Capitalising on incommensurability

By Darryn Reid

Darryn Reid (biography)

How can we harness incommensurability as a pivotal enabler of cross-disciplinary collaboration?

Effective cross-disciplinary research across multiple traditional disparate fields of study hinges on logical incommensurability, which occurs because, in general, those ideas will have been constructed using incompatible frameworks to solve distinct problem formulations within dissimilar intellectual traditions.

In other words, the internal logical consistency of a discipline’s way of approaching problems is no guarantee of ability to be integrated with another discipline’s way of approaching problems. Incommensurability should come as no surprise to anyone involved in cross-disciplinary activities. What is pivotal here, however, is the view that incommensurability is not an obstacle to be avoided or feared but an enabler. Moreover, it is the central enabler – worthy of celebration – and the focal point of cross-disciplinary advancement of knowledge.

I support this contention by reviewing the similarities between the philosophies of Thomas Kuhn and Karl Popper. This is followed by a quick dive into the creativity arising from the incommensurability between the theories of general relativity and quantum mechanics.

Revisiting the philosophy of science

The sociological explanation about the observed historical conduct of science provided by Thomas Kuhn represented an important break from unhealthy positivist doctrines. It is distinct from the critical rationalist account of science of Karl Popper, who had previously offered a firmly logically-oriented epistemology and methodology. Arguably, Kuhn has been much more influential in fields such as the social sciences – after all, his insight is really much more sociological than epistemological as such – while Popper has been much more influential in the mathematically oriented empirical sciences.

While Kuhn and Popper are sometimes seen in opposition, this is, at best, a gross oversimplification.

What Popper disputed was not Kuhn’s counter to positivism. Popper rejected positivist doctrines much more convincingly on more formal logical grounds. Nor did Popper dispute Kuhn’s observation about adherence with paradigms interspersed with periods of disruption. Popper had a similar distinction, but as manifestations of distinguishing science from non-science.

Kuhn started from the condition that an epistemology and methodology should align with the history of science, leading to the conclusion that this sociological pattern is necessary or even inevitable. Given the inherent logical asymmetry between confirmation and refutation, Popper contested that periods of ‘normal science’ are not normal but undesirable aberrations and that science can and should aim to maintain a perpetual state of Kuhnian revolution.

Kuhn built his picture starting from incommensurability to reveal why the history of science manifests the inability of proponents of different ideas to connect them effectively. He rejected notions that science advances through mere accumulation of facts converging on ultimate truth. Popper had already rejected cumulative notions of scientific knowledge, but as a direct consequence of the logical asymmetry of universal propositions.

Incommensurability, in this setting, means that different ideas are difficult or impossible to directly compare and hence cannot be simply integrated into a larger coherent whole because they rely on different underlying concepts to address different and incompatible problem conceptions.

Imre Lakatos later aimed to combine Popper’s focus on logical validity of theory in relation to empirical observation with Kuhn’s sociological insight about agreement around conventional theories. Lakatos distinguished core theory from surrounding auxiliary hypotheses, distinguishing progressive and regressive development depending on whether changes to auxiliary hypotheses increase explanatory power or merely serve to protect the core from refutation. Extending this to the cross-disciplinary setting, Lakatos’ notion of regressive change must be expanded to anything that serves to hide incompatible problem conceptions from view.

General relativity versus quantum mechanics

The crucial role of incommensurability can be seen at work within almost any field worthy of the name. While there are numerous examples of incommensurability from which to draw, its presence dividing the two major theories of physics has been what has disproportionately driven physics forward.

General relativity, which explains the large-scale structure of space-time, and quantum mechanics, which explains the behaviour of matter and energy on atomic and subatomic scales in terms of electromagnetism and the two nuclear forces, are individually pinnacles of exquisite empirical success. They are also fundamentally logically incompatible descriptions of reality.

Roughly, general relativity says the universe is smooth and continuous. Quantum mechanics says it is chunky and jumpy. Moreover, time in general relativity is an internal dynamical variable, while in quantum mechanics it is background (external and independent). Straightforward resolution of the two great theories by integrating them, equivalent to interpreting each within the other, generates abject nonsense.

What has emerged from this incommensurability is a whole raft of new theories aimed at solving new problems. These include string theory, which can be seen as a generalisation of quantum field theory which, in turn unifies special relativity and quantum mechanics; M-theory that unifies variants of string theory; and loop quantum gravity.

Without empirical refutation of either general relativity or quantum mechanics, it has been the relationships between the theories and particularly their incommensurability that has had the greatest influence in driving theoretical physics forward.

None of this emphasis on incommensurability diminishes the importance of creative propositions and attempted logical and empirical refutation to determine reliable theories. Rather, all three aspects are deeply entwined into the bedrock of effective scientific collaborations that span multiple disciplines.

Where does this leave us?

This emphasis on incommensurability has accentuated the need for better structuring in notions of knowledge development. It requires a far more explicit problem-solving structure than described by Kuhn or even Popper.

It means that problems, like solution options, are also choices to be made and later overturned when logical and empirical vulnerabilities trace back to them. The growth of scientific knowledge is better understood through successive revolutions in problem conceptions than in the evolution of solutions.

