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Incommensurability and Scientific Progress

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Abstract. I aim to resolve a difficulty that has plagued post-Kuhnian philosophy of science. This difficulty stems from a simultaneous commitment to two theses: (1) that successive paradigms are incommensurable to such an extent that they define different puzzles and therefore different worlds, and (2) that each paradigm ‘improves’ on the one it replaces in a non-trivial way. I work through Davidson’s objection to the idea of a conceptual scheme (of which a scientific paradigm is a special case), as well as Kuhn’s response, to get in view a notion of ‘incommensurability’ that admits substantive conceptual differences between theories while still allowing for a non-arbitrary choice to be made among them. I argue that Kuhn’s response adequately addresses Davidson’s concerns, and work out in a deeper way than Kuhn how this response can pave the way for an account of scientific progress.

Surely one of the most puzzling aspects of Kuhn’s Structure of Scientific Revolutions is his simultaneous insistence that (1) successive paradigms are incommensurable to such an extent that they define different puzzles and therefore different worlds, and (2) each paradigm ‘improves’ on the one it replaces in a non-trivial way. Given the puzzle-solving nature of normal science, asking which paradigm is better than another seems as silly as asking whether chess is better than checkers; each has its own set of rules, legitimate problems, and accepted solutions, and therefore ‘truth’ and genuine, cumulative progress make sense only relative to a particular paradigm. F=ma in Newton’s system, but not in Einstein’s, and asking which is closer to the way the world ‘actually is’ is impossible, since there is no way in which the world ‘actually is’ apart from a given set of categories to rend it apart. Kuhn says that the improvement is unidirectional and irrevocable, and he lists some criteria for so judging: “Accuracy of prediction, particularly of quantitative prediction; the balance between esoteric and everyday subject matter; and the number of different problems solved.”[1] All of these criteria, though, depend crucially on ‘sameness of subject matter’. It would be absurd to judge a scale for measuring weight better than an instrument for measuring radioactivity on the basis of accuracy; they need to be measuring the same sort of thing. But Kuhn also insists, for instance, that a pendulum and a constrained fall are two genuinely different entities; true statements about one may be false statements about the other. Judging one way better than another depends, therefore, upon sameness of subject matter in some sense; but what sense could that be given the nontrivial ways in which different paradigms really do define different worlds?

At the root of this confusion lies the troublesome question of what precisely ‘incommensurability’ means. This issue, or some variant of it, vexes interpretation of Structure and post-Kuhnian philosophy of science. My aim is to sort out, in at least a preliminary way, what precisely Kuhn can mean by ‘incommensurability’, given his description of normal science as puzzle-solving and his insistence on the reality of scientific progress through paradigms. I draw the basic Kuhnian frame from Structure, but my main thematic focus will be on Davidson’s critique of Kuhn’s position in On the Very Idea of a Conceptual Scheme (VICS), and Kuhn’s response in Commensurability, Comparability, Communicability (CCC). Though these essays are not in direct dialogue—Davidson addresses conceptual schemes in contexts broader than science, and Kuhn answers many critics, not just Davidson—the main lines of argument presented therein cut fairly deeply into the confusion surrounding the notion of incommensurability itself, and I shall therefore take them as archetypal instances of the sorts of arguments at issue. I argue that Kuhn’s distinguishing between interpretation and translation adequately addresses Davidson’s structural critique of the notion itself, but that Kuhn fails to address the question how scientific progress is possible. I take this to be a sin primarily of omission rather than commission, and I propose a way of using the above argument between Kuhn and Davidson to pave the way toward a more complete and intelligible account of scientific progress through paradigms.

I proceed in three parts. First I sketch the main thrust of Davidson’s argument in VICS, and work through Kuhn’s response to that type of criticism in CCC. Then I evaluate Kuhn’s response, asking what of Davidson’s argument it does and does not address. Finally, I briefly use Kuhn’s distinction between translation and interpretation to develop a more explicit account of scientific progress than does Kuhn, one that does not undermine genuine failure of translation between paradigms.[2]


Davidson’s goal in VICS is to show that any assertion that there are incommensurable (untranslatable) conceptual schemes is either trivial or false.[3] His argument is long and slightly meandering, but the basic idea remains relatively consistent throughout. Without getting mired in too much detail, the basic form is this: First he reduces the claim of incommensurable conceptual schemes to sets of mutually untranslatable languages. Then he describes the various metaphors people use to talk about different conceptual schemes, showing that each of them implicitly depends upon some sort of calibration between the languages. (For example, the metaphor of each scheme providing a different point of view depends on a common coordinate system on which to plot them.) Then, in the meatiest part of the essay, he exposes a crucial assumption underlying of the very idea of conceptual schemes: the scheme/content dualism. The idea behind it, he says, relies on two separate but not entirely unrelated metaphors: a scheme either organizes or fits something, and the something that it organizes or fits is either experience or the world.

