Incommensurability, plain difference and communication in interdisciplinary research

By Vincenzo Politi

Vincenzo Politi (biography)

Where does the term incommensurability come from? What is its relevance to interdisciplinarity? Is it more than plain difference? Does incommensurability need to be reconceptualized for interdisciplinarity?

Incommensurability: its origins and relevance to interdisciplinarity

‘Incommensurability’ is a term that philosophers of science have borrowed from mathematics. Two mathematical magnitudes are said to be incommensurable if their ratio cannot be expressed by a number which is an integer. For example, the radius and the circumference of a circle are incommensurable because their ratio is expressed by the irrational number π.

In philosophy of science, the term is used in a metaphorical sense: two competing scientific theories, paradigms or research projects are said to be incommensurable when there is no common ground for their rational comparison and choice. The effects of incommensurability become visible during debates surrounding scientific revolutions, when the supporters of two competing paradigms or research projects attach different meanings to the same words, thus ending up experiencing communication breakdowns.

Recently, scholars interested in interdisciplinarity have started to use the concept of ‘incommensurability’ to describe some of the difficulties surrounding interdisciplinary research (see the blog posts by Andi Hess on Two types of interdisciplinary scholarship and Britt Holbrook on Interdisciplinarity and evil – Understanding incommensurability; see also Holbrook 2013). The different disciplines involved in an interdisciplinary project may not share the same vocabulary. In such cases, the specialists working on the project may find themselves in the same situation as scientists talking at cross-purposes during a scientific revolution.

Incommensurability or difference?

Not everybody agrees with the idea that the concept of incommensurability is useful in discussing interdisciplinarity. It may be argued, in fact, that the disciplines involved in an interdisciplinary project are not properly incommensurable, but just different. Incommensurability is more than mere difference: as indicated earlier, philosophers introduced this concept to describe problems associated with the choice between two competing paradigms during periods of revolutionary scientific change. However, many disciplines are not in competition at all, since they are just about different domains.

Since they are not in conflict or in competition, the different disciplines involved in interdisciplinary collaborations can be thought of as complementary, rather than incommensurable. Furthermore, the very existence of interdisciplinary collaboration seems to be evidence against the idea that there is some sort of incommensurable barrier which is an obstacle to cross-disciplinary communication.

This argument urges us to distinguish more sharply between incommensurability and plain difference, since the latter does not necessarily imply the former.

In the same way in which the existence of incommensurability among different disciplines should not be uncritically presupposed, however, the idea that different disciplines are just complementary should not be taken for granted. Whether different specialists can actually integrate their skills, knowledge and styles of reasoning for the resolution of a complex problem can be determined only within the actual context of the problem-solving practice and, often, only after the interdisciplinary collaboration has revealed itself to be fruitful. Different disciplines do not spontaneously ‘fall into place’ by virtue of their being complementary, nor does interdisciplinarity happen by fiat.

Reconceptualising incommensurability for interdisciplinarity

I suggest that there are two key issues relevant to genuine incommensurability in the context of interdisciplinary research (Politi 2017). These require some reconceptualisation of the original ideas about incommensurability.

First, I suggest that incommensurability in this context should not be conceived as an a-temporal, universal and logical relation, as it is in mathematics. Rather, we should look at interdisciplinarity from a dynamical/historical perspective. It is true that different disciplines are not necessarily incommensurable. By virtue of their historical trajectories, however, different disciplines may become incommensurable.

This happens when they end up converging towards an overlapping area of research: after all, the whole idea of interdisciplinarity is founded on the belief that different disciplines may have something to say about a common range of problems. In these cases, (parts of) different disciplines may find themselves offering incompatible (and maybe competing) solutions to problems pertaining a common sub-domain. Each discipline, in fact, may have its own way of conceptualising and modelling such problems and neither effective collaboration nor integration are guaranteed.

Second, I propose that incommensurability should not be regarded as a purely semantic problem affecting communication and arising from the way in which different scientists use the same terms. Finding a way to communicate across specialties may be necessary but not sufficient for successful interdisciplinarity. It is perfectly plausible to suppose that scientists coming from different disciplines may learn each other’s theoretical language and communicate with one another without too many problems. Successful communication, however, does not imply total agreement about the problem-solving methodologies to implement.

