thesis not only to revolutionary theory change but to the relationship between any two sufficiently different theories. Second, he drew explicitly anarchist conclusions: if there are no common standards for comparing theories, then the proliferation of alternative theories (even ones that are “refuted” by current standards) is epistemically valuable because it reveals presuppositions that are invisible from within a single theoretical framework.

The meaning variance thesis is the core of the semantic dimension of incommensurability. It holds that the meanings of scientific terms are theory-dependent: the meaning of “mass” is determined by the theoretical principles governing its use, and since these principles differ between theories, the meaning of “mass” differs as well.

This thesis was challenged by several philosophers. Israel Scheffler argued in Science and Subjectivity (1967) that Kuhn and Feyerabend conflated the meaning of a term with the beliefs associated with it. When we move from Newton to Einstein, our beliefs about mass change (we no longer believe it is velocity-independent), but the reference of “mass” — the property in the world that the term picks out — may remain the same.

Hilary Putnam's causal theory of reference provided further ammunition against the meaning variance thesis. Putnam argued that the reference of natural kind terms like “water” or “gold” is determined not by the descriptions associated with them but by causal-historical chains linking current uses to an original act of naming. On this view, “water” referred to H₂O even before anyone knew its chemical composition, and “mass” in Newton's theory referred to the same physical property as “mass” in Einstein's theory, even though Newton and Einstein had different beliefs about that property.

The debate over meaning variance and reference remains one of the central issues in the philosophy of language as it applies to science. Advocates of the meaning variance thesis argue that the causal theory of reference cannot be straightforwardly applied to theoretical terms, which (unlike natural kind terms) do not pick out their referents ostensively. The question of whether “mass” in Newton's theory and “mass” in Einstein's theory refer to the same property depends on deep questions about the nature of reference, theoretical terms, and the relationship between language and the world.

The concept of mass provides the most discussed example of alleged incommensurability. In Newtonian mechanics, mass is an intrinsic, invariant property of a body — it does not change with the body's velocity, position, or any other variable. In special relativity, mass (at least in one formulation) depends on velocity: a body's relativistic mass increases as it approaches the speed of light, approaching infinity at c.

Are these the same concept or different concepts? The answer depends on one's theory of meaning. On a descriptive or inferential-role theory of meaning (where the meaning of a term is determined by the theoretical principles governing it), Newtonian mass and relativistic mass are different concepts, since they are governed by different principles. On a causal-referential theory (where the meaning of a term is determined by what it refers to in the world), they may be the same concept if they refer to the same physical quantity.

The situation is complicated by the fact that modern physics distinguishes between rest mass (invariant mass) and relativistic mass. Rest mass is velocity-independent, just like Newtonian mass. Many physicists now prefer to use “mass” to mean rest mass exclusively, in which case Newtonian mass and (rest) mass in relativity are more continuous than Kuhn suggested. But this retrospective tidying-up was not available to physicists working through the transition, and it does not resolve the deeper philosophical question about the nature of conceptual change.

“The Newtonian term ‘mass’ and the relativistic term ‘mass’ differ in meaning. The former is a property of an object which is independent of the object's velocity; the latter is not... Newtonian mass is conserved; Einsteinian mass is convertible with energy. Only at low relative velocities may the two be measured in the same way, and even then they must not be conceived to be the same.”— Thomas Kuhn, The Structure of Scientific Revolutions (1962), p. 102

The mass example has been endlessly debated. Critics argue that Kuhn overstates the discontinuity: in the limit of low velocities, relativistic mechanics reduces to Newtonian mechanics, and the two concepts of mass converge. Defenders argue that this mathematical correspondence does not establish conceptual identity, since the same formula can express different concepts in different theoretical contexts. The debate highlights the difficulty of separating questions about formal structure from questions about conceptual content.

