Abstract

MAAREFI, Mohammad. Lange on Mathematical Explanation, Grounding, and the Divergence Thesis. Crítica (Méx., D.F.) [online]. 2025, vol.57, n.169, pp.23-57.  Epub Aug 25, 2025. ISSN 0011-1503.  https://doi.org/10.22201/iifs.18704905e.2025.1658.

Mark Lange has defended the view that mathematical explanation and grounding explanation diverge. In this paper, I argue that at least one type of grounding relation is immune to his criticisms. After fixing a minimal separatist theory of ground, I show that his arguments mostly rely on another thesis about grounding (I’ll call it “atomic grounding thesis”), which is not supported. Furthermore, a second attempt at using purity is not entirely satisfactory.

Keywords : mathematical practice; philosophy of mathematics; grounding relation; grounding explanation; separatism.

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