He attacks each of the metaphors separately. The first, that of organizing experience or the world, cannot function as a metaphor for separate conceptual schemes because it depends upon already individuated entities to organize in the first place. One cannot organize a simple entity. But given already individualized entities, we can talk about other languages lacking in particular entities within the world only if the two languages largely “share an ontology common to the two languages, with concepts that individuate the same objects.”[4] Local failures can only be made intelligible in the light of overwhelming similarity. The metaphor of organizing experience fares little better, since a language must do more than organize experience—it must form entities out of those experiences, and thereby populate an actual world. But, as observed above, local untranslatability between worlds given by various languages depends on a largely similar ontology; if two schemes were drastically different, then we could not talk about one using the other at all. Failures must be highly localized, in a way that fails altogether to make sense of genuinely different conceptual schemes.

Davidson then dispenses with the second metaphor, that of a scheme ‘fitting’ experience (or the world as it is experienced), by arguing that it depends upon some sort of raw, unmediated notion of ‘sensory experience’ that cannot be made intelligible in any way other than talk of ‘being true’. What does a sentence within a theory fit, exactly? The sentence ‘it is cold’ fits exactly those cases in which it is cold. That is to say, ‘it is cold’ fits a state of affairs. But that is just to say that the sentence is true. Nothing more fundamental than this may be expressed, since no thing makes sentences true; at the root of ‘fitting’, therefore, lies the irreducible notion of ‘truth’. “Our attempt,” he says, “to characterize languages or conceptual schemes in terms of the notion of fitting some entity has come down, then, to the simple thought that something is an acceptable conceptual scheme or theory if it is true.”[5] But we cannot make any sense whatever of ‘truth’ independently of our ability to translate into a language we understand; ‘truth’ makes sense only when stated within a comprehensible language. Thus even this ‘fitting’ metaphor implicitly depends upon the ability to translate purportedly untranslatable languages.
Above is a rather sketchy picture of the argument that Davidson gives; there are other considerations, but no substantially different style of argumentation. The overwhelmingly important idea underlying all of it is that asserting the existence of incommensurable conceptual schemes already depends upon a basic structure and ontology that they share; if there were a conceptual scheme so different from ours that it could not be translated, then it also could not be talked about, and in no real way could be called a conceptual scheme in the first place. The ability to translate other schemes is, then, a necessary condition for talking about them at all.

It is precisely this kind of criticism with which Kuhn primarily concerns himself in CCC. He organizes complains against his position into two main groups. The first contends that “if there is no way in which the two [languages] can be stated in a single language, then they cannot be compared, and no arguments from evidence can be relevant to the choice between them” (670).[6] This is the puzzle that began this paper. The second, related criticism is that “people like Kuhn tell us that it is impossible to translate old theories into a modern language. But they then proceed to do exactly that, reconstructing Aristotle’s or Newton’s or Lavoiser’s or Maxwell’s theory without departing from the language they speak everyday” (670). It is the latter criticism that fits Davidson’s, and it is the one to which Kuhn devotes most of his attention. Working through Kuhn’s response to the latter criticism will shed light on the former.

