Maarefi, Mohammad (2025) Mathematical Explanation, Metaphysical Grounding, and Explanatory Chains. [Preprint]

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Abstract

This paper develops a theory of mathematical explanation through the lens of a separatist metaphysical grounding framework. I argue that mathematical explanations delivered by proofs are best captured by a non-causal determination relation between mathematical facts—a metaphysical grounding relation where the \textit{explanans} determines the \textit{explanandum}, where the relevant why questions at each step are answered; an explanatory proof is the one that establishes an explanatory chain between the \textit{explanans} and the \textit{explanandum}. Through a case study in algebra (e.g., the infinity of fields with characteristic zero), I argue how this relation establishes objective dependencies in terms of determination relations that answer why-questions about mathematical facts. By adopting a ground-first separatist approach—where grounding relations back explanations but are distinct from them—the theory aligns with mathematical practice, supports proof plurality, and addresses gaps in existing accounts.

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Item Type:	Preprint
Creators:	Creators Email ORCID Maarefi, Mohammad md.maarefi@gmail.com 0000-0002-6671-8942
Keywords:	mathematical explanation, separatism, explanatory chain, metaphysical grounding
Subjects:	Specific Sciences > Mathematics > Explanation Specific Sciences > Mathematics
Depositing User:	dr Mohammad Maarefi
Date Deposited:	09 Sep 2025 18:29
Last Modified:	09 Sep 2025 18:29
Item ID:	26442
Subjects:	Specific Sciences > Mathematics > Explanation Specific Sciences > Mathematics
Date:	2025
URI:	https://philsci-archive.pitt.edu/id/eprint/26442

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