Math Over Mechanism: New Structuralism as a General Theory of Scientific Explanation in Light of the Limitations of New Mechanism

This dissertation argues that the leading contemporary candidate for a general theory of scientific explanation, New Mechanist Explanation (NME), is unsuitable for the role, and that a Relational Structuralist theory of explanation (RSE), or "New Structuralism," offers the framework the philosophy of science has been in search of. The argument proceeds in four stages. First, I develop a set of motivating criteria (the GAME criteria) for what a general model of scientific explanation must accomplish, and review the historical models of explanation—deductive-nomological, statistical relevance, causal-mechanical, unificationist, structural—in light of those criteria. Second, I take New Mechanism on its own terms and document, through extended case studies across biology, chemistry, ecology, and physics, the substantive areas in which NME fails to capture working scientific explanation. The failures are not isolated edge cases but a coherent pattern: where the explanatory relations are not causal-productive among local parts—where they are structural, topological, statistical, or mathematical-relational—NME cannot do the work, and the working scientific explanations in these areas are not amenable to mechanistic reconstruction. Third, I locate much of NME's difficulty in its inability to ground mathematical explanation. I argue that mathematical explanation is genuine, indispensable explanation, that programs to eliminate it from science have not succeeded and arguably cannot succeed, and that Wigner's puzzle of "the unreasonable effectiveness of mathematics in the natural sciences" receives a natural answer once explanation is read as relational. Fourth, I propose Relational Structural Explanation. RSE rests on three philosophical commitments: the primacy of relation, the ratio reading of relation, and the invariance reading of structure. I develop nine criteria for RSE, demonstrate that RSE meets each of the GAME criteria, work through extended examples (the periodic table, the action potential, the Königsberg bridges, GHZ multipartite entanglement, predator-prey dynamics), and recover the historical models of explanation as sub-classes of RSE corresponding to different relational primitives. I provide a rubric for selecting among sub-classes in particular cases and respond to nine objections to the position. I situate RSE in relation to ontic structural realism, to existing accounts of structural and topological explanation, and to convergent recent work in foundations of physics and metaphysics of science. The dissertation closes by arguing that philosophers of science should adopt RSE as a working general theory of scientific explanation, treating NME as a successful local account of a sub-class of explanations rather than as a candidate for the general role NME has, until now, been advanced to fill. Among the dissertation's specific contributions: (1) NME's defenders face a trapdoor dilemma—either NME retains its parts-and-activities commitments and fails on structural, topological, and field-theoretic cases, or it expands to cover them and ceases to be recognizably mechanistic; (2) the ratio reading of relation, tracing the conceptual ground of explanation through the Latin ratio, the Greek logos, measurement theory, dimensional analysis, Noether's theorem, and topological quantum field theory, dissolves Wigner's puzzle by showing that mathematics is effective in science because both disciplines study the same kind of object, relational structure; (3) the deformation-invariance criterion—that explanatorily robust relations are those surviving continuous deformation of the system—resolves the Newman problem that has challenged structural realism since 1928, by specifying for the first time a principled filter for which structures carry explanatory content; and (4) the four-party entanglement propositions prove, via explicit monogamy-of-entanglement inequalities and the Verstraete–Dehaene–De Moor–Verschel