<p>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 <i>explanans</i> determines the <i>explanandum</i>, where the relevant why questions at each step are answered. 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.</p>

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Metaphysical grounding and mathematical explanation

  • Mohammad Maarefi

摘要

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 explanans determines the explanandum, where the relevant why questions at each step are answered. 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.