It should not be forgotten, for example, that incommensurability also possesses some important methodological aspects. For example, one group of scientists may prefer a theory which is more accurate and consistent, while another group of scientists may prefer a theory which seems to be more fruitful for future research. This type of disagreement has little or nothing to do with problems of translation or with the meaning of scientific terms: two groups may continue to disagree even when they fully communicate and understand each other, without experiencing any ‘communication breakdown’. Incommensurability can also have cognitive or perceptual aspects: different specialists may literally see, and therefore conceptualise, the same problem in different ways.


It makes little sense to speak of incommensurability in absolute and a-historical terms. Rather, incommensurability should be invoked when different disciplines converge towards the same domain. In these cases, mere difference can become incompatibility and competition, that is incommensurability.

Moreover, incommensurability is not only a linguistic problem preventing successful communication. Different scientists may communicate and understand each other very well but, successful communication notwithstanding, they may just ‘agree to disagree’.

What do you think? Do these ideas resonate or do you see things differently?

Holbrook, J. B. (2013). What is interdisciplinary communication? Reflections on the very idea of disciplinary integration. Synthese, 190: 1865–1879

Politi, V. (2017). Specialisation, interdisciplinarity, and incommensurability. International Studies in the Philosophy of Science, 31: 301–317

Biography: Vincenzo Politi PhD is a postdoctoral researcher at CEA – Commissariat à l’énergie atomique et aux énergies alternatives (French Alternative Energies and Atomic Energy Commission) in Paris-Saclay, France. He works on philosophical issues concerning scientific change and on the ethics of science.

13 thoughts on “Incommensurability, plain difference and communication in interdisciplinary research”

  1. Stepping back from incommensurability in the contexts of interdisciplinary work and scientific paradigms, I’ve found the term to be very useful in my work on “wicked problems” ( One way to characterize a wicked problem is that the stakeholders cannot agree on what the problem is, much less what would constitute a broadly acceptable “solution”. Given the extreme differences in sociological and historical perspectives among stakeholders that characterize highly complex social issues such as “right to life” vs “right to choose”, I’ve found it useful to consider the perspective that the incommensurability of language among stakeholders is the source of the “wickedness” that makes dialogue among the stakeholders seem impossible.

  2. Thank you very much for this article and this attempt to debunk the metaphoric vagueness of so many concepts that are used in the context of interdisciplinarity. Plenty of other concepts can be analyzed like that: something complicated does not necessarily means something complex; integration of scientific elements from another discipline does not mean that you understand completely these elements; interactions does not mean symmetrical interactions, and so on.

    ID is familiar with such grandiloquent concepts. In my opinion, it is because ID is a general conception of science linked to an institutional conception, and not an attempt to describe actual or even potential science. Compared to the multiplicity of situations in science to which ID can be ascribed (from the creation of new disciplines, such as genomics, to the basic scientific interest stemming from the listening of a conference of an exogenous discipline), ID seems in the same time too general to distinguish what can be and cannot be counted as ID.

    This comment follows your general idea : there is plenty of work to do to understand and describe the multifarious interactions in science. But we have to be very careful using general concepts that have been developed as institutional incentives (in that respect, ID can be compared with key words such as Innovation ; Nano-technology; Big Data, etc.). The purpose of your article seems to be associated with this approach: once you have let aside this general idea of incommensurability, it becomes possible to analyze real problems of interactions in science: is it possible to use the scientific materials from another discipline without having a background knowledge? Is it different to borrow a theory, a concept, a method, data, problems form another disciplines? What is the difference between understanding scientific elements and being able to use them in an appropriate context? An so on….

