Mechanistic Explanation and Explanatory Proofs in Mathematics
Philosophia Mathematica 22 (2):231-248 (2014)
Abstract
Although there is a consensus among philosophers of mathematics and mathematicians that mathematical explanations exist, only a few authors have proposed accounts of explanation in mathematics. These accounts fit into the unificationist or top-down approach to explanation. We argue that these models can be complemented by a bottom-up approach to explanation in mathematics. We introduce the mechanistic model of explanation in science and discuss the possibility of using this model in mathematics, arguing that using it does not presuppose a Platonist view of mathematics and allows one to gain insight into why a theorem is true by answering what-if-things-had-been-different questionsAuthor Profiles
DOI
10.1093/philmat/nku003
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Citations of this work
There Are No Mathematical Explanations.Jaakko Kuorikoski - 2021 - Philosophy of Science 88 (2):189-212.
Explanation in mathematics: Proofs and practice.William D'Alessandro - 2019 - Philosophy Compass 14 (11):e12629.
Proving Quadratic Reciprocity: Explanation, Disagreement, Transparency and Depth.William D’Alessandro - 2020 - Synthese (9):1-44.
Philosophy of mathematical practice: A primer for mathematics educators.Yacin Hamami & Rebecca Morris - 2020 - ZDM Mathematics Education 52:1113–1126.
Is Mathematics a Domain for Philosophers of Explanation?Erik Weber & Joachim Frans - 2017 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 48 (1):125-142.
References found in this work
Making Things Happen: A Theory of Causal Explanation.James Woodward - 2003 - Oxford University Press.
Thinking about mechanisms.Peter Machamer, Lindley Darden & Carl F. Craver - 2000 - Philosophy of Science 67 (1):1-25.