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  1. Beauty Is Not Simplicity: An Analysis of Mathematicians' Proof Appraisals.Matthew Inglis & Andrew Aberdein - 2015 - Philosophia Mathematica 23 (1):87-109.
    What do mathematicians mean when they use terms such as ‘deep’, ‘elegant’, and ‘beautiful’? By applying empirical methods developed by social psychologists, we demonstrate that mathematicians' appraisals of proofs vary on four dimensions: aesthetics, intricacy, utility, and precision. We pay particular attention to mathematical beauty and show that, contrary to the classical view, beauty and simplicity are almost entirely unrelated in mathematics.
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  2.  20
    Functional Explanation in Mathematics.Matthew Inglis & Juan Pablo Mejía-Ramos - forthcoming - Synthese:1-24.
    Mathematical explanations are poorly understood. Although mathematicians seem to regularly suggest that some proofs are explanatory whereas others are not, none of the philosophical accounts of what such claims mean has become widely accepted. In this paper we explore Wilkenfeld’s suggestion that explanations are those sorts of things that generate understanding. By considering a basic model of human cognitive architecture, we suggest that existing accounts of mathematical explanation are all derivable consequences of Wilkenfeld’s ‘functional explanation’ proposal. We therefore argue that (...)
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  3.  71
    Using Corpus Linguistics to Investigate Mathematical Explanation.Juan Pablo Mejía Ramos, Lara Alcock, Kristen Lew, Paolo Rago, Chris Sangwin & Matthew Inglis - 2019 - In Eugen Fischer & Mark Curtis (eds.), Methodological Advances in Experimental Philosophy. London: Bloomsbury Academic. pp. 239–263.
    In this chapter we use methods of corpus linguistics to investigate the ways in which mathematicians describe their work as explanatory in their research papers. We analyse use of the words explain/explanation (and various related words and expressions) in a large corpus of texts containing research papers in mathematics and in physical sciences, comparing this with their use in corpora of general, day-to-day English. We find that although mathematicians do use this family of words, such use is considerably less prevalent (...)
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  4.  32
    Advances in Experimental Philosophy of Logic and Mathematics.Andrew Aberdein & Matthew Inglis (eds.) - 2019 - London: Bloomsbury Academic.
    This book explores the results of applying empirical methods to the philosophy of logic and mathematics. Much of the work that has earned experimental philosophy a prominent place in twenty-first century philosophy is concerned with ethics or epistemology. But, as this book shows, empirical methods are just as much at home in logic and the philosophy of mathematics. -/- Chapters demonstrate and discuss the applicability of a wide range of empirical methods including experiments, surveys, interviews, and data-mining. Distinct themes emerge (...)