In his later work, particularly The Road Since Structure (collected posthumously in 2000), Kuhn reformulated the incommensurability thesis in more precise terms. He abandoned the broad, multidimensional incommensurability of Structure and focused on a narrower, purely semantic version: taxonomic incommensurability.

The key idea is that scientific theories impose taxonomies — systems of classification — on the world. Two theories are incommensurable when their taxonomies cut up the world in ways that cannot be mapped onto each other. This happens when a term that picks out a single kind in one theory corresponds to overlapping or cross-cutting kinds in another.

Kuhn gave the example of the Ptolemaic and Copernican classifications of celestial bodies. In the Ptolemaic system, the Sun was a “planet” (a wandering body) and the Earth was not. In the Copernican system, the Earth became a planet and the Sun became a star. The term “planet” does not simply change its extension from one system to the other; the very criteria for what counts as a planet are reorganized. The Ptolemaic category “planet” cannot be straightforwardly translated into the Copernican vocabulary because it cross-cuts the Copernican categories.

Kuhn formulated what he called the “no-overlap principle”: within any taxonomic scheme, no object can belong to two different kinds at the same taxonomic level unless one is a species of the other. When a new theory violates the no-overlap principle of the old taxonomy — when, for instance, it classifies the Sun and the Earth as the same kind of thing (celestial body) while the old theory classified them differently — the taxonomies are incommensurable.

This reformulation is more precise than Kuhn's earlier version, but it also narrows the scope of incommensurability considerably. Taxonomic incommensurability is a local phenomenon — it affects only those terms whose taxonomic placement changes across theories — rather than a global feature of paradigm change. Many critics have argued that this more modest version of incommensurability, while defensible, lacks the dramatic implications of Kuhn's original thesis.

A crucial distinction in the incommensurability debate is between translation and interpretation(or understanding). Critics of incommensurability, including Donald Davidson, argued that if two theories are truly incommensurable — if we cannot even understand what the other theory says — then we cannot know that they are rival theories at all. Incommensurability, on this view, is self-undermining: the very statement that two theories are incommensurable presupposes that we understand both of them well enough to see that they conflict.

Kuhn responded by drawing a sharp distinction between translation and interpretation. Translation, in the strict sense, requires finding expressions in one language that have the same meaning as expressions in another. Interpretation (or what Kuhn sometimes called “language learning”) is the process of learning to think in a foreign language or conceptual scheme without necessarily being able to translate it into one's own.

“Incommensurability thus becomes a sort of untranslatability, localized to one or another area in which two lexical taxonomies differ. The affected statements can be stated in either language but not translated from one into the other... Members of one community can acquire the taxonomy employed by members of another, as the historian does in learning to understand old texts. But the process which permits understanding produces bilinguals, not translators, and bilingualism has a cost.”— Thomas Kuhn, “Commensurability, Comparability, Communicability” (1982), p. 683

On this view, incommensurability does not prevent understanding; it prevents translation. A historian of science can learn to think in both Ptolemaic and Copernican terms — can become, in effect, bilingual — without being able to produce a systematic translation from one framework to the other. The inability to translate does not entail the inability to compare; it entails only that comparison must proceed through interpretation rather than through point-by-point equivalence.

This distinction has been influential but also controversial. Critics have questioned whether the line between translation and interpretation can be drawn as sharply as Kuhn suggests, and whether “interpretation without translation” is a coherent notion. If we can understand a foreign theory well enough to compare it with our own, have we not, in effect, translated it? The debate touches on deep questions in the philosophy of language about the nature of meaning, understanding, and the limits of communication.

Among the most important defenders of the incommensurability thesis are Howard Sankey and Paul Hoyningen-Huene, who have developed and refined Kuhn's position in significant ways.

Howard Sankey has argued that incommensurability is compatible with scientific realism. On his view, incommensurability is a feature of the concepts scientists use, not of the world those concepts describe. Different paradigms may carve up the world differently at the conceptual level while nevertheless describing the same underlying reality. This “referential stability” across paradigm change allows for genuine comparison and progress, even in the presence of conceptual incommensurability.