This is where incommensurability as tool of cross-disciplinary collaboration comes in. Particularly in a multi-discipline setting, it doesn’t really pertain to solutions. Instead, incommensurability between our pet theories bears directly against our distinct – though overlapping – problem choices, illuminating them and thus pointing us in the direction of better problems from which to initiate our collaborative creation and testing of future candidate solutions.

Kuhn and Popper, whose ideas remain influential in different modern fields, are not so incommensurate after all. That said, the key to utilising incommensurability, especially in collaborations that span traditional disciplines, is to normalise scientific revolution and to do so upon a basis of tolerance and cooperation between people in the creation – and intense but ingenuous scrutiny – of competing ideas.

My experience with cross-disciplinary collaborations has reinforced the practical as well as theoretical importance of logical incommensurability as a centrepiece of effective collaboration, to the point where its discovery is openly celebrated. My collaborators and I come together around the incompatibility of theories excited, not to integrate components of existing knowledge, but to surpass them.

Do you have experience with the identification and use of incommensurability to promote cross-disciplinary progress and generate new ways of being creative?

Biography: Darryn Reid PhD is Principal Scientist in Joint and Operations Analysis Division, Defence Science and Technology (DST) Group in Adelaide, Australia. He has research interests in pure and applied mathematics, meta-mathematics, theoretical and applied computer science, philosophy, military theory and economics, and is also an artist. In other words, he knows just enough to understand how ignorant he is.

22 thoughts on “Capitalising on incommensurability”

  1. Everybody has “.. experience with the identification and use of incommensurability to promote cross-disciplinary progress and generate new ways of being creative”. The universe works in this way. As Spencer Brown showed: “make a distinction” (well, he said “draw”, but I prefer “make”) leads to both logic, paradox and the existence of this universe. One needs to make a distinction to identify. And from that reality emerges. (Maybe I should have written The One, ;-))

    Because the paradox of identity (or identification, identifying, see Smith and Berg, Paradoxes of Group Life) induces incommensurability. You can not have the one – identity (and discipline) – without the other – incommensurability.

    Incommensurability cannot be measured, because it’s not about quantity, but a quality. An identity cannot established. It’s about relationships – the qua-li-ty, relating with others and reality. (Webster writes: broadly : lacking a basis of comparison in respect to a quality normally subject to comparison ).

    We construct (make up) “our” identity from a group (or discipline) we (want to, need to) belong to. You identify yourself with (different) group(s) of people, who in return discipline each other – and you -. That’s why we call it “disciplinary measures” and “disciple”.. . Measuring uses a yard stick defined by the group – discipline – which (also) is measuring itself.

    Of course, I’m using ambiguity in meaning of expressions, which people in any discipline try to reduce, or deny, in order to “safe” or “defend” that very discipline.

    Identity is a true fiction (as proven by Vaihinger, in The Philosophy ‘As-If’). We use “identity” identity as a useful fiction, which we create (as in being creative) and maintain, because it “works”, it’s useful within a discipline. Vaihinger compares the fiction of thinking with a machine: a machine makes work lighter and a fiction makes doing the work of thinking easier. I say, we use it as a “place holder” of a thought. ‘Hold that thought”.

    That a fiction – like identity, discipline, individuality – can be useful, doesn’t make really exist, nor make it true. They’re a kind or “true metaphors”, in carrying over “meaning”.

    Tensions between identities make up incommensurabilities and these “generate” creative opportunities. It takes one to know one.

  2. Dr. Reid points us in a valuable direction, which I am afraid may be lost in the use of the term incommensurability. Over the last 50 years, I fear this term has become fetishized and I despair when I watch it send people down rabbit holes chasing what Kuhn meant by it (or originally meant by it, or meant by it later, or should have meant by it, or what he should have used instead of it, or what’s wrong with it, etc.). I knew Tom in his later years and I think he lamented it too…. But back to the valuable direction. In his post, Dr. Reid reminds us of something that Mol tried to persuade of 20 years ago, which is to have the humility, or what Reid calls the abilities of tolerance and cooperation, to recognize that often in conversations across disciplines there is even as much as multiple ontologies at play and that the starting point for collaboration is recognizing this and then doing the right thing.

    In Mol’s example, that recognition was used to paper over differences of interpretations in order to retain the coherent story of a single ontology (this would be doing the wrong thing), but the papering over let the cat out of the bag (to mix my metaphor), only because each player was working from their own ontological starting point was papering over necessary. The question left unanswered in the blog post – and to be fair, it’s only a blog post – is how one enters into and engages in collaborations in a way that makes cross-disciplinary discovery possible.

