When Aristotle said that a body has "weight," he meant something quite different from what Newton meant by "weight" — and Newton meant something different from what Einstein meant. The words are the same; the concepts are not. After a scientific revolution, scientists in the new paradigm use some of the same vocabulary as their predecessors, but the words have been redefined, often in ways that are not fully translatable across the revolutionary divide.
This phenomenon (the partial untranslatability of concepts across paradigms) is what Kuhn calls incommensurability. It is his most provocative claim and the one that has generated the most controversy. Does incommensurability mean that scientific revolutions cannot be judged rationally? That the shift from phlogiston to oxygen chemistry was not an improvement but a change (a different way of seeing, not a better one)? That there is no scientific progress in any objective sense?
Kuhn's answer is subtle, and getting it right requires distinguishing incommensurability from relativism — a distinction that Kuhn himself sometimes struggled to articulate clearly, and that his critics often flattened.
The three dimensions of incommensurability
Kuhn's mature account of incommensurability (developed and refined through the 1970s and 1980s) distinguishes three aspects:
-
Conceptual incommensurability: Key terms change meaning across paradigm boundaries. "Mass" in Newtonian mechanics is an intrinsic property of a body; "mass" in relativistic mechanics is energy-dependent, frame-relative, and connected to spacetime curvature. These are not the same concept refined; they are different concepts that share a name. The conceptual change reflects a different picture of what the physical world is.
-
Perceptual incommensurability: Scientists trained in different paradigms literally perceive experimental results differently. Pre-Lavoisier chemists saw phlogiston escaping from burning materials; post-Lavoisier chemists saw oxygen combining with them. Same flame, different world. Kuhn's claim is not that perception is entirely theory-determined (a position he rejected in his later work) but that paradigm training shapes perceptual categories in ways that are deep enough to constitute a genuine difference in what is seen.
-
Methodological incommensurability: Competing paradigms employ different standards for what counts as a legitimate problem, an acceptable solution, and convincing evidence. Pre-quantum physicists demanded deterministic laws; quantum physicists work with irreducibly probabilistic ones. These different methodological standards mean that a quantum physicist cannot fully satisfy a classical physicist's demand for explanation — not because the quantum explanation is inadequate by any neutral standard, but because the two communities are operating with different criteria of adequacy.
The no-common-measure claim
The term "incommensurable" derives from Greek mathematics: two lengths are incommensurable if no common unit can measure both exactly (the diagonal and side of a square are incommensurable in this sense). Kuhn's application of this concept to paradigms means that there is no neutral, paradigm-independent standard against which competing paradigms can be fully evaluated. This is weaker than it is sometimes taken to be. Kuhn does not claim that no comparison is possible at all — he is not saying that pre- and post-Copernican astronomy are equally good. He is saying that the comparison cannot be made by applying a set of universal, context-independent rules that both parties must accept. The comparison is possible but requires what he calls "partial translation" and interpretation — a kind of cross-paradigm hermeneutics that is genuinely difficult and fallible.
"The normal-scientific tradition that emerges from a scientific revolution is not only incompatible but often actually incommensurable with that which has gone before... Successive paradigms tell us different things about the population of the universe and about that population's behavior... In some important respects... the two are really incommensurable." Progress without teleology
Kuhn's treatment of scientific progress is his most philosophically original contribution to the incommensurability debate. He distinguishes two senses of progress:
-
Teleological progress: Progress toward a fixed goal — toward Truth, toward the accurate picture of Nature as it really is independently of any paradigm. This is the traditional picture: science converges on reality, and later theories are closer to the truth than earlier ones.
-
Evolutionary progress: Progress from a current state — the new paradigm is better at solving the problems that matter to the current scientific community, better at incorporating what has been learned, better at generating productive new research. This is analogous to biological evolution: species do not evolve toward an ideal form, but each generation is adapted to its environment by a selection pressure that doesn't aim at any final destination.
Kuhn rejects teleological progress while affirming evolutionary progress. Later paradigms typically solve more puzzles, with greater precision, over a wider domain than the paradigms they replace. This is genuine progress. But it is not progress toward the Truth — there is no guarantee, and no evidence, that science is converging on a final picture of reality as it exists independently of all paradigms. This position is sometimes called internal realism or pragmatic realism: science is genuinely progressive and produces genuine knowledge, but the knowledge is not a correspondence-relation between theories and mind-independent reality — it is a relationship between theories and the problems, data, and standards of a scientific community.
Classical mechanics and quantum mechanics
The transition from classical to quantum mechanics (1900–1930) is the richest illustration of Kuhnian incommensurability available. In classical mechanics, every physical system has a definite position and momentum at every moment; measurement reveals these values without disturbing them; causation is deterministic; and the state of a system is a precise point in phase space. In quantum mechanics, the position and momentum of a particle cannot both be precisely defined simultaneously (Heisenberg uncertainty principle); measurement creates definite values rather than merely revealing pre-existing ones; causation is irreducibly probabilistic; and the state of a system is a superposition of possibilities until measurement collapses it.
These are not merely numerical refinements of classical physics. They represent a conceptually incompatible picture of what physical reality fundamentally is. The classical physicist's "definite trajectory" and the quantum physicist's "wave function collapse" are not translations of each other; they reflect different conceptual worlds. When classical physicists first encountered quantum mechanics, many found it literally incoherent — not because they were stupid, but because the concepts required to understand it were genuinely foreign to their trained perception. Albert Einstein never fully accepted quantum mechanics for exactly this reason.
The progress from classical to quantum mechanics is real: quantum mechanics explains phenomena — blackbody radiation, the photoelectric effect, atomic spectra, chemical bonding — that classical mechanics cannot account for. But the relationship between the two theories is not one of simple addition or refinement; it is a paradigm replacement, and the replacement involved genuine conceptual rupture.
The most powerful challenge to Kuhn's incommensurability thesis comes from the correspondence principle in physics: new theories typically reduce to older ones in appropriate limiting cases. Einsteinian relativity reduces to Newtonian mechanics at low velocities; quantum mechanics reduces to classical mechanics for large quantum numbers. Does this not show that theories are commensurable — that the new paradigm includes the old one as a special case?
Kuhn's response: the correspondence principle shows that the predictions of new theories numerically match those of old theories in certain domains — but this is not the same as conceptual identity. Relativistic mass and Newtonian mass give the same numbers at low velocities, but they are conceptually different, embedded in different theoretical frameworks, and connected to different pictures of reality. The numerical convergence is real but shallow; the conceptual incommensurability is real and deep. There is also a challenge from realism: if science is genuinely progressive, doesn't this require that later theories are more accurate representations of mind-independent reality? The antirealist consequences of Kuhn's position — his denial that science converges on Truth — have troubled scientific realists, who argue that the predictive and explanatory success of mature science is best explained by the hypothesis that scientific theories are approximately true. Kuhn's pragmatic response — that success is explained by better problem-solving, not by truth-approximation — strikes many realists as inadequate.
Kuhn's incommensurability thesis has had wide effects outside philosophy of science. It has:
- Supported social constructivist accounts of science, which emphasize the role of social and cultural factors in shaping scientific knowledge
- Informed postcolonial science studies, which argue that Western scientific paradigms have marginalized or suppressed non-Western knowledge systems in ways that parallel Kuhn's analysis of how dominant paradigms suppress anomalies
- Generated the "science wars" of the 1990s, in which scientists (most famously in Sokal's hoax) accused humanistic scholars of using Kuhn to license relativism about scientific truth
Kuhn himself always insisted that he was not a relativist — that he believed science makes genuine progress and that paradigm choices can be rationally justified, even if not algorithmically determined. Whether this insistence is coherent with his account of incommensurability is a question philosophers of science continue to debate.
With the concepts of paradigm, crisis, revolution, and incommensurability in hand, the final reading examines Kuhn's relationship to his great contemporary rival — Karl Popper — and asks how Kuhn's framework applies to contemporary scientific controversies.