From Grounding to Stabilisation: Adequacy as a Criterion for Scientific Explanation

TL;DR

The paper challenges the traditional grounding-based view of scientific explanation, arguing that grounding yields an infinite regress at framework level. It proposes a formal adequacy criterion, captured by the schema $C \to P(I)$, where explanations succeed if invariants $I$ persist under admissible transformations within tolerance $\varepsilon$ across transformations generated by an update operator $F$. Through examples in physics and mathematics (e.g., Lorentz and gauge invariance) and a paradigmatic black hole event horizon, the approach reframes theory change, quantum measurement, and emergence as stability audits of relational invariants rather than searches for final substrates. This stabilisation framework offers a falsifiable, apparatus-sensitive, and broadly applicable account of scientific explanation with modest realism, and it is complemented by companion work that operationalises protocols across quantum, thermodynamic, and relativistic domains.

Abstract

This paper develops a process-based account of scientific explanation that reconceives grounding in terms of stabilisation. Grounding theories capture hierarchical dependence but lack criteria for when explanations remain adequate under model updates, perturbations, and theory change. Stabilisation is formally defined by a schema \(C \to P(I)\), where explanatory relations are sufficient when they preserve specified relational invariants under admissible transformations. This replaces the search for ultimate foundations with operational adequacy tests indexed to measurable invariance, resolving infinite regress worries while preserving a modest scientific realism. Applications show unifying power: theory change becomes an empirical question about structural continuity; quantum measurement becomes apparatus-dependent pattern selection; the effectiveness of mathematics reflects convergence on transformation-invariant descriptions; and emergence versus reduction reduces to stability of cross-level mappings. The black hole event horizon illustrates how ontologically identical states can diverge in admissible evolution, revealing process as explanatorily fundamental. Companion work develops apparatus-dependent adequacy protocols, including pointer-basis rotation and coupling-spectra methods, turning the framework into a falsifiable research programme across quantum, thermodynamic, and relativistic domains.