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Project
Mathematical Explanation: A philosophical analysis of the explanatory value of mathematical proofs (FWOTM926)
The aim of the proposed research is to advance our grasp of the notion mathematical explanation. It is often observed that in practice a mathematician is guided by, besides the aim of establishing the truth of a mathematical result, the aim of finding a better
explanation of a mathematical result. In my doctoral dissertation I analysed the notion explanatory proof. An explanatory proof contributes to, following our previous line of thought, a better understanding of why the theorem is true. Several philosophers have proposed criteria for distinguishing explanatory from non-explanatory proofs. While working on my dissertation it became clear that, although many philosophers hint at explanations in mathematics beyond the relation between proof and theorem, the philosophical analysis of mathematical explanation has a particular focus on explanatory proofs.
With this project, I aim at increasing the scope of this philosophical discussion. Instead of looking at the relation between proof and theorem, I am interested in what it would mean to explain a mathematical concept. This explanation might potentially come from a proof, but can also come from other pieces of mathematics. In order to explore these new types of mathematical explanation, I will look into several case studies from the history of the number concept. This will allow for a critical interaction between actual mathematical practices and the theoretical literature on explanation.
explanation of a mathematical result. In my doctoral dissertation I analysed the notion explanatory proof. An explanatory proof contributes to, following our previous line of thought, a better understanding of why the theorem is true. Several philosophers have proposed criteria for distinguishing explanatory from non-explanatory proofs. While working on my dissertation it became clear that, although many philosophers hint at explanations in mathematics beyond the relation between proof and theorem, the philosophical analysis of mathematical explanation has a particular focus on explanatory proofs.
With this project, I aim at increasing the scope of this philosophical discussion. Instead of looking at the relation between proof and theorem, I am interested in what it would mean to explain a mathematical concept. This explanation might potentially come from a proof, but can also come from other pieces of mathematics. In order to explore these new types of mathematical explanation, I will look into several case studies from the history of the number concept. This will allow for a critical interaction between actual mathematical practices and the theoretical literature on explanation.
Date:1 Oct 2018 → 30 Sep 2022
Keywords:mathematical number concepts
Disciplines:Philosophy of mathematics