Incommensurability as Cognitive Deficiency: Three Mechanisms and Two Complexity Barriers

Kuhnian incommensurability is standardly treated as a single, symmetric relation between paradigms. This paper argues that it is instead three distinct, individually formalizable mechanisms, and that conflating them is what has made it resist clean analysis. Working in a Horn-logic model of an individual's cognitive structure — where understanding is reconstruction within the reachable closure of a relation cluster — I distinguish *unactivated reachability* (the target is reachable but no rule oriented toward it is activated), *contradiction blockage* (acquisition requires a consistency-restoring revision of entrenched structure), and *prerequisite depth* (the path is consistent and legal but too long). Two complexity results locate the difficulty in computation rather than meaning: computing a minimal cognitive deficiency is NP-complete, and computing a minimal consistency-restoring contraction — required whenever acquisition triggers a contradiction — is likewise NP-complete. The mechanisms are illustrated through the transition from Aristotelian to Newtonian physics and the phlogiston–oxygen episode. On this account, incommensurability is not a barrier between worldviews but a feature of the cost landscape of individual learning: the symmetric "gap" of the Kuhnian tradition is the surface appearance of three different asymmetric structures underneath.