Are aesthetic judgements purely aesthetic? Testing the social conformity account
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ORIGINAL ARTICLE
Are aesthetic judgements purely aesthetic? Testing the social conformity account Matthew Inglis1 · Andrew Aberdein2 Accepted: 6 April 2020 © The Author(s) 2020
Abstract Many of the methods commonly used to research mathematical practice, such as analyses of historical episodes or individual cases, are particularly well-suited to generating causal hypotheses, but less well-suited to testing causal hypotheses. In this paper we reflect on the contribution that the so-called hypothetico-deductive method, with a particular focus on experimental studies, can make to our understanding of mathematical practice. By way of illustration, we report an experiment that investigated how mathematicians attribute aesthetic properties to mathematical proofs. We demonstrate that perceptions of the aesthetic properties of mathematical proofs are, in some cases at least, subject to social influence. Specifically, we show that mathematicians’ aesthetic judgements tend to conform to the judgements made by others. Pedagogical implications are discussed. Keywords Mathematical aesthetics · Hypothetico-deductive method · Social conformity · Hypotheses
1 The hypothetico‑deductive method in the study of mathematical practice Understanding expert mathematical practice is an interdisciplinary endeavour involving philosophers, historians, mathematics educators, psychologists and sociologists. Inevitably this implies that a diverse array of different research approaches has been used to gain insights into the behaviour of mathematicians. An indication of this diversity can be seen by studying the contents of Larvor’s (2016) recent edited volume. The contributors to that collection drew conclusions about mathematical practice by studying historical episodes (e.g., Barany, 2016), by interviewing mathematicians (e.g., Johansen & Misfeldt, 2016), by analysing This work was first presented at the 15th Congress of Logic Methodology and Philosophy of Science. We are grateful to Dirk Schlimm for organising the “Mathematical beauty: A challenge for empirically informed philosophy of mathematics” symposium. Data and analysis code associated with this manuscript are available at https://doi.org/10.17028/rd.lboro.c.4679399. * Matthew Inglis [email protected] 1
Centre for Mathematical Cognition, Loughborough University, Loughborough LE11 3TU, Leicestershire, UK
Florida Institute of Technology, Melbourne, USA
2
cultural artefacts (e.g., Pantsar, 2016) and by conducting detailed case studies of a particular mathematical notation (e.g., De Toffoli & Giardino, 2016). All these approaches are well-suited for generating insights about mathematical practice but are not always useful strategies if one wishes to test hypotheses that already exist, especially if those hypotheses involve causal claims. Our goal in this paper is twofold. First, we outline the socalled hypothetico-deductive method (H–D), an approach that relatively few empirical studies focused on mathematical practice have adopted to date. Second, we exemplify the
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