Limiting Reduction and Modified Gravity

TL;DR

The paper investigates whether MOND can be justified as a limiting reduction to Newtonian gravity, using Nagelian/Nickles’ framework and Butterfield’s physicality criterion. It analyzes classical and relativistic MOND formulations, showing that MOND can meet the formal limit and physicality conditions but fails to satisfy a stronger non-arbitrariness requirement due to the ad hoc interpolating function, unless downward theoretical grounding is provided. Through Planck’s law and general relativity as benchmarks, the authors argue for a refined, twofold grounding (downward and upward) that can distinguish genuinely justified reductions from pathological ones. The result is a refined account of limiting reduction that clarifies when novel theories, not yet empirically established, can be considered reduction-wise justified and highlights the methodological importance of embedding or grounding in more fundamental theories.

Abstract

Modified Newtonian Dynamics (MOND) is a framework of theories that adjust Newton's laws of gravity to explain effects such as galactic rotation anomalies, offering an alternative to dark matter. This essay examines the justification of MOND by assessing its inter-theoretical relationship to established theories across relevant scales, in particular its connection to Newtonian gravitation. We argue that MOND fails a key condition for a theory's justification--what we call 'reduction-wise justification'--since it does not adequately reduce to Newtonian gravity in a fully non-arbitrary way. More precisely, despite satisfying the standard formal criteria for successful limiting reduction, MOND does not properly reduce to Newtonian gravitation because of (i) the absence of a fundamental theoretical framework to justify the interpolating function introduced in MOND and (ii) the lack of a unified mathematical structure working across all scales, independent of Newtonian theory. Hence, the case study of MOND provides crucial results for the general debate on inter-theoretic reduction in science: MOND's failure as a case of reduction highlights important limitations in standard accounts of limiting reduction. We respond by proposing a more refined framework for limiting reduction that introduces two additional criteria to better distinguish successful from pathological reductions. More broadly, this case illustrates how analysing reduction-wise justification can serve as a powerful tool for evaluating the validity of novel theories that are not yet empirically established.