Much of Kuhn’s response in CCC is quite technical, addressing such things as Ramsey definitions and the Quinian translation manual, but, luckily for us, the main argument against Davidson’s type of position is clear and relatively straightforward. People like Davidson, Kuhn says, err by failing to distinguish translation from interpretation. Translation is something “done by a person who knows two languages,” where “the translator systematically substitutes words or strings of words in the other language for words or strings of words in the text in such a way as to produce an equivalent text in the other language” (672). The exact meaning of ‘equivalent’ can quickly become a thorny issue, but Kuhn does not concern himself with it: “let us simply say that the translated text tells more or less the same story, presents more or less the same ideas, describes more or less the same situation as the text of which it is a translation” (672). The point is that translation is a direct function from sets of symbols in one language to sets of symbols in the other. Interpretation, on the other hand, depends only upon an initial knowledge of a single language. The interpreter is confronted by a text that is completely unintelligible to him, and his goal is to make sense of it. He “observes behavior and the circumstances surrounding the production of the text, assuming throughout that good sense can be made of apparently linguistic behavior” (673). The ability to interpret does not imply the ability to translate; an interpreter can give sense to ‘gavagai’ without ever being able to find an equivalent English word. Going back to scientific paradigms, an interpreter can make sense of Aristotle’s theory without ever being able to translate it into Newton’s or Einstein’s.
Once we make this distinction, Kuhn says, Davidson’s type of argument loses almost all of its bite. Recall that his argument revolved around the claim that talking about or giving any sense whatever to another conceptual scheme presupposes a way of translating it into one’s own. Kuhn can now simply say that it does indeed presuppose the ability to interpret the other scheme, but not to translate it. There need not be equivalent symbols in one scheme as another; not all languages are isomorphic.[7] To address this argument, Davidson would have to show either that the distinction between translation and interpretation is not a real one, or that the ability to interpret another conceptual scheme still renders ‘incommensurability’ impotent.


In the preceding section I stayed quite close to the Davidson’s and Kuhn’s structure and language. As I noted, though, the two are not in completely direct dialogue, and the preceding section may make it seem as though the two are, in a certain sense, talking past each other. In particular, while Davidson’s main point is a critique of the scheme/content dualism, Kuhn nowhere mentions any such thing in CCC. It is my aim in this section to show that, while Kuhn does not address the scheme/content dualism directly, his distinction between translation and interpretation undermines much of Davidson’s argument against the very idea of it, and that the rest of Davidson’s argument unfairly attributes to Kuhn a dependence on ‘raw, unmediated experience’—a concept that Kuhn directly repudiates in Structure. All of the above argument will assume the reality of the distinction between translation and interpretation; I conclude the section by arguing that the distinction is indeed a real and apt one, and that it gives clearer sense to ‘incommensurability’ that does Structure itself.

Let us assume, then, the reality of Kuhn’s distinction. Can Davidson still show that Kuhn is nonetheless guilty of an untenable dualism between scheme and raw content, or does Kuhn’s distinction undermine that argument? Davidson attacked mainly the metaphors people use to give sense to distinct conceptual schemes, and to those metaphors I here return. Kuhn’s position now amounts to saying that two schemes are different if and only if they cannot be translated—which is to say, if there is no isomorphism from strings of words in one scheme to strings of words in another. To take an example, this is to say that there is nothing in Einstein’s system that directly corresponds to Newton’s ‘force’. This is not to say that the two systems have nothing to do with each other—remember, interpretation is always possible—but the point is that the symbols in one system do not correspond directly to symbols in the other. Einstein and Newton speak of the same world in the sense that experiments in Newton’s system can be explained in Einstein’s, but the symbols they use to describe that world are not inter-translatable.

To this example let us apply Davidson’s argument directly. The idea, he would say, is that both systems ‘fit’ or ‘chop up’ the experience of observing a moving object, or simply a moving object within the world. (I use Davidson’s quadripartite division, without inquiring which one fits Kuhn’s language best; in truth, all metaphors are at work in interrelated ways, making it prudent to consider them all.) The two theories cannot be said to ‘chop up’ anything while remaining genuinely separate theories because to speak thus presupposes already individuated entities, and thus an ontology common to each of them—they are really largely the same theory, expressed in different symbols. As for each theory ‘fitting’ something (sensory experience or the world), to say that they ‘fit’ the world or experience is just to say that they are largely true; but to judge that something is largely true one must be able to translate it into his language. Thus they are inter-translatable.

With the distinction between translation and interpretation in hand, it becomes clear that the above line of reasoning proves only the ability to interpret the other theory, not the ability to translate it. Just because the theories are nontrivially co-referential, at least insofar as a Newtonian and an Einsteinian would agree that they are both describing ‘that entity moving on the table’, gives no faith for supposing that the concepts that they use to describe the entity are isomorphic. Indeed, Kuhn argues persuasively and at length that they are not; the terms in Einstein’s system and in Newton’s, while they both pick out many of the same particular physical entities, really do mean different things, and, crucially, stand in different relations to each other.[8] Thus the theories are interpretable but not translatable, and Davidson’s argument is moot.

