Limiting Reduction and Modified Gravity

TL;DR

This paper critically examines MOND's theoretical foundations, arguing it fails to properly reduce to Newtonian gravity due to lack of a unifying framework, thus challenging its status as a successful limiting reduction.

Contribution

The paper introduces a refined framework for limiting reduction, adding criteria to better evaluate the reduction success of novel theories like MOND.

Findings

MOND does not adequately reduce to Newtonian gravity due to missing fundamental framework.

Standard formal criteria for reduction are satisfied, yet MOND fails reduction-wise justification.

The new framework helps distinguish successful from pathological reductions.

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.