Projection and Invariance in Scientific Explanation

Abstract: Scientific knowledge exhibits three structural features that the standard picture of progressive replacement does not adequately explain: the persistence of superseded theories, the stable coexistence of incompatible frameworks, and the productivity of multiple descriptions of the same domain without any single one being uniquely correct. This paper argues that all three features share a common explanation in the structure of scientific projection. A projection is a principled mapping from underlying complexity to a structured descriptive space that partitions underlying states into compatibility classes, thereby making invariants visible. On this account, every theoretical framework has two separable components - representational structure and substrate interpretation - that can come apart in both logic and history. Two legitimacy criteria govern the adoption of projections: empirical adequacy and ontological consonance. A projection is explanatorily successful when the variation it suppresses within a compatibility class is irrelevant to the invariants the theory seeks to capture. The framework distinguishes two kinds of explanatory cases. Vertical cases - including the Newtonian-Einsteinian transition and Darwin's theory before genetics - exhibit successive refinement, with earlier projections surviving as limiting cases of more general ones. Horizontal cases - including Gresham's Law, traffic flow dynamics, and universality classes in statistical mechanics - reveal level-specific invariants that are constitutively irreducible to finer-grained descriptions. The distinction reconciles scientific realism with principled explanatory pluralism, offers a structural account of theory change, and yields a normative criterion for distinguishing genuine theoretical progress from mere replacement.