    • Dear Romain Sauzet,

      thank you very much for your wonderful comment. You put things very well indeed. If you want, check the article on which this post is based (Politi, V. 2017. Specialisation, interdisciplinarity, and incommensurability. International Studies in the Philosophy of Science, 31: 301–317). IAs for the “grandiloquent concepts” coming from an institutional conception of science, I feel like the analysis of “buzzwords” (ID, Responsible Research, Innovation, Open Science, Citizen Science, Public Engagement of Science, etc.) may become a sub-field of research on its own…

  3. Vincenzo, I think some of the common myths you disabuse in the last part of your post still retain power because they use the words “incommensurable,” “successful communication,” “collaboration,” and “disagree” differently than you do. Can you please define each of these terms from your perspective? Perhaps also “incompatibility,” which you mention in the post.

    • Dear Bethany,

      thank you for your two comments. This reply will attempt to answer to both of them.

      To begin with, I am not sure whether your ‘all-is-different-not-incommensurable’ perspective fully persuades me. You claim that, in principle, everything can be integrated via metaphors. The problem is how we define ‘integration’. I subscribe to the view for which science is a problem-solving activity. Therefore, my idea of ‘integration’ in ID is that for which different theories, methods and perspectives are blended together and co-create a new theory, method and perspective capable of solving a set of specific problems in the scientific practice. In my view, integration results in a whole which exceeds the sum of its parts, and it does so in order to solve some problems scientifically. I am not sure whether establishing analogies and similitudes via metaphors leads to this sort of result. The construction of metaphors may help in the first stages of ID, but it is not in itself sufficient to guarantee its success.

      Furthermore, I feel that the role of metaphors in ID risks to be somehow overstated. For example: we can ‘metaphorically’ regard the stock market as a sort of physical system and, therefore, we can take a model which has been successful in, let’s say, Statistical Mechanics and apply it to Economics. Does it mean that, in so doing, we have “successfully integrated” Physics and Economics? I would tend to answer in the negative: economists do not need physicists to use a model which has been borrowed from physics; furthermore, when a model ‘migrates’ to another discipline or domain, it is re-interpreted and re-adjusted for the new context. After all, we wouldn’t say that Bohr ‘integrated’ astronomy and micro-physics when he used the metaphor of the little solar system to represent the structure of the atom!

      In any case, your point is very interesting and I hope that others will express their views on this issue too.

      Your second comment gives me the opportunity to clarify a few things.

      First of all, while incommensurability is the source of disagreement, not every disagreement is caused by incommensurability. Disagreement and dissent are endemic in the scientific practice, even among scientists practicing from within the same paradigm or with the same perspective. The disagreement originated by incommensurability, however, is of a special kind: namely, a disagreement about ‘fundamental’ issues. It is not the disagreement between those who claim that we should run the experiment ‘n times’ and those who claim that we should run the experiment ‘n+1 times’. Rather, it is the disagreement between those who say that we should run this experiment and those who don’t even see the point in running this experiment to begin with.

      Similarly, while incommensurability can express itself through communication problems, not every communication problem is underlied by incommensurability. Sometimes, miscommunication is caused by vagueness or ambiguity, and all it takes to have a successful communication is a bit of clarification. If there is incommensurability, however, you may clarify as much as you like but, in the end, even though scientists will be able to see each other’s point they will still disagree on fundamental issues.

      I do hope my reply clarifies these concepts and thanks a lot again for your contribution to the discussion!


  4. Thank you for reminding us of the helpful distinction between “incommensurable” and “just different.” The more I study and practice ID, the more I wonder if nothing is incommensurable but all is just different. (The exception is when we can’t integrate two things for social reasons, like stubbornness, not epistemic reasons). The main reason I lean towards this all-is-different conclusion is because, in the end, we can integrate anything using metaphor. For example, “Multiple linear regression and ethnography are both explorers of the frontier, it’s just MLR is Manifest Destiny and ethnography is a teenager on gap year in Europe.” (I jest.) I really can’t think of a case where this fails in principle. What do others think?

  5. Commensurability or incommensurability is not threatening anymore when one considers the following.
    Choose for a length and construct a square. What happens is that you have a square with a length of the diagonal incommensurable with the length that you did choose (if you choose for the length as unity, you get a length of the diagonal of the root of 2, incommensurable with 1). What is the difference? You choose a length, you construct something in reality and you get also a length that you cannot choose but that happens in reality. For sure you can choose to use the length of the diagonal to construct a new square. What do you get? A length of the diagonal of the new square incommensurable with what you could choose.
    There is no difference with interdisciplinary work: all stakeholders choose something and get also something different that could not be chosen by that stakeholder.
    The essence is that all stakeholders construct something together in reality and that they accept that also something different will happen that is incommensurable with what they would have chosen.

