By Darryn Reid
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.