There is, however, one part of Davidson’s complaint that could be brought to bear on Kuhn’s picture—that is, if Kuhn held any such thing in the first place. Part of Davidson’s argument against the scheme/content dualism—indeed, the part of it that Kuhn nowhere mentions in CCC—is the insistence that it relies on something like ‘raw, unmediated experience’ or ‘formless content’ out of which conceptual schemes give shape. And indeed, if Kuhn’s system did depend on this, he would be in considerable trouble, for Davidson’s argument would still have a solid foothold. Clearly something is amiss here, though, since one of the notions Kuhn actively repudiates in Structure is the idea that we can make any sense whatever of raw content unmediated through already existing concepts. Davidson would have to show, then, that for all of Kuhn’s insistence that there is no such thing, his theory stealthily depends on the notion. The question then becomes: Does talking of a conceptual scheme at all depend upon unmediated content to which the scheme may be applied (either to break up the content or to fit the content)? Davidson argues that it does; there is no scheme without raw content to put into it.

The argument that Davidson provides is one that depends mostly on grammar. The grammar of ‘schemes’ seems to require something to fit into a scheme. The scheme, that is, provides what Davidson calls ‘posits’. “It is reasonable,” he says, “ to call something a posit if it can be contrasted with something that is not. Here the something that is not is sensory experience.”[9] The posits then ‘fit’ or ‘break up’ the raw experience. This structure depends, it seems, on raw experience to break up in the first place. Thus having different schemes make sense only if ‘raw experience’ makes sense; ‘raw experience’ does not make sense; therefore there are no different schemes. At least, that is the basic idea.
I argue that, though this is a tempting line to take, it is overhasty and leaves room for substantial objection. It is enough to undermine Davidson’s argument to show that the metaphor can depend on something other than raw, unmediated experience, and that is what I intend to do, following a pseudo-Kuhnian line. I agree that there is no way of talking about sensory experiences apart from any set of categories or concepts; else there would be no experience, only dumb perception (I use the distinction in Kant’s sense). But this is not the only way of rendering intelligible two untranslatable ways of talking about experience. There is no way of talking about a pendulum or a constrained fall apart from those (or other) determinate categories; Davidson then infers that talking about both of them as different schemes about the same sort of thing depends upon each of them fitting the same raw, unmediated sense perception. But why not take a merely pragmatic approach? The two schemes pick out the same entity if and only if an inhabitant of one scheme and an inhabitant of another agree that it is the same entity—a necessary step in interpretation, and one that does not necessarily imply translation. They need not try to sort out what raw experience underlies their schemes—indeed, they need not even posit such a thing. It is enough that they can interpret each other well enough to understand that it is the same physical entity—that their schemes are, in at least this case, locally co-referential. Their having a scheme need not depend on raw, unmediated experience; it need depend only on the mutual ability to interpret each other. Thus raw experience need not make sense in order for conceptual schemes to make sense. All that is required is interpretation. In this way, then, there can be untranslatable schemes—or at least, Davidson’s argument that there cannot be falters. The scheme does indeed give rise to content, but it is not ‘raw, unmediated’ content. The scheme is what makes any content at all possible, and the ability to interpret allows the two schemes to pick out some of the same things without requiring ‘raw experience’ underlying them, whatever that could be.

Therefore, if the distinction between translation and interpretation is a real and apt one, Davidson’s argument fails, and there we can indeed make sense of untranslatable (though not uninterpretable) schemes.[10] I do not intend to give an exhaustive argument for the reality of the distinction, but I shall address two possible complaints against Kuhn’s distinction that someone like Davidson could make. The first is that the bar for translation is so high as to include only relatively specialized formal languages. The second is that the claim of the ability to interpret but not to translate various schemes still amounts to a trivialization of the notion of conceptual schemes.

Translation is something that occurs between symbols; one can program a computer to do it, and no reference to the world is required. I substitute ‘casa’ for ‘house’ without knowing or caring what content these terms have. This is why translation is so clean, and why it provides an extremely strong notion of ‘sameness’. But is such a thing usually possible at all? Defining the distinction thus seems to render much of what we call ‘translation’ mere interpretation. Indeed, Kuhn says, “if a gloss is required, we shall have to ask why.”[11] But my copy of Being and Time includes hundreds of linguistically relevant footnotes; if that is not a translation, what is? Clearly base 10 arithmetic and base 3 arithmetic can be translated in this strong sense; there is absolutely no loss of information, merely different symbolic ways of expressing the same exact thing. But besides mathematical and computer languages, it seems as though there can never be such a thing as genuine translation. Thus the distinction is inapt at best and pigheaded at worst; most every sort of calibration between languages worth talking about is just interpretation.