  6. I find this to be a highly problematic post and will only scratch the surface of my concerns in an effort to send readers to more informative sources on this topic. Incommensurability entered the philosophy of science literature through Fleck, Feyerabend, and then, most famously Kuhn (1962). For none of them was the sense of the term related to mathematics; for Kuhn, in fact, he chose the term to try to speak to the idea of Gestalt switch — in the sense that to understand a scientific idea as it moves from one paradigm to the next, one must accomplish something like a Gestalt switch to follow it. In fact, pace Dr. Politi, all three of those thinkers saw incommensurability as operating in a historical (and never an ahistorical mathematical) context. Kuhn, who popularized the term (and indeed his use of it) is the most cited author/idea in the second half of the 20th century; to have neglected this history, and indeed the hundreds and hundreds of authors who have taken up interpretations, challenges, and affiliations with him/it, seems to me to be dangerously neglectful. What Kuhn was pointing out was that the practices (cognitive, conceptual, theoretical, physical, technological, and methodological, etc.) and the assumptions and taken for granted meanings that go with all of those practices that make up a way of thinking/observing/experimenting about something (a discipline, a paradigm, a field), give rise to ways of making expressions about the things observed/seen/ found or the things done or methods or theories used, that get their meanings from all of those things that go into that way of seeing/understanding things. So when two very different disciplines or successive disciplines separated by a scientific revolution use terms or expressions or ideas that make sense within their approach they are very likely not to make the same sense (and sometimes show up as nonsense) in other disciplines. This always needs to be paid attention to in ID situations; it may not always be a problem and it may not necessarily appear to be a problem when in fact it is causing mis (or impoverished or sloppy) understanding (and so less than rigorous science), but it can never be resolved by thinking you can stand in some neutral position and translate from one discipline to another (because you are standing somewhere too). Incommensurability is a very complicated issue that is important for anyone interested in ID, and I encourage those who are to wade deeply into the writings of Fleck, Feyerabend, and Kuhn to try to get a handle on the issues they were trying to address when they coined this term.

    • Dear professor David Stone,

      thank you very much for reading my post and for taking the time to comment on it. Thank you for expressing your concerns, which will allow me to specify my position a bit better.

      First of all, I have never claimed that Fleck, Feyerabend or Kuhn used the term ‘incommensurability’ in its original mathematical sense. However, to say that “For none of them was the sense of the term related to mathematics” is a bit misleading: in fact, although thay used it in a metaphorical sense, they were very much aware of the mathematical origin of the term. This is what Thomas Kuhn himself tells us quite explicitly in the first two pages of his “Commensurability, Comparability, Communicability” (1982), from which I have even borrowed the example of the ration of the radius and the circumference. As a side remark, I would also like to add that it is incorrect to say that Kuhn “chose the term to try to speak to the idea of Gestalt switch”. In the Structure of Scientific Revolutions, Kuhn spoke about the Gestalt switch to explain what goes on during a change of paradigm; he got all these ideas from the works in experimental psychology of Bruner and Postman. While all the concepts ‘incommensurability’ and ‘paradigm change’ are clearly inter-related, they should not be confused: in fact, to say that changing a paradigm is like undergoing a Gestalt switch does not imply, in itself, that the two paradigms in question are incommensurable. (It must also be considered the fact that, soon after Structure, Kuhn abandoned the talk about Gestalt switches, because he was interested in the dynamics of the community of scientists, not in the psychology of the individual; he did not abandon the talk on incommensurability however.) I do agree with you when you say that “all … those thinkers saw incommensurability as operating in a historical (and never an ahistorical mathematical) context”; but, again, I never claimed that they saw incommensurability as operating in an ahistorical mathematical way. Therefore, I don’t understand what you are concerned about exactly.

