Explanatory proofs and grounding in mathematics: a reply to Maarefi

• Marc Lange ^[1]
  1. [1] Rutgers University

     Rutgers University

     City of New Brunswick, Estados Unidos

     
• Localización: Crítica: revista hispanoamericana de filosofía, ISSN 0011-1503, Vol. 57, Nº. 170, 2025, págs. 99-113
• Idioma: inglés
• DOI: 10.22201/iifs.18704905e.2025.1694
• Enlaces
  • Texto completo
• Resumen
  • español

    Las demostraciones explicativas deteoremas en matemáticas derivan supoder explicativo en virtud de que proporcionan información sobre los fundamentosde los teoremas que explican? He argumentado que no (Lange 2019), y ofrezcomi propia explicación sobre lo que hace quealgunas demostraciones matemáticas,y otras no, sean capaces de explicar por qué un teorema es válido (Lange 2017).Recientemente, Maarefi (2025) ha criticado tanto estos argumentos como esa expli-cación en apoyo de una concepción de las demostraciones explicativas basada enfundamentos. A continuación respondo a algunas de sus críticas

  • English

    Do explanatory proofs of theorems in mathematics derive their explanatory power by virtue of providing information about the grounds of the theorems they explain? I have argued that they do not (Lange 2019), and I have offered my own account of what makes certain mathematical proofs but not others able to explain why some theorem holds (Lange 2017). Recently, Maarefi (2025) has critiqued both these arguments and that account in support of a grounding-based conception of explanatory proofs. Here I respond to some of his critiques.

• Referencias bibliográficas
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