Sankey distinguishes between “semantic incommensurability” (which he accepts) and “methodological incommensurability” (which he rejects). While the meanings of terms may change across paradigms, the methods for evaluating theories — empirical adequacy, predictive accuracy, internal consistency — are sufficiently stable to allow rational comparison. This allows Sankey to accept the semantic insights of the incommensurability thesis while preserving the possibility of rational theory choice.

Paul Hoyningen-Huene has provided what is widely regarded as the most careful and sympathetic reconstruction of Kuhn's philosophy. In Reconstructing Scientific Revolutions(1993), Hoyningen-Huene argues that Kuhn's position is best understood as a form of neo-Kantian constructivism: the “world” that scientists study is a phenomenal world, partly constituted by the paradigm's conceptual framework. On this reading, the claim that “after a revolution, scientists work in a different world” is not a metaphysical thesis about mind-independent reality but an epistemological thesis about the world-as-experienced.

Hoyningen-Huene argues that this interpretation rescues Kuhn from the charge of relativism while preserving the force of the incommensurability thesis. If the phenomenal world is paradigm-dependent, then paradigm change genuinely involves a change in the world scientists study, even though the underlying “world-in-itself” (in the Kantian sense) remains the same. This provides a framework for understanding why paradigm shifts feel revolutionary without committing Kuhn to the view that reality itself changes with our theories.

The most pressing question raised by the incommensurability thesis is whether scientific progress is possible. If successive paradigms are incommensurable — if they cannot be directly compared — then it seems we cannot say that later science is closer to the truth than earlier science. Scientific change would be change, but not necessarily improvement.

Kuhn himself was careful to distinguish between two senses of progress. He denied that science progresses towarda fixed goal (truth), comparing the development of science to Darwinian evolution, which proceeds fromancestral forms without being directed toward any predetermined endpoint. Later paradigms may be better than earlier ones in various specifiable respects (they solve more problems, they are more precise, they encompass a wider range of phenomena), but this does not mean they are “closer to the truth” in any absolute sense.

“We may, to be more precise, have to relinquish the notion, explicit or implicit, that changes of paradigm carry scientists and those who learn from them closer and closer to the truth... The developmental process described in this essay has been a process of evolution from primitive beginnings — a process whose successive stages are characterized by an increasingly detailed and refined understanding of nature. But nothing that has been or will be said makes it a process of evolution toward anything.”— Thomas Kuhn, The Structure of Scientific Revolutions (1962), p. 170

This position has been widely debated. Some philosophers (notably Larry Laudan) have argued that a non-teleological account of progress is perfectly coherent: we can say that science progresses by becoming more effective at solving problems, without needing to invoke the concept of truth. Others (notably Hilary Putnam and Philip Kitcher) have argued that the concept of progress requires a realist notion of truth-approximation, and that without it, Kuhn's account collapses into relativism.

The debate over incommensurability and progress has had lasting effects on the philosophy of science. It has stimulated the development of more sophisticated accounts of scientific realism (including structural realism, which identifies the content of science with mathematical structure rather than with specific ontological claims), and it has led to a more nuanced understanding of the relationship between conceptual change and scientific advance.

• Incommensurability comes in several varieties: methodological, perceptual, and semantic (including taxonomic).
• Feyerabend's version emphasizes radical meaning variance; Kuhn's later version focuses on local taxonomic differences.
• The causal theory of reference provides a partial response but does not fully resolve the problem for theoretical terms.
• Kuhn's distinction between translation and interpretation offers a way to maintain incommensurability without irrationalism.
• Defenders like Sankey and Hoyningen-Huene have shown that incommensurability is compatible with realism and rational theory choice.
• The implications for scientific progress remain contested: can we speak of progress without a fixed goal?
• The debate continues to shape work in philosophy of language, philosophy of science, and the history of science.