      Having clarified these things, it is also necessary to specify that my post makes references to different things, but this does not mean that it aims at explaining all of them in depth. In my post, I speak about:

      1. the general meaning of the term ‘incommensurability’ (i.e., its original mathematical meaning)
      2. how philosophers have used ‘incommensurability’ (with reference to scientific revolutions, etc.)
      3. how and why ‘incommensurability’ has entered the discourse about interdisciplinarity

      Given the nature of this blog, the interests of its audience, and the fact that what I wrote is, indeed, a blog post and not an academic paper, my main concern here has been with 3. But in order to address 3, I had to spend a few words about 1 and 2. Therefore, when you say that “to have neglected this history, and indeed the hundreds and hundreds of authors who have taken up interpretations, challenges, and affiliations with him/it, seems to me to be dangerously neglectful” I feel that you have dangerously misunderstood both the aims and the format of this blog post. Since I am actually specialist in Kuhnian studies, I can ensure you that in my published works and in the book I am writing I do not neglect the history of incommensurability. But, as I said, in this blog post, and within its obvious limits, I wanted to speak in an accessible and popular way of how and why ‘incommensurability’ has entered the discourse on interdisciplinarity. I discussed whether it makes sense to speak about ‘incommensurability’ in cases in which we have just ‘different, non-competing disciplines’. I also suggested to move beyond the idea that incommensurability is a linguistic/semantic issue which may cause some problems to communication, since the fact that two groups can communicate and understand each other does not imply that they agree on fundamental issues nor that they will be able to integrate their theories and methods.

      In case you are interested in this argument and the context from which it has been developed, you are invited to read my paper “Specialisation, interdisciplinarity, and incommensurability” (

  7. Thanks for this very interesting exploration of incommensurability. Two issues arise in my mind after reading your text. The first issue begs the second. The first issue is this: what if two scientists considering the same set of methods arrive at two opposing views? One says the methods are incommensurable, the other says the methods represent a healthy pluralism. What tools do we have for weighing the evidence of these arguments? Then, as a second issue, what if power dynamics are related to the opposing view points? What methods do we have for studying privilege related to methods identities? Could privilege be related to arguments about incommensurability? About pluralism?

    • Dear Kirsten Kainz,

      thank you very much for your interesting comment. About your first point: instead of regarding ‘incommensurability’ and ‘pluralism’ as two separate things, one may think that ‘pluralism’ is actually driven by ‘incommensurability’ (the argument would be: these views are irreconcilable because they are incommensurable; therefore, it makes no sense to try to unify them; therefore, pluralism). In a sense, Kuhn himself got to a similar conclusion. In some of his late papers (some of which have been collected in The Road since Structure, 2000, edited by Conant and Haugeland). He said that, sometimes, a scientific community can simply ‘break’; this is how new specialties and sub-specialties are formed and this whole process of specialization is indeed driven by incommensurability. The overall emerging picture of science is indeed very pluralistic: a plurality of groups and sub-groups of specialists, separated by an incommensurable divide, each devoted to the study of a restricted part of reality. When it comes to interdisciplinarity, however, it is not entirely clear whether this pluralism is also a ‘healthy pluralism’ – especially considering that the idea behind interdisciplinarity is, indeed, collaboration and hopefully integration. In the light of these considerations, we wouldn’t even need to weigh the evidence in favour of who says that there is incommensurability and who says that there is pluralism: they may be both right after all, but the problem remains about how we solve incommensurability, or how we integrate the plurality of different views.

      The second issue you highlight is immensely interesting. In my blog post I urged not to treat ‘incommensurability’ as a purely linguistic/semantic problem. In my paper “Specialization, Interdisciplinarity, and Incommensurability” (, for instance, I speak about methodological and cognitive issues which go beyond the level of the problems with communication. It would be very interesting to expand ‘incommensurability’ in order to include precisely what you say – that is, power relations and how some methods are considered to be better than others. I have a forthcoming paper on the rhetorics of interdisciplinarity which touches upon these issues. However, my work has been mainly descriptive, as I don’t have any general “recipe for interdisciplinarity”. (Part of my work is concerned, more or less implicitly, with the very possibility or usefullness of speaking about ‘interdisciplinarity in general’).


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