It is worth remembering, though, that the primary question at issue in this paper is the nature of scientific paradigms. A scientific paradigm, whatever it is, depends on formal and mathematical vocabulary. Normal science may well be an activity learned by doing something, but the something that one does is to try to fit nature into the mathematical equations that characterize one’s paradigm. Seen in this way, the distinction is still an apt one. As Kuhn demonstrates in Structure, the equations that govern special relativity really cannot be translated into the equations that govern the Newtonian universe; they consist of entirely different mathematical apparatuses. This holds even of the less mathematical sciences, like chemistry. Kuhn argues at length that a phlogiston cannot be translated legitimately into modern terminology without destroying intelligibility. Interpretation is therefore necessary; one must look to the world, not only to symbols. Furthermore, something like translation can obtain here: I can do Newtonian physics in Spanish or English while still doing the same physics. The distinction therefore makes sense at very least when dealing with the activities of science. I leave its impact on more everyday uses of the term undecided, but I do not think it is a stretch to say that my copy of Being and Time does indeed require a bit of interpretation to supplement what is otherwise a translation (implying some sort of local untranslatability between German and English). Indeed, since interpretation is required to learn another language in the first place, translation must always be founded on prior interpretation.

The second complaint that someone like Davidson could lodge against the distinction is that even admitting the ability to interpret another scheme renders the very idea of a conceptual scheme trivial. If any other scheme can be interpreted, then why call them different at all? We can describe one in terms of the other fairly well, if not symbolically faithfully, and therefore truth-values of one can be evaluated with respect to the other. ‘Incommensurability’ winds up amounting to a failure only to substitute symbols for symbols, not actually to compare the two theories in a meaningful way. Theories are untranslatable in Kuhn’s sense, but so what? They still amount to more or less the same thing, differing only on were the boundaries for concepts are drawn.

This complaint is more substantial than the last. It calls for a more extended discussion, one that will need to get clear on what sort of ‘sameness’ we can ascribe to different scientific paradigms. We have said that the ability to interpret requires at least being able to tell when two theories are largely co-referential; in order to understand Newton’s theory, we need to be able to pick out some of the same entities as described by Einstein’s theory, and, while failing to make systematic symbolic substitutions a la translation, still interpret the former to the extent that we can see that ‘what it is about’ can be made to resemble in some way the entities that populate Einstein’s universe. The worry here, then, is that this amounts to saying that the theories really are the same in a non-trivial way—they pick out the same entities, and thus the claim that they are ‘incommensurable’ amounts to saying nearly nothing of importance for anything a philosopher of science might want to ask. Since they are about the same entity, where the theories differ, one or both are simply wrong, and the bite of incommensurability is gone.

We are finally at the point of addressing the question with which this paper began: how is there incommensurability but still ‘sameness of subject matter’ in some nontrivial sense? I answer that we need a distinction between types of ‘sameness’, one that will hopefully dispel these worries. The idea is this: Two theories can be largely co-referential within the world while still defining completely different worlds. Here is how it works:

