Incommensurable

Feyerabend traced the origins of his notion of incommensurability back to his ‘thesis I’ in “An attempt at a realistic interpretation of experience” (1958a), a condensed version of his 1951 doctoral thesis Zur Theorie der Basissätze (On the Theory of Protocol Sentences). In his (1958a), Feyerabend criticized two conceptions of meaning. He argued against the logical positivist idea that the meaning of an observational term is determined by immediate experiences, as well as against the Wittgensteinian idea that the meaning of an observational term is determined by its use. Instead, Feyerabend argued for the idea that the meaning of a term, even an observation term, is determined by its theoretical context, or more precisely, by the theoretical principles that govern its correct use according to our best theories. For example, according to Feyerabend, the correct meaning of the term ‘temperature’ is not determined by its everyday use, but by the principles of statistical thermodynamics. From this perspective, Feyerabend developed ‘thesis I’, according to which the interpretation of an observation language is determined by the theories that we use to explain what we observe, and it changes as soon as those theories change (1958a, 163). Feyerabend proceeded to argue that when older theories are replaced, the meanings of the observational terms used to test the theories change. Just as in (1962), the result is incommensurability: The idea that successive scientific theories are conceptually incompatible and consequently logically disjoint. Feyerabend's ‘thesis I’ is thus an early version of his incommensurability thesis. In his (1958a), with this notion of incommensurability, Feyerabend challenged an implicit conceptual conservativism in logical positivism: The assumption that theoretical terms derive their meaning solely through their connection with experience, and that experience itself is a stable (or unchanging) foundation on which theoretical meaning can be based. Instead of such a bottom-up version of the relation of experience and theoretical knowledge, according to which experience determines the meanings of our theoretical terms, Feyerabend argued for a top-down version, according to which our theories determine the meaning we attach to our experiences. According to Feyerabend, experience cannot be taken for granted as some kind of fixed, neutral basis for comparing theories. Rather, it takes on its particular character in light of the theories we bring to it. An investigation of the source of these ideas reveals the founding father of the notion of incommensurability in the contemporary history and philosophy of science.
Oberheim and Hoyningen-Huene. "The Incommensurability of Scientific Theories" in The Stanford Encyclopedia of Philosophy.
In resume:

1. The interpretation of observations is implicitly influenced by theoretical assumptions. It is therefore impossible to describe or evaluate observations independently of theory.
2. Paradigms often have different assumptions about which intellectual and operational scientific methods result in valid scientific knowledge.
3. Paradigms can be based on different assumptions regarding the structure of their domain, which makes it impossible to compare them in a meaningful way. The adoption of a new theory includes and is dependent upon the adoption of new terms. Thus, scientists are using different terms when talking about different theories. Those who hold different, competing theories to be true will be talking over one another, in the sense that they cannot a priori arrive at agreement given two different discourses with two different theoretical language and dictates.