    From the work I have done in this area, I can say that there is a lot of difficult work that one needs to do on themselves to arrive at Dr. Reid’s “tolerance and cooperation.” Here, I do think Kuhn is helpful. He was the first to unpack (some) of the work that goes into turning regular people into disciplinary thinkers and practitioners – ways of thinking (abstractions, assumptions, logics, ideals, theories, approaches, ways of formalizing, functionalizing, and mathematizing everyday things into scientific objects, etc.), ways of doing (methods, experimental practices, sequences, field practices, etc.), ways of valuing/feeling (parsimony, symmetry, beauty, simplicity, objectivity, subjectivity, etc.), ways of training (the use of exemplars, which then give rise to paradigms of thought and approach), and yes, ways to talking, writing, communicating, using words, terms, shorthands, that disciplines employ to operate internally in precise and predictable ways. When all of that comes together, one gets an internally self-referential and self-reinforcing arrangement of practice and thought (akin to what Heidegger called a world and which Kuhn tried to get at with the term paradigm).

    At the risk of overstating it, what one develops through the course of being trained in a discipline is a disciplinary identify (which many find difficult to separate from the rest of their identity), and it turns out to be very difficult to turn all that off or put it aside. More precisely, what is really challenging is to understand who you are when you are in a meeting to undertake a collaborative scientific project if you are not your disciplinary self – what self are you supposed to be that brings with you your disciplinary understanding about how the problem should be framed or named or approached or understood, and yet is fully open to other ontologies, approaches, frames, and names? If this was as easy as coming to that meeting with an open mind and a generous heart, then most of us could readily do it, but the clear reality is that this is much harder than making an attitude adjustment, and no one teaches us how to do it. Toward that end, I started a non-profit called the Institute for Transformational Education and Responsive Action in a Technoscientific Age (ITERATA). One of my goals for this year is to announce a grant program to provide funding for people who can help address this problem. Stay tuned.

    • Hi David, thank you for sharing your thoughts. You are probably right about the unfortunate loading of the term: I tend to talk about ‘logical incommensurability’ to place some emphasis on the fact that I intend something both stronger and easier to define than what Kuhn described, but ‘semantic incommensurability’ would probably be closer to the mark. I think Kuhn asked some really interesting questions even though I don’t always fully support his answers. The problem with the latter term has been that it takes some explanation to outline exactly what ‘semantic’ means (pun intended!) before getting to ‘incommensurability’ in this sense. I won’t presume to potentially insult you too much with a lecture about this here, but just for completeness: I’m driving at really fundamental incompatibilities in meaning that different theories that are individually successful can nonetheless manifest, rather than differences in how things are expressed. These incompatibilities can have highly nontrivial structures, so different theories can express concepts not expressible in each other, and they can support different conclusions because they utilise incompatible notions, for instance how time in General Relativity and Quantum Mechanics are mismatched distinct concepts.

      In the collaborations that I have the privilege of leading, we have gone to considerable effort to frame the basis for collaboration very carefully to obtain effectiveness with respect to bringing together multiple fields and backgrounds to best effect. I did work in economics theory to establish an economic basis that I hoped would be reasonably comprehensive for effective collaboration, which has had impact in terms of enabling the development of new kinds of agreement structures to better support collaboration for Defence, which I will link for you in case you happen to be interested in this. Of course, this was about effective allocation of resources and the issues that arise as a result that can be inimical to collaboration effectiveness, but this does not itself address the present questions about what goes on within those collaborations in relation to handling potentially many semantically dissimilar theories or models.

      We have taken considerable strains to try to get this as right as we can, with the enthusiastic support and participation of all the collaborators. Just making behavioural expectations clear and binding in the sense of property rights described in the economics paper has been valuable, and has given a basis for both keeping people away who could disrupt things – it takes only one disingenuous person to really wreck a good collaboration – and for then enabling free and open discourse on the relative merits and weaknesses of different fields and their ideas. Debates in which people defend ideas they do not really hold to help someone else advance their own arguments has been a valuable type of exercise and one that participants clearly enjoy greatly.

      I would probably say that humility in the face of pesky reality providing evidence that illuminates weaknesses and failures still leaves something to be desired in the science community overall but I also think that dealing with incommensurability effectively is something where there is even greater potential for improvement. I would also acknowledge here that unfortunately a lot of the points I can make from experience with it are altogether too anecdotal: systematic research on effective problem-solving using incommensurability to enlighten either better decisions directly or longer-term better theory development is very difficult, because collaborative adventures are so individual and they take a long time to develop and play out. However, towards trying to chip away a little at this, I am also looking at utilising our extensive wargaming experience and knowledge towards setting up collaborative problem-solving situations for examining and evaluating different ways of handling both refutation and incommensurability in a systematic empirical manner. I cannot and will not completely resolve matters, of course, but I think a series of such studies might do much to at least identify definitively what does not work.

      Thanks again for your excellent thoughts.–managing-the-impediments-to-cooperation-nesQ.php?article_id=4796

      If you would like, you may always contact me for a copy of the published article or the more extensive pre-published version.

    • First, no apologies for peppering my observations with cliché catchphrases, they are intended to illustrate my point about ‘getting published’ standing in the way of good science. This is a growing challenge in contemporary academia, papers need to be catchy and ‘positive’, often worse, and once a hypothesis is framed around a buzzword one must stick to reiterations of this anchor, even when reasoning leads to or lends itself better to a ‘pivot’.