Recall the pendulum and the constrained fall. In order for us to be able to interpret the one that is not within our paradigm, we need to be able to say that the two refer to the same entity in some cases and in some sense. That is, I agree with an Aristotelian that this particular physical object, which I observe within the world, and which he calls a constrained fall and I call a pendulum, is the same. How do we determine that it is the same? With a particular, physical entity within the world, this is not difficult—we can pick it out by pointing, or, to be more pedantic, by picking up the entity and moving it, and mutually verifying that it was the selfsame entity that we moved.[12] Our theories are co-referential at least in this sense. But this does not undermine the sense in which Kuhn says that the two entities are genuinely different entities. That is, the theoretical apparatus that we use to refer to the entity differ completely. One entity falls with difficulty; the other keeps going with difficulty. One essentially falls, while the other essentially keeps going according to sinusoidal equations. These are two different descriptions that, in this particular case, can be brought to bear on same entity. And we can agree that our theories are co-referential in many cases. Going forward one major paradigm, I can describe most particular physical entities using Einsteinian or Newtonian vocabulary; I acknowledge that it is the same physical entity, but depending on which way I describe it, I subsume the physical entity under a different theoretical model. ‘Space’ means different things depending on whether you ask Einstein or Newton, but when I ask it to bear on a particular thing—asking whether this table is in space, for instance—they agree.
Perhaps the analogy will be cleaner if we abstract into the world of mathematics. Whatever sort of space we live in, it is homeomorphic to R^3 (this just means that locally it looks and acts very much like R^3). I can describe this world, though, by using linear algebra (treating it as an actual instantiation of R^3), or algebraic topology (treating it as curved in some more complicated structure). Whichever way I adopt, I commit myself to a genuinely different way that the world looks. But in any local neighborhood (ours, say), we mostly agree on how the world behaves. Given any particular entity within this world, we agree that it looks three-dimensional, and that, whatever version of space we adopt, this particular entity is in space. It is only when we abstract to the theoretical that we differ—that is, when we ask what ‘space’ means. Thus we have genuinely different theories about how the world looks, but these theories agree on the behavior of most particular entities within the world. The table is really a different thing depending on which way I adopt—but it differs in the theoretical description, not in the physical instantiation. The equations for describing motion are completely different in either model (they are not at all translatable), but they can both approximately fit any particular entity I can observe. I propose that in a quite similar way this is how scientific paradigms can describe completely different worlds yet remain locally co-referential. They can agree that they are each ‘about’ some of the same particular entities, but still disagree about the fundamental nature of any particular entity. [13] A pendulum and a constrained fall refer to the same physical entity, but describe two different entities. This difference is, at very least, not wholly trivial—at least insofar as the difference between a curved space and a non-curved one is not trivial. The analogy is not perfect, since in mathematics both spaces are subsumed under a strict well-defined notion of ‘topological space’, and also the two spaces can be mapped onto each other in a continuously invertible way, whereas nothing of the sort is possible between scientific paradigms, but the basic idea holds nonetheless. The ‘sameness of subject matter’ with scientific paradigms comes from asking the theory to bear on the world, just as the ‘sameness of subject matter’ with R^3 and a curved space comes from being able to describe the world in one way or the other in such a way as to make the world look genuinely different whichever way we adopt.


Now that we have a more explicit account of incommensurability—incommensurable theories may be interpreted but not translated, interpretation entails discovering where theories are mostly co-referential, theories can be largely co-referential while defining genuinely different worlds—we are in a position to give a better account of scientific progress. The problem, as Kuhn describes it in CCC, is that if two paradigms define genuinely different worlds, then “no argument from evidence can be relevant to the choice between them.”[14] This is because each theory includes different and untranslatable entities. Newtonian space is flat, while Einsteinian space-time is curved; phlogiston is not translatable into oxygen. But given that the entities are different, how can one appeal to evidence in support of one theory over another? Scientific paradigms seem different from natural languages in this respect: one need not decide whether Spanish is a better language than English. The scientific community, though, must decide between Newton and Einstein. The two theories are mutually incompatible. But any argument from evidence, it seems, could not privilege one theory over another. Since theories define different puzzles and hence worlds, different things are admissible as evidence in each theory. Evidence about a constrained fall may not be evidence about a pendulum, since they are essentially different entities.

Adding to the difficulty, Kuhn says, is the fact that each theory is circular at its base. An Einsteinian cannot appeal to evidence to undermine a Newtonian’s version of space, because the latter defines space in a particular way. To be more concrete, consider the equation ‘F=ma’. Here we define force as ‘that which, when applied to a certain mass, yields constant acceleration’, and then we go on to define mass as ‘that which accelerates constantly when a constant force is applied’. Kuhn argues that neither of these terms is primitive. No argument from evidence could undermine this system, because it is self-justifying (and so is Einstein’s). Furthermore, each of these systems uses its equations to establish what counts as evidence in the first place; a Newtonian could say to an Einsteinian that the latter’s ‘evidence’ for the curvature of space was simply not about space in the first place, because space just means something flat. How could we possibly appeal to evidence to privilege one over another if the standard for evidence varies?
With the conclusions of the preceding section in hand, the answer to this puzzle (which Kuhn mentions but abandons in CCC) follows with at least some clarity. Incommensurable means untranslatable, but not uninterpretable. An Einsteinian can interpret Newtonian physics without ever translating the concepts and equations it employs into his own paradigm. And a necessary step in interpreting another scientific paradigm is determining where it is co-referential with one’s own. One cannot interpret Newtonian physics properly without being able to describe a Newtonian object in its own language, and to identify it as the same object one can also describe using the Einsteinian model. We established the necessity of ‘sameness of subject matter’ at least in this sense, and argued that it depends on interpretation, but not on raw sense-data.

