
14Mathematical Explanation beyond Explanatory ProofBritish Journal for the Philosophy of Science 71 (2): 581603. 2020.Much recent work on mathematical explanation has presupposed that the phenomenon involves explanatory proofs in an essential way. I argue that this view, ‘proof chauvinism’, is false. I then look in some detail at the explanation of the solvability of polynomial equations provided by Galois theory, which has often been thought to revolve around an explanatory proof. The article concludes with some general worries about the effects of chauvinism on the theory of mathematical explanation. 1Introdu…Read more

111Proving Quadratic Reciprocity: Explanation, Disagreement, Transparency and DepthSynthese 144. 2020.Gauss’s quadratic reciprocity theorem is among the most important results in the history of number theory. It’s also among the most mysterious: since its discovery in the late 18th century, mathematicians have regarded reciprocity as a deeply surprising fact in need of explanation. Intriguingly, though, there’s little agreement on how the theorem is best explained. Two quite different kinds of proof are most often praised as explanatory: an elementary argument that gives the theorem an intuitive…Read more

92Teaching and Learning Guide for: Explanation in Mathematics: Proofs and PracticePhilosophy Compass 14 (11). 2019.This is a teaching and learning guide to accompany "Explanation in Mathematics: Proofs and Practice".

249Explanation in mathematics: Proofs and practicePhilosophy Compass 14 (11). 2019.Mathematicians distinguish between proofs that explain their results and those that merely prove. This paper explores the nature of explanatory proofs, their role in mathematical practice, and some of the reasons why philosophers should care about them. Among the questions addressed are the following: what kinds of proofs are generally explanatory (or not)? What makes a proof explanatory? Do all mathematical explanations involve proof in an essential way? Are there really such things as explanat…Read more

192Viewingas explanations and ontic dependencePhilosophical Studies 177 (3): 769792. 2020.According to a widespread view in metaphysics and philosophy of science, all explanations involve relations of ontic dependence between the items appearing in the explanandum and the items appearing in the explanans. I argue that a family of mathematical cases, which I call “viewingas explanations”, are incompatible with the Dependence Thesis. These cases, I claim, feature genuine explanations that aren’t supported by ontic dependence relations. Hence the thesis isn’t true in general. The first…Read more

66Mathematical Explanation beyond Explanatory ProofBritish Journal for the Philosophy of Science. 2017.Much recent work on mathematical explanation has presupposed that the phenomenon involves explanatory proofs in an essential way. I argue that this view, ‘proof chauvinism’, is false. I then look in some detail at the explanation of the solvability of polynomial equations provided by Galois theory, which has often been thought to revolve around an explanatory proof. The paper concludes with some general worries about the effects of chauvinism on the theory of mathematical explanation.

404Arithmetic, Set Theory, Reduction and ExplanationSynthese 195 (11): 50595089. 2018.Philosophers of science since Nagel have been interested in the links between intertheoretic reduction and explanation, understanding and other forms of epistemic progress. Although intertheoretic reduction is widely agreed to occur in pure mathematics as well as empirical science, the relationship between reduction and explanation in the mathematical setting has rarely been investigated in a similarly serious way. This paper examines an important particular case: the reduction of arithmetic to …Read more

706Explicitism about Truth in FictionBritish Journal of Aesthetics 56 (1): 5365. 2016.The problem of truth in fiction concerns how to tell whether a given proposition is true in a given fiction. Thus far, the nearly universal consensus has been that some propositions are ‘implicitly true’ in some fictions: such propositions are not expressed by any explicit statements in the relevant work, but are nevertheless held to be true in those works on the basis of some other set of criteria. I call this family of views ‘implicitism’. I argue that implicitism faces serious problems, where…Read more

Ludwig Maximilians Universität, MünchenMunich Centre for Mathematical PhilosophyPostdoctoral fellow
Chicago, Illinois, United States of America
Areas of Interest
Epistemology 
Metaphilosophy 
Aesthetics 
Logic and Philosophy of Logic 