      Sticking with the notion that the contemporary tendency to fetichize resonant themes can end up a barrier to finding or even making ongoing progress towards sound answers, your contribution provides a very instructive ‘nudge’ by appending a phenomenological perspective to this argument. A ‘paradigm shift’ at a boundary of incongruous disciplinary knowledge necessitates an acceptance of a conceptual transgression, a trespass beyond the familiarity of one’s worldview.

      Even more so, in collaborative settings, this implies adopting formalisms of foreign disciplines, in effect internalising principles which may appear incommensurable and often incongruous. A breach of the legacy safety zone, the abstraction of indoctrination you comprehensively elicited as “turning regular people into disciplinary thinkers and practitioners”. My appeal to Dr. Darryn Reid is to build upon the phenomenological perspective instead of defending the semiotics etc. of a catchy byword in his argument.

      • I understand the sentiment about published standing in the way of good science, so it’s a great thing that for me in my role the motivation for what you describe is precisely zero. Moreover, the game as you outline it is not one that can be played in mathematical sciences, where the more typical publishing game is breaking up work into the smallest separately publishable units. Once again, I do not experience any incentive to do this in my position either.

        Were I to have described this as ‘oombilidodah’ instead of ‘incommensurability’, I’m sure you would have objected to this as well, on the basis that ‘incommensurability’ is established as a term covering a number of interrelated meanings, including the semantic one I’m focussing on, and so you should have, too. I did not raise terminology as a point, but it was raised legitimately because the term does have a range of related meanings; I clarified the one that I intend, which is among those in the literature.

        Were your claim accurate that I’m playing publication games with semiotics, then stripping away the terminology should leave us with nothing. What we have instead is my central point: the phenomenon that base differences in the construction of concepts mean that separate individually successful theories cannot be integrated. We have the phenomenon of General Relativity and Quantum Mechanics being deeply incompatible to illustrate. We have the phenomena that occur in the collaborations in general and even in those between mathematical scientists, let alone across fields more broadly, of theories as solutions to distinct but overlapping problems not being amenable to integration. We also have the phenomena of using this to drive new research by changing the scope of the research problem, and we have the phenomena of informing decisions using multiple incommensurate theories. Or should I say multiple oombilidodah theories? My point is focussed on these phenomena.

        If we strip away the terminology then we have my central point: the phenomenon that mere terminological differences are insufficient to explain cross-theory integration difficulties, and that this represents an opportunity to embrace. My appeal is to approach topics in good faith while avoiding the temptation to project legitimate general concerns as accusations at those who do not share in them.

        • Surely, there is a token of good will to be found in recognising the possibility of seeking out conceptual bridges on phenomenological grounds, e.g. at a higher level of abstraction or as you’ve now clarified “changing the scope of the research problem”, in addition to providing a path for reflections on potential barriers to such cross-disciplinary work. I for one, found David Stone’s insights on theoretical and routine confines of familiar silos we take comfort in compelling enough, as well as very likely complementary to fleshing out your hypothesis in practical terms. Frankly, a facet of your proposition, which at least from my point of view, doesn’t appear to match the sense of positioning it as an enabling utility or in fact a tool as you claim. In a nutshell, despite the illustrations, I didn’t actually see a methodology in ‘incommensurability’.

          • Thanks, Piotr. What we have in this little back and forth is a precise microcosm of the whole of what is commonly called the literature on inter (or cross or multi or trans) disciplinarity. Everyone in that “literature” writes from a disciplinary standpoint (their own academic or professional background) without usually trying to (and even when they try, never fully successfully) lay out that disciplinary standpoint. They then proceed to use words and concepts (yes, terminology) about interdisciplinarity that they simply assume to be shared and commonly understood (like paradigm or discipline). The reality, however, is that readers from other disciplines do not read those terms in precisely the ways we mean them, nor can they see the assumptions and other paradigmatic baggage we build into them (back to phenomenology) as we discuss ID or TD or MD or give examples of them or derive insights (or create theory or other kinds of generalizations) from those examples (or other data). And so, just like this conversation, there exists a whole “literature” (which I think shouldn’t really be called one) where everyone subtly (and sometimes not so subtly — think of poor Tom Kuhn) talks past each other, misreads each other, builds on those misunderstandings (or covers them over when they see some of them like the doctors in Mol’s study did – see Anne Marie Mol’s book The Body Multiple). Forty years of concerted study have not sharpened our understandings of ID or MD, they have certainly not brought us closer to any kind of truth about them (as though all of us as readers could even begin to agree that that is either possible or desirable). Instead, what we have is a twirling kaleidoscopic babel (which, agreeing with Darryn, goes deeper than terminology and into logic, epistemology, ontology, and other crawl spaces). In a number of writings, I have proposed a way out of this morass through the use of a transparent but non-disciplinary standpoint (which is a combination of hermeneutic and phenomenological moves) – see reference below. Absent a move like that, I’m afraid all this work will simply continue to chase its own tail.

            Stone, DA, (2013) Beyond Common Ground: A Transdisciplinary Approach to Interdisciplinary Communication and Collaboration, in O’Rourke M, Crowley S, Eigenbroad S, and Wulfhorst JD (eds.), (pp. 82-102). Enhancing Communication and Collaboration in Interdisciplinary Research, Thousand Oaks, CA: Sage Publications

  3. Thanks for this contribution Darryn, it is a stimulating contribution. The way I would identify the potential of incommensurability is when we experience an “Aha!” moment. A not longer leads to B, but rather A leads to C, and, by the way, B never existed.

    This is the moment in which we recognize that an old way of thinking is no longer sufficient to cover the new information that is being received. The original mental model that we started with, created by a specific training, background and environment, needs to be adapted. For this adaptation to be successful, however, requires more than new information. It also requires a willingness and openness to change the way we perceive reality and I guess this last part is more difficult than being able to understand the new information itself.

    At ETH Zurich in Switzerland, we have been teaching a curriculum known as “Integrated Systems and Design Thinking” that aims to help students identify the moments of insight and helps them, at the same time, to incorporate new knowledge to create an interdisciplinary understanding of environmental systems. Insights come from discussions with people from diverse walks of life, literature reviews and observations. The incommensurability that you discuss here, if I understand it correctly, is all around us and not only between disciplines, but also at every junction where mental representations of reality differ.

    • Hi BinBin, thank you for your comment. I really appreciate your interest: my enduring fear is not of being wrong but rather of being boring, so your reaction is deeply appreciated. Yes, this is a very good picture you paint here of the notion of incommensurability I have in mind, though I might also be careful to distinguish between logical incommensurability itself and its manifestations, which do occur all around us. I take a similar approach to the nature of uncertainty in terms of the presence of underlying irreducibly cyclic logical structures and their manifestation as unknowability – as opposed to the merely unknown – in so-called ‘wicked’ problem environments where the future and past are not symmetric.

      Your views here bring me to a point I sometimes emphasise in relation to the nature of knowledge, because it is common for people to think about this in terms only of explicit representations or explanations of phenomena observed: knowledge applies as much to implicit systems of expectations such as those instantiated in any living thing about the nature of its environment, and similarly applies to tacit assumptions that are often built in at the base of policy choices and designs of systems. I tend to think that the more clear we are about these assumptions and the more explicit we can be about the underlying reasons for incommensurability, the better handle we will have on the webs of incommensurability effects we experience in practice. This makes not only dealing effectively with these effects in collaborative settings much more effective but also represents, more or less, a precondition for being able to take advantage of them.

      A fair degree of focus for me is on enabling a future where our systems (especially Artificial Intelligence) as well as organisational practices support this much better than at present.

  4. Dear Darryn,

    This resonates very strongly with things I am thinking about, so thank you for the post – I appreciate it. I am a Professor at the School of Regulation and Global Governance which is an interdisciplinary school that works on ways to better understand and influence complex problems. We do this across a variety of areas, including some that might be close to home for you (eg our current work on developing frameworks for integrating thinking about economics, security and technology given emerging geoeconomic tensions, which we are doing with a Defence Strategic Policy Grant

    I am interested in developing ways to better teach systems thinking and complexity thinking, but in particular to focus on how to get people comfortable with holding multiple paradigms, models, metaphors and analogies in their heads simultaneously to look for the productive tensions that they create through their incommensurability. Part of what you are describing here is also well picked up by some people like Roger Martin who talks about the Opposable Mind and also Diaminds. Here is a paragraph I write about that in a book I have coming out in October where we explore 6 different narratives about the pushback against globalization:

    “The importance of broad-ranging synthesis and integrative thinking is also stressed by former Rotman School of Management dean Roger Martin. When Martin interviewed exceptional business leaders, he found that the common denominator in their thought processes was their ability to engage in integrative thinking, which he defined as the ability to hold (at least) two diametrically opposed ideas in one’s head and then, instead of simply picking one or the other, producing a synthesis that is superior to either opposing idea. He and his coauthors have variously described this sort of thinking as resulting from an opposable mind (in analogy to opposable thumbs) and diaminds (referring to the ability to understand reality through a variety of opposing plans and models and to still be able to act by producing dialectical and dialogical solutions to complex problems). Such minds combine informational breadth with logical depth. They embrace difference, ambiguity, conflict, and tension instead of seeking to reduce the world’s complexity into simple, one-right-way approaches to seeing, thinking, and feeling.”

    My sense is that we need to do more at universities and also in policymaking to teach systemic thinking and complex integrative thinking under conditions of ambiguity, uncertainty and fast-paced change. This is a bigger, longer term project but one that I think is needed! Your post speaks strongly to the sort of change in mindset that this requires and the sort of systemic thinking and cognitive flexibility that we should be aiming to achieve.

    Best, Anthea

    • Hi Anthea, sorry it took a little while to get back to you. I have had a look at the overview of the book and it seems interesting, especially given I have strong research interests in economics theory as well, so I have it on my reading list. I note pleasingly that the point is described in terms of giving all the positions their due. Arguing for a particular position to an audience that already agrees with it is more common in this space, which tends to be reflective more of ideological stances than of really informing decisions that include ongoing detection and subsequent problem-solving in relation to inimical effects and thereby avoid catastrophic outcomes.

      You also make an interesting point that I take as aligned with my fundamental theme here about the ability to simultaneously hold multiple points of view that do not necessarily fit neatly together. I would probably go so far as to say that this is what scientists should aim for, both individually and collectively in collaborations. I tend to avoid talking about “integration” because this usually invokes images of simply coalescing things together to supposedly obtain a bigger and more comprehensive account of matters; yet ideas can be logically incommensurate (which is deeper than the incommensurability as described by Kuhn but I kind of brushed over this a little for brevity), and not all ideas are of equal value either. Consequently, there are two problems this sets up: an integration based on really casting a bigger problem formulation, which I emphasised because this is essential in my work which primarily concerns the growth of scientific knowledge; and integration based on decision options evaluation using incommensurate theories.

      You bring a fairly strong emphasis in your comment on the latter point which is really about informing decisions – policy choices in particular – using the incommensurate accounts we have available now, so I will expand on this with a few thoughts (subject, of course, to change in light of better thoughts later). I do think this requires not just an integration in a mechanistic sense of the outcomes, so not just a look at the points that bear negatively against any decision option exposed by each relative to the other positions, but careful judgement about both the reliability of the theory with respect to the particular potential refutation it reveals, the significance of the effect on something or someone that this refutation might indicate, and the ability to effectively mitigate it. I guess the point here is that I do not hold that decision-level integration will generally be well represented by merely a Pareto optimality construction relative to the cumulative account of potentially negative outcomes. I don’t think in general there will be a single partial order and localisation will also be a aggravating concern.

      • Thanks Darryn.

        I agree that we should not see integration in mechanistic terms. I see it as providing a meta-framework for thinking about different approaches and holding them together in tension even if you can’t reconcile them. I think we often have incommensurate ways of understanding the world or values that are not just different but are non-tradable that we are pursuing and that often integrating up one level allows you to think about both without having to pick one or the other.

        I’m influenced here by some of the work of psychologists (like Tetlock and Suedfeld on integrative complexity and dragonfly eyes) as well as by complexity theorists. It reminds me of a quote by Niels Bohr: “The opposite of a correct statement is a false statement. The opposite of a profound truth may well be another profound truth.”

        Attempts to translate values from one frame to another can also go very poorly eg with sacred values. Here is an article on that that I think is really interesting. I explain it to my students in class re integrating economic and security values/viewpoints re when do we treat them as different but tradable (eg apples and oranges) and when do we treat them as different and not tradable (eg love and money).

        Btw, I am sure you know this already, but your piece also reminds me a bit of the two poles of economic thought articulated by Brian Arthur: He is obviously landing on the complexity side, but I find his crisp identification of the two poles and different underlying world views to be a helpful way to explain this to people, along with the two approaches in physics.

        Nice to chat by the way – it is great to see you thinking like this in science and I think we need to be thinking more like this in the social science space too. A great and thought provoking post!

        Best, Anthea

        • Hi Anthea,
          I wasn’t aware of the Tetlock and Suedfeld work, so thanks for pointing me towards this. I have seen the work by Arthur previously, though as papers rather than compiled as the book. The issue you raise here about incompatibilities in value structures is a really important one that lies close to the notion in Operations Analysis of ‘wicked’ problems, going back to Rittel and Webber in around 1973 (I think). Operations Analysis, which is a substantial part of the organisational backdrop in which I work, developed from mathematical methods for relatively closed well-defined problems in the two World wars (though it had its roots back in the 19th Century with things like railway scheduling and postal delivery problems). By even around the late 1950s and early 1960s it had become manifest that this was not capable of addressing many problems where there were multiple relevant agendas that were incompatible, and this gave rise to a separate social sciences oriented side of Operations Analysis by the late 1960s. An enduring problem that remains to this day is that the two sides of Operations Analysis do not work all that well together. Reinterpreting Rittel and Webber in our present context: distinctions in value structures are deep rather than shallow.

          This difficulty is part of the backdrop for my broader work, which has been about integrating these sides of Operations Research much better, and, as described in the article, this takes more than naive or mechanistic integration but rather a better foundational problem conception. The one I have put forward as the research direction is about grounding ‘wicked’ problems in the nature of uncertainty and therefore how to systematically deal with it; incommensurability shows up here as the implication that the criticisms of both sides of Operations Research directed at the other have much merit. In other words, the problem conception grounded really in deep mathematics and computer science together with a healthy dose of economics, and with a fair amount of military theory too, has the traceable consequence that both sides of Operations Analysis as it has stood are ultimately wrong, or to put it perhaps more gently, the problem concepts at their foundations are incomplete compared with the future capability we seek. Incomensurability of the kind I am describing here is an inevitable feature given all problem concepts are ultimately incomplete in some way. While this shouldn’t be at all shocking scientifically, it has taken both really good people well positioned in their science and a whole lot of effort to establish a solid basis for progress.
          But I am allowing my passions to run away with me here. I really appreciate your discussion and thank you for the additional information that you have provided to me.

  5. Thanks Darryn, These insights are really helpful in reflecting on multi-, inter-, and trans-disciplinary research as they are practiced. Three issues that interest me are: problem framing, integration and slow science. I draw on other blog posts to highlight some key points.

    Problem framing

    A real strength of multi-disciplinarity is that each discipline reflects on the issue or problem from its own frameworks, which has the potential to make the differences in problem conceptualizations very evident.

    See: In praise of multidisciplinarity by Gabriele Bammer

    Although inter- and trans-disciplinarity both highlight the importance of problem framing, there is rarely enough time in practice to draw out the relevant multi-disciplinary insights, let alone use incommensurabilities to come up with creative new problem framings.

    This is compounded when perspectives of stakeholders – both those affected by the problem and this in a position to do something about the problem – are added to the mix.

    See: A heuristic framework for reflecting on joint problem framing by BinBin Pearce and Olivier Ejderyan


    To date the primary focus in multi-, inter-, and trans-disciplinary research has been on integration of different perspectives. Thinking about what this means and how to integrate well is starting to mature.

    See, for example,
    Integration: The IPO model by Stephen Crowley and Graham Hubbs
    Metacognition as a prerequisite for interdisciplinary integration by Machiel Keestra
    Epistemological obstacles to interdisciplinary research by Evelyn Brister
    Integration, part 1: The “what” by Julie Thompson Klein
    Integration, part 2: The “how” by Julie Thompson Klein

    Mostly incommensurability is seen as an obstacle, as you say, and it tends to be put aside in the integrative effort. What you are pointing to is the need to not just look for easy wins in integration, but also to mine the incommensurabilities for what they might offer.

    Slow science

    It takes time to build the relationships among disciplinary experts and stakeholders that allow the full benefits of cross-disciplinary efforts to be realized. The slow science movement encapsulates this well.

    Particularly relevant here is:
    How is transformative knowledge ‘co-produced’? by Andy Stirling, Adrian Ely and Fiona Marshall

    I am also struck by Ismael Rafols’ recent blog post
    Addressing societal challenges: From interdisciplinarity to research portfolios analysis
    Especially his statement “‘Solutions’ to societal challenges will not emanate from 1,000 labs with the same combination of disciplines, but from labs of various epistemic combinations and social embeddings.”

    Some useful tools include:
    Responding to unacknowledged disciplinary differences with the Toolbox dialogue method by Graham Hubbs, Michael O’Rourke and Steven Hecht Orzack
    Using discomfort to prompt learning in collaborative teams by Rebecca Freeth and Guido Caniglia
    Embracing tension for energy and creativity in interdisciplinary research by Liz Clarke and Rebecca Freeth

    Other blog posts on incommensurability can be found at

    Thanks again. I think your insights could really move multi-, inter-, and trans-disciplinary research forward.

    • Hi Gabriele, thanks for sharing your thoughts. I will have to go through them in detail and that will take more time than I have today, but I wanted to post quickly a couple of thoughts since certain elements of your response have stuck in my mind, even if I change or extend them to make a better response later. I think I can pick up on all three aspects – problem-framing, integration and slow science – by drawing out a bit of a theme I’ve been progressing in close relation to the incommensurability observation. This is about framing decision-making more by using what is not known – or to be more formally correct, using what is known to be not knowable within the problem context – rather than how decision-making is more commonly cast fairly exclusively against what is known. This means avoiding assuming by default that what is known is complete or virtually so relative to the problem. The point of this is to use what is not knowable to advantage as well as to avoid unmanageable exposure by basing decisions in what may end up being pretending to know. From an adversarial standpoint, this is closely related to core concepts in military theory about strategy formulation, but I think it holds in economics and other problem types as well.

      Multiple incommensurate problem formulations can directly bear on decision-making by directly harvesting them for areas of conflict. These would generally bear on the limitations of each problem formulation relative to the others. The important point is that each might offer a point of refutation for a decision option, depending on the significance of the difference in terms of outcomes, that might be invisible to others. So integration is not integration of theories here but integration of refutations of possible decision options in order to inform about their weaknesses or limitations.

      This is a distinct thread that can operate in the relative short term in parallel with the longer term research, where the goal is more to redress the limitations and weaknesses in the different problem concepts by developing a new problem concept, so I would associate the slowness of research here closely with the problem framing – indeed, I hold that scientific progress is not marked in better solutions but in better problem conceptualisations. I have focussed more in this article on this explicit drive for progress in this sense since in my problem areas this is the primary motivation, but it’s also true that I have been careful to structure research programmes with the ability to yield results at all points more or less along the lines described above, with incommensurate theories that are all relevant to the circumstances being assembled relative to action choice rather than comprehensive model or theory.

      I will take some time to go through your points more carefully so if I detect error as I do then I will change this initial reply to reflect what will then be my improved state of knowledge thanks to your help.

      • That’s a really smart way to bring unknowns into the picture. It could also be useful in shifting a group’s mindset away from defending particular ‘turf’ to jointly exploring new terrain.

        • I agree that it can be used in this way. We’ve used this as a deliberate tool or mechanism in some collaborations but probably my view on it has been grounded long ago now in looking at decision-making in the sense of military strategy formulation and especially about deception and resistance to deception. We started looking at possibly using entropic measures or curvature based methods to put some formalism to it but priorities have really been elsewhere; the work is still relevant to this but is focussed differently now: characterising the effects of uncertainty around properties of problem environments as invariant conditions that can be composed into abstract environment models.

