Seonglae ChoIncommensurability is a concept that different scientific theories cannot be compared using common measurements. The term originally referred to geometric concepts like the side and diagonal of a square having no common unit of measurement.
The criteria for evaluating theories (simplicity, scope, errors, etc.) also vary between paradigms, leading to the view that there are no absolute comparative standards (methodological incommensurability).
Different theories cannot establish strict deductive relationships due to semantic differences (semantic incommensurability) between their core concepts
The Incommensurability of Scientific Theories
The term ‘incommensurable’ means ‘to have no common
measure’. The idea traces back to Euclid’s
Elements, where it was applied to magnitudes. For example,
there is no common measure between the sides and the diagonal of a
square. Today, such incommensurable relations are represented by
irrational numbers. The metaphorical application of the mathematical
notion specifically to the relation between successive scientific
theories became controversial in 1962 after it was popularised by two
influential philosophers of science: Thomas Kuhn and Paul Feyerabend.
They appeared to be challenging the rationality of science and so were
often considered to be among “the worst enemies of
science” (Theocharis and Psimopoulos 1987, 596; cf. Preston
et al. 2000). Since 1962, the incommensurability of
scientific theories has been a widely discussed, controversial idea
that was instrumental in the historical turn in the philosophy of
science and the establishment of the sociology of science as a
professional discipline.
https://plato.stanford.edu/entries/incommensurability/#RevoParaThomKuhnInco