In 1962 the philosopher Thomas Kuhn published The Structure of Scientific Revolutions, a book that shook the history of science and laid important groundwork for an entirely new field – the sociology of science. In this contentious volume, Kuhn portrayed scientific revolutions as extended periods of intellectual conflict that he called “extraordinary science”. Older theories, during such times, can no longer account for new phenomena.

A famous example of such a revolution is the “ultraviolet catastrophe” of the early 1900s. That was when classical physics predicted that the energy emitted by a black body should increase to infinity as the wavelength of the radiation falls. This prediction disagreed with experiments, which showed the energy peaking before dropping away again, forcing physicists to turn to something entirely new: quantum theory.

By emphasizing discontinuity, Kuhn did not think new paradigms have to “fit” or share scientific vocabulary with previous ones. To use his language, he said they are “incommensurable” with each other. In proposing incommensurability, Kuhn was challenging the widely held assumption that scientific knowledge accumulates linearly over time. Instead, he argued, science switches to new paradigms, defined by new concepts, methods and worldviews.

Kuhn’s 1962 book initially received a chilly reception. But as the 1960s and 1970s rolled by, it started having a widespread impact on philosophy, history and even political science. Many philosophers took incommensurability to mean that scientific theories just change from one form to another and can’t therefore be compared across paradigms. Kuhn, it seemed, had abandoned the assumption that science progresses to ever-improving states of knowledge.

Others said Kuhn’s position smacked of relativism – that our knowledge, in other words, is only true “relative” to our current paradigm. Kuhn’s book was also criticized for seeming to do away with the supremacy of rational argumentation in paradigm shifts. Kuhn describes how it could be rational for scientists to dismiss contradictory evidence by modifying existing theories to fit their beliefs or by rationalizing away exceptions to their point of view. It was a view that prompted some to even accuse Kuhn of introducing “mob psychology” into science.

Unfortunately, the basic message of his book was widely misunderstood. Sure, Kuhn was a counterweight to “linearized” narratives of history, but what he really wanted to do was make the notion of progress more nuanced, not discard it altogether. Indeed, in 1969 Kuhn published a postscript to his book, in which he abandoned the term paradigm in favour of “exemplars”. These are concrete, ideal examples such as the “inclined plane” and the “infinite square well”, which students encounter in their education and shape their views about science. He resisted attempts to use rival approaches, such as sociology and psychology, to explain how science progresses.

Bojana Mladenovic, a philosopher at Williams College in the US, has done a great service with her new book The Last Writings of Thomas S Kuhn. Containing the unfinished draft of a book that Kuhn was still working on when he died in 1996, Last Writings brings much needed clarity to Kuhn’s philosophy and his understanding of how science develops. The book also includes two previously unpublished papers by Kuhn entitled “Scientific knowledge as historical product” and “The presence of past science”.

Kuhn essentially said the only way to model how scientific theories change is to take into account the shared lexicon of concepts and methods of scientists living at the time

In her introduction, Mladenovic charts Kuhn’s direction of thinking from the Structure to his unfinished draft, titled Plurality of Worlds: an Evolutionary Theory of Scientific Development. As Mladenovic makes clear, Kuhn never entirely gave up the idea of incommensurability, but revised the concept extensively in Plurality of Worlds. Far from reducing science to psychology or sociology, Kuhn essentially said the only way to model how scientific theories change is to take into account the shared lexicon of concepts and methods of scientists living at the time.

Historians cannot, for example, compare different theories about the behaviour of waves without examining how the terms “wave”, “sound” and “light” varied in meaning in the 18th and 19th centuries. Similarly, we cannot judge theories of temperature without understanding how the concepts of “hot” and “cold” differed widely among scientists after the invention of the mercury thermometer in 1714. For Kuhn, the ideas that our knowledge about waves or heat simply improved conceals conceptual differences – incommensurability – that resist easy comparisons.

As for Kuhn’s essay “The presence of past science”, it offers fairly standard critiques of the “whiggish” approach to history, which essentially judges the past from the point of view of the present. Also known as “presentist” history, it assumes the past has little to tell us about current events. Presentist accounts, in other words, tend to favour historical insights that serve as precursors to “modern” thinking and treat past viewpoints as less advanced than those that followed. Most historians today are aware of the flaws in this approach and in some sense Kuhn’s essay foreshadowed current thinking.

Taken together, Last Writings makes clear that Kuhn thought history must deal with its own incommensurability to model progress, which is done by “rediscovering” the achievements of past science. So instead of writing history with the benefit of hindsight, Kuhn’s aim was to reconstruct the intelligibility and the reasoning of scientists at the time. That way, we can see shifts, merits and deficiencies that motivate us to take up one lexicon over another. Kuhn deemed that what was necessary to ground incommensurability is a “theory of meaning” and Plurality of Worlds takes serious steps to flesh out this project.

Kuhn veered between the two extremes of historicism and naturalism. Like his fellow philosophers Noam Chomsky and Ludwig Wittgenstein, he believed that human beings perceive and classify nature in similar ways while reflecting distinct cultural inheritance and practices. At the same time, Kuhn’s incommensurability suggests that no two distinct lexicons, even with overlapping terms that appear to describe the same objects, typify nature in the exact same way.

The hard road then, and perhaps one worth taking, is to make sense of our common ground without presuming a one-to-one correspondence between terms or trying to translate every statement for a given set of lexicons. In saying that lexicons are distinct but communicable, Kuhn’s goal was ambitious but well-conceived. It’s therefore unfortunate Kuhn never had time to finish his final book because he showed a strong sense of what is needed to answer his own questions about incommensurability.

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The second part of Plurality of Worlds tries to give structure to Kuhn’s theory of meaning by discussing various types of entities using cognitive psychology. In doing so, Kuhn draws a distinction between natural phenomena, like biological taxonomy, and human-made tools, which he dubs “artefactual terms”. He further distinguishes these from physics terms such as “mass”, “extension” and “motion”, which he calls “singletons”.

Unlike the informal vocabulary of everyday life, Kuhn regarded singletons as unique, deliberate formalizations in theoretical science. They are law-like generalizations that formalize everyday observations. Kuhn’s choice to label “singletons” as neither purely natural nor artefactual shows promise because he gives meaning to physical terms without taking our models literally or simply regarding them as useful tools for doing calculations.

Kuhn was perhaps right that we cannot strip concepts of their lexical context and carelessly judge them from today’s point of view

Some may find Kuhn’s notion of incommensurability just as tricky to grasp as when he wrote Structure back in 1962. Despite his revisions, Kuhn still does not think we can say, for example, that Alessandro Volta was wrong about the direction of electrical current, since his notion of “current” differed from present-day usage. But what can we say then? Misreads of relativism aside, Kuhn too often reverts to denying our ability to compare scientific concepts over vast periods of time.

Kuhn was perhaps right that we cannot strip concepts of their lexical context and carelessly judge them from today’s point of view. Just think of Aristotle’s notion of “nothingness”, which he called “the void”. We can’t simply mix that idea with our own methods of evaluation. For Aristotle, the non-existence of void was a tautological truth. For us, the existence of the void is a fact about vacuum.

However, as far as I can tell, what is missing is a way of translating concepts from one theory to another without losing the original meaning. After all, Aristotle’s notion of void is not a vacuum as we now know it, but surely it corresponds with something from modern science. Granted, Kuhn’s work was unfinished, but hopefully, the Last Writings will reinvigorate conversations about incommensurability for years to come.

• 2022 University of Chicago Press 312pp $27.50hb