          Thanks so much for the effort that went into putting together your excellent comment. I will look more into all the linked articles and this will help me assemble a better account of things as a result.

  6. Thank you Darryn, I feel this important although I realise I don’t grasp it all. I work in humanitarian aid focusing on what I might now recognise as the incommensurability of processes of autonomous, organic communal self-help among emergent groups in crisis affected populations v. the institutionalised, externally-planned, top-down mainstream aid of donors, UN and aid agencies. Shouldn’t be a battle twixt the two – it would be great to be more constructively enabling in seeking more effective ways of building resilience in what are highly uncertain environments in which different actors have very different perspectives and operate under very different incentives. What can I read that is less difficult to understand and can point me in the right direction? Many thanks

    • Hi Justin, thanks for your interest. There really isn’t all that much literature directly expanding on the topic as I’ve presented the matter here, since this presentation involves a novel formulation. I have an invite to write more on the topic for a journal. However, incommensurability is discussed a fair bit by way of background in the philosophy of science, so by authors including Kuhn, Feyerabend (of whom I’m personally not really a fan), Lakatos, Popper and others since Popper such as Jarvie and Miller. I think Oberheim and Hoyningen-Huene did work examining what they describe as meta-incommensurability in relation to notions of science, and Best looked at incommensurability between theories about meaning (so what for me amounts to model theory whereby mathematical systems are ascribed meaning in relation to one another). Best describes how first-order meaning (so allowing quantification over individual variables) requires second-order theory of meaning (so where quantification can range over sets of variables as well), so one can have meta-incommensurability because of the presence of different second-order theories of meaning. This is easily seen in deep mathematics but Best was describing this in a philosophy of science setting.

      Possibly the central thing here to take away is that logical incommensurability between fields or stakeholders is not really a bad thing at all, because it represents very high value opportunity. The bad is more in how people sometimes react to it rather than the natural and inevitable phenomenon itself, and I think raising awareness of the opportunity can help to defuse this. Yet taking advantage of the opportunity means not merely integrating stuff together but rather it compels moving to a bigger and more interesting problem conception from which to then develop new solutions.

      • I guess just to pick out something that may not have been clear enough: the logical based view of incommensurability by people along the lines of Best is actually deeper than the relatively weak notions of incommensurability of Kuhn and Lakatos. I think it is fair to say that the relatively weak view common in philosophy of incommensurability as essentially syntactic and terminological in nature, as Vincenzo mentioned in a separate comment, traces to this basis. I’ve taken a strong view, in contrast, that comes from mathematics and hence that aligns much more with Best and similar authors.

  7. Thanks Vincenzo, I appreciate your having read my article and your comment, and I look forward to having a read of the paper. I am also critical of Kuhn but careful not to overlook the value of his work either. I think he overreached: I disagree with the base premise that an epistemological and methodological account of the nature of science must account for any past account of how science actually unfolded in practice – I think this fails to sufficiently respect both science itself and the humans who undertake it – yet I do place significant value in the sociological insight he established about how it has often occurred in practice and how it has often fallen short of its ideals. In other words, I think that there can be a gap between principles for the growth of knowledge and how knowledge development plays out in practice when people get together to do it. This distinction is crucially important here.

    I agree too that there is a view that remains commonplace seeing incommensurability as more or less syntactic or terminological, from which we would then rightly conclude that different fields are not really incommensurate at all. The problem is that the premise here is mathematically false, and easily shown to be so: deep semantic distinctions occur between distinct mathematical theories that even share the same syntactic structures making them logically incommensurate. I drew here from the case of General Relativity and Quantum Mechanics because these also reflect this kind of deep semantic incommensurability in a really direct, interesting and much celebrated field of enormous practical importance.

    The cross-disciplinary research efforts in which I am deeply invested work so well in part because there is both an appreciation of these effects and a strong desire to use them to advance the state of knowledge. I think it reflects an intellectual maturity that I also wanted to convey here.

    Thank you for your comment and for pointing me to your paper!

  8. Dear Prof Darryn Reid,

    thank you so much for this interesting and important post. As you know, Kuhn has been widely criticised by philosophers and not too many of them have appreciated the potential of his notion of incommensurability to understand some of the features of cross- and inter-disciplinary research. It is therefore with great pleasure that I have read your considerations, which come from your actual experience in cross-disciplinary research activities (and not just from pure philosophical arguing). Many philosophers are still stuck with the idea that incommensurability has to do only with meanings and meaning variations, not with problem formulation and solution appraisal. For this reason, I liked your view on ‘logical incommensurability’.

    Other philosophers think that incommensurability has nothing to do with cross- and inter-disciplinary research because ‘different’ disciplines are not ‘incommensurable’. I respond to this argument in one of my papers, which I invite you to read if you are interested:

    In the paper I also mention ‘methodological incommensurability’, which may be similar to your ‘logical incommensurability’.

    I would like to know if you have published some academic papers on these issues, or if you are planning to do it. (I am currently working on a paper on incommensurability in cross-interdisciplinary research based on a qualitative study on an actual cross-disciplinary research, and your ideas may be useful for me).

    Thanks a lot!


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