I now invoke the criteria for judging ‘betterness’ that Kuhn provides in Structure: “Accuracy of prediction, particularly of quantitative prediction; the balance between esoteric and everyday subject matter; and the number of different problems solved.”[15] These criteria do depend on sameness of subject matter in some sense, and now we are in a position to say what sort of sense that is. Since interpretation allows the inhabitant of one theory to give sense to the other and locate the places where the two theories are co-referential, one can ask which theory makes, for instance, more accurate quantitative prediction. An Einsteinian cannot translate Newton’s experiments into the mathematical vocabulary of relativity, but he can explain ‘the same’ experiment using either paradigm, and ask which one can predict the behavior of the particular entity more accurately. This does not describe an act of translation, but rather an act of interpretation. The other criteria Kuhn lists likewise make sense under this model; I can solve ‘more’ different puzzles using Einstein than I can using Newton, and I am not comparing checkers and chess. I can interpret the puzzles of either one, I just cannot translate one theory into the other. In particular, and perhaps most importantly, Einstein’s theory can interpret and satisfactorily deal with the crises that destroyed Newton’s theory, while explaining equally well many of the other things that Newton predicts. This may be the most important sense in which one theory is better than the other: one has not yet reached crisis, while the other has, and the better theory can explain (interpret) the crisis of the other theory in its terms. Since scientific theories imply what sort of entities there are in the world, those theories are beholden to the behavior of the entities they predict. Einstein’s equations may not be translatable into Newton’s, but once we have each theory with each admitting certain things as evidence, each theory is beholden to the observed behavior of the entities within the world. Again, this need not imply a raw sense-data language describing the entities. All that is required is that the theory gives rise to certain entities, and that these entities which are in the world then hold the theory accountable. Einstein’s theory can be accountable to the behavior of the entities in more cases than Newton’s, even if the theories are incommensurable.

The above gives a coherent picture that can account for scientific progress without undermining real incommensurability between paradigms. I shall conclude by extending Kuhn’s puzzle-solving metaphor in a way, hopefully, that will better illustrate the above picture.

Normal science is puzzle-solving; it has the characteristics of a game, with entities defined by certain rules. Thus the activity of doing normal science is much like playing chess. But there are no crises in chess; why do they occur in normal science? The answer is that doing normal science is like playing a game with nature, where nature has not agreed on the rules beforehand. As soon as someone thinks to treat nature as though one could supply determinate rules that govern its behavior, one begins to play the game, and one makes certain moves (experiments) to observe how nature responds. A paradigm develops when a group finally agrees that a certain base level structure of the game can be taken for granted, and the group begins testing it, making new moves and filling in more details. Occasionally, though, nature makes a move that the paradigm explicitly disallows—remember, nature did not agree to play our game. Crisis then occurs, and the foundational structure of the game must be reevaluated. Neglecting all of the intermediary steps, a new paradigm develops to account for the anomalous move. The makers of this paradigm have the benefit of all of the past moves, and so their paradigm must also account for them. The new paradigm then creates what may well amount to an entirely different game structure, and must completely reinterpret nature’s actions prior to the crisis that were explained adequately well with the old paradigm.[16] The paradigms must be mutually interpretable enough to call each individual move ‘the same’, but the rules that describe the game may be completely different, having absolutely nothing to do with each other except that they agree on some particular cases of moves. This does not imply a raw sense-data language describing the moves, since one cannot have any notion of moves apart from a particular game. The games must only be mutually interpretable. And, finally, the two games are incommensurable. The rules of one game may be untranslatable with respect to the rules of the other. In this sense the game looks completely different from the perspective of either set of rules. But the later version of the game is nonetheless an improvement on the earlier one, since it can interpret all of the moves that the old one could interpret and more. The games are not inter-translatable, but there is progress nevertheless. Paradigm shifts work in a similar way.[17]

I have argued, following the general outline of the above metaphor, that scientific paradigms can be incommensurable while still allowing for a non-trivial account of scientific progress through paradigms. The key is interpretation, which can undermine both the structural complaints Davidson lodges against the very idea of a conceptual scheme itself, and the complaint that asking which of two incommensurable theories is better is impossible. These questions now have adequate answers, grounded in Kuhn’s distinction between translation and interpretation, and the distinction between mere co-reference and having the same meaning (defining the same world).


  1. Kuhn, Thomas S. The Structure of Scientific Revolutions. 3rd ed. Chicago: University Of Chicago Press, 1996. 206
  2. Throughout the paper I use ‘translation’ and ‘interpretation’ in the senses Kuhn reserves for them (see below), except when quoting or channeling Davidson, for whom there is no such distinction.
  3. For the purposes of this paper, I treat a scientific paradigm as a special case of what Davidson calls a conceptual scheme. Whether this substitution is entirely fair I leave undecided, but at very least, Davidson and Kuhn treat them thus.
  4. Davidson, Donald. “On the Very Idea of a Conceptual Scheme.” In The Essential Davidson. New York: Oxford University Press, USA, 2006. 203
  5. Davidson, Donald. “On the Very Idea of a Conceptual Scheme.” In The Essential Davidson. New York: Oxford University Press, USA, 2006. 205
  6. The remaining citations in this section are all from Kuhn, Thomas S. “Commensurability, Comparability, Communicability.” PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association Two (1982): 669-688.
  7. Technical vocabulary is often odious, but sometimes helpful; here I believe it to be the latter. An isomorphism is just a function that is one-to-one and preserving all the relevant structures. The term, while in use primarily in mathematics, can also be used of non-formal languages: ‘Ich habe drei Beine’ is isomorphic to ‘I have three legs’. Each word in one sentence has an equivalent in the other without intermediary loss of meaning, and the way in which they are put together yields the same sense. By contrast, ‘to be’ cannot be translated into Spanish in this way; we have two choices, ‘estar’ and ‘ser’, between which we choose depending on context. By ‘translation’, Kuhn means something like a loose version of ‘isomorphism’.
  8. See Structure, 101.
  9. Davidson, Donald. “On the Very Idea of a Conceptual Scheme.” In The Essential Davidson. New York: Oxford University Press, USA, 2006. 204
  10. Actually, there are probably some cases of uninterpretability, but they are far removed from those with which we are concerned. For example, it may well be that one cannot interpret chess using the rules for scrabble. But these are highly localized and contrived games, not large-scale conceptual schemes for describing something like the world. And, in any case, both chess and scrabble can be interpreted in English.
  11. Kuhn, Thomas S. “Commensurability, Comparability, Communicability.” PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association Two (1982): 672
  12. Of course, this can be difficult when there are no living Aristotelians. But even in this case we are not totally helpless; we can read the description of their experiments, and use our interpretive powers to reconstruct what it was that they were doing.
  13. Different theories often commit one to the existence of different physical entities—some theories include electrons while others do not, and so no statement about ‘electrons’ can be interpreted in the theory that does not—but interpretation nonetheless requires that we can find some entities that both theories can describe (tables, for instance).
  14. Kuhn, Thomas S. “Commensurability, Comparability, Communicability.” PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association Two (1982): 670
  15. Kuhn, Thomas S. The Structure of Scientific Revolutions. 3rd ed. Chicago: University Of Chicago Press, 1996. 206
  16. It is important that one does not obtain the same game structure with more complicated cases and exceptions to the old game. A necessary condition for science, it seems, is precisely not accepting exceptions to general rules. The picture, then, is not as though nature is playing chess, and up until move n no pieces have been able to jump any other piece, and at move n+1 nature uses the knight to jump over another piece, and we modify the game to allow for this one particular move. At that point we must reevaluate what the entity ‘knight’ is, and supply general rules that account for all observed cases of its behavior. Even this case could be accounted for with modification, and for the most part we would need to make little departure from normal science. For more profound paradigm shifts we may have to redo the entire game—for example, if we thought we were playing chess and all of a sudden nature moved its piece off of what we thought was the board.
  17. Readers of Kuhn will note that I am oversimplifying slightly; in particular, Kuhn says that there are almost always anomalies within paradigms, and that not all anomalies lead to crisis. I do not here address what other characteristics an anomaly must have in order to lead to crisis. This is another issue, one that does not seem to get adequate treatment in Structure. His account there is mainly sociological, going something like, “Well, some do and some don’t, and we can tell which is which based on how the scientists within the paradigm respond to it,” without asking what particular characteristics of an anomaly tend to evoke that response.

Ethan Jerzak (’10) is a Philosophy and Allied Fields major at the University of Chicago

Cover art by atomfuer

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