The concept of incommensurability was introduced into the philosophy and historiography of science, independently, by Thomas Kuhn and Paul Feyerabend.
The most well known, and discussed, application of the concept is due to Kuhn, given the role that it played in his work on the structure of scientific revolutions. His book on the structure of scientific revolutions, as we know, is one of the most cited of the 20th century. The picture Kuhn painted is a familiar one, so I need not tally into any great detail.
The transition from “normal science” to “new science”, mediated by anomalies that spark crisis, is revolutionary because new science comes in new paradigmatic packages that are incommensurable with the old, “normal,” science.
The concepts and very methodology of new science are incommensurable with that of the old as there exist no common measure to compare theories, given that the meaning of concepts and criteria of justification are not transcendental rather they inhere within the very paradigmatic structure within which new and old science are framed.
Some take from this that science is not as rational as we have supposed, that the transition from normal to revolutionary science occurs for sociological rather than intellectual reasons, and that science does not progress as the traditional enlightenment temper had it.
There exists a veritable cottage industry that explores whether Kuhn himself regarded incommensurability as having these implications, that is that Kuhn was an epistemological relativist, but I think that the former, that is the non progressive nature of science, is entailed by the concept of incommensurability whatever Kuhn’s intentions.
I tend to have a different conception of science to that prevailing in fashionable circles. Accuse me of being old fashioned, even a reactionary if you like and if you be given to sipping a latte or two over discourse, but I think that science does progress.
I have the tendency, not fully developed so kind of sketchy, that scientific revolutions (I am of the old school here too as I like to think of scientific revolution in the singular rather than plural), are really processes of scientific unification.
We regard physics as the queen of the sciences but we forget that this majestic status we granted recently, toward the end of the 19th century. For most of history astronomy was the queen of the sciences, and I tend to regard the scientific revolution as a sort of longue duree that unified astronomy with physics.
Astronomy made important advances, with Copernicus, Brahe, Kepler, Galileo, that challenged the Aristotelian picture of reality. In other words, astronomy was incommensurable with physics and it took a long process of intellectual upheaval, culminating with Newton, to resolve this incommensurability.
This required new conceptions of the physical.
The same thing happened with chemistry. The work of chemists advanced so far that the picture of the world it provided was incommensurable with hitherto prevailing physics. It took the quantum revolution in physics to resolve this incommensurability and that not through reduction but through the unification of chemistry with physics.
That too required new conceptions of the physical.
So my contention is this. Incommensurability is not so much a result of scientific revolutions rather they are their impetus and scientific revolution, really scientific unification, resolves incommensurability.
That is to say, science does progress, science is cumulative, and reasoned justification is critical to that endeavour we call science.
Scientific revolutions are moments of epistemic unification as much, if not more than, moments of epistemic rupture.
[The book pictured above is a great read, by the way]