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These striking claims are defended by considering a small number of historical examples of revolutionary change. Kuhn focused most on the Copernican revolution, on the replacement of the phlogiston theory with Lavoisier’s new chemistry, and on the transition from Newton’s physics to the special and general theories of relativity. So, for example, he supported the doctrine of conceptual incommensurability by arguing that pre-Copernican astronomy could make no sense of the Copernican notion of planet (within the earlier astronomy, the Earth itself could not be a planet), that phlogiston chemistry could make no sense of Lavoisier’s notion of oxygen (for phlogistonians, combustion is a process in which phlogiston is emitted, and talk of oxygen as a substance that is absorbed is quite wrongheaded), and that theories of relativity distinguish two notions of mass (rest mass and proper mass), neither of which makes sense in Newtonian terms.

All of these arguments received detailed philosophical attention, and it became apparent that the conclusions can be met by adopting a more sophisticated approach to language than that presupposed by Kuhn. The crucial issue is whether the languages of rival paradigms suffice to identify the objects and properties referred to in the terms of the other. Although Kuhn was right to see difficulties here, it is an exaggeration to suppose that the identification is impossible. From Lavoisier’s perspective, for example, the antiquated term dephlogisticated air sometimes means “what remains when phlogiston is removed from the air” (in which case, because there is no such substance as phlogiston, the term fails to pick out anything in the world). But at other times it is used to designate a specific gas (oxygen) that both groups of chemists have isolated. As far as conceptual incommensurability is concerned, it is possible to see Kuhn’s examples as cases in which communication is tricky but not impossible and in which the parties respond to and talk about a common world.

The thesis of observational incommensurability is best illustrated via Kuhn’s example of the Copernican revolution. In the late 16th century, Johannes Kepler (1571–1630), a committed follower of Copernicus, assisted the great astronomer Tycho Brahe (1546–1601), who believed that the Earth is at rest. Kuhn imagined Tycho and Kepler watching the sunrise together, and, like Hanson before him, suggested that Tycho would see a moving Sun coming into view, while Kepler would see a static Sun becoming visible as the Earth rotates.

Copernicus, Nicolaus: heliocentric systemEngraving of the solar system from Nicolaus Copernicus's De revolutionibus orbium coelestium libri VI, 2nd ed. (1566; “Six Books Concerning the Revolutions of the Heavenly Orbs”), the first published illustration of Copernicus's heliocentric system.The Adler Planetarium and Astronomy Museum, Chicago, Illinois

Evidently Tycho and Kepler might report their visual experiences in different ways. Nor should it be supposed that there is some privileged “primitive” language—a language that picks out shapes and colours, perhaps—in which all observers can describe what they see and reach agreement with those who are similarly situated. But these points, while they may have been neglected in earlier philosophy of science, do not yield the radical Kuhnian conclusions. In the first place, the difference in the experiential reports is quite compatible with the perception of a common object, possibly described correctly by one of the participants, possibly accurately reported by neither; both Tycho and Kepler see the Sun, and both perceive the relative motion of Sun and Earth. Furthermore, although there may be no bedrock language of uncontaminated observation to which they can retreat, they have available to them forms of description that presuppose only shared commonsense ideas about objects in the vicinity. If they become tired of exchanging their preferred reports—“I see a moving Sun,” “I see a stationary Sun becoming visible through the Earth’s rotation”—they can both agree that the orange blob above the hillside is the Sun and that more of it can be seen now than could be seen two minutes ago. There is no reason, then, to deny that Tycho and Kepler experience the same world or to suppose that there are no observable aspects of it about which they can reach agreement.

The thesis of methodological incommensurability can also be illustrated through the Copernican example. After the publication of Copernicus’s system in 1543, professional astronomers quickly realized that, for any Sun-centred system like Copernicus’s, it would be possible to produce an equally accurate Earth-centred system, and conversely. How could the debate be resolved? One difference between the systems lay in the number of technical devices required to generate accurate predictions of planetary motions. Copernicus did better on this score, using fewer of the approved repertoire of geometrical tricks than his opponents did. But there was also a tradition of arguments against the possibility of a moving Earth. Scholars had long maintained, for example, that, if the Earth moved, objects released from high places would fall backwards, birds and clouds would be left behind, loose materials on the Earth’s surface would be flung off, and so forth. Given the then-current state of theories of motion, there were no obvious errors in these lines of reasoning. Hence, it might have seemed that a decision about the Earth’s motion must involve a judgment of values (perhaps to the effect that it is more important not to introduce dynamical absurdities than to reduce the number of technical astronomical devices). Or perhaps the decision could be made only on faith—faith that answers to questions about the behaviour of birds and clouds would eventually be found. (This illustrates a point raised in an earlier section: namely, that attempts to justify the choice of a hypothesis rest on expectations about future discoveries. See Discovery, justification, and falsification.)

Methodological incommensurability presents the most severe challenge to views about progress and rationality in the sciences. In effect, Kuhn offered a different version of the underdetermination thesis, one more firmly grounded in the actual practice of the sciences. Instead of supposing that any theory has rivals that make exactly the same predictions and accord equally well with all canons of scientific method, Kuhn suggested that certain kinds of large controversies in the history of science pit against each other approaches with different virtues and defects and that there is no privileged way to balance virtues and defects. The only way to address this challenge is to probe the examples, trying to understand the ways in which various kinds of trade-offs might be defended or criticized. Responses

One way to think about the Copernican example (and other Kuhnian revolutions) is to recognize the evolution of the debates. In 1543 the controversy might have seemed quite unsettled; the simplification of technical machinery might have inspired some people to work further on the Copernican program, while the dynamical problems posed by the moving Earth might have prompted others to articulate the more traditional view. If neither choice can be seen as uniquely rational, neither can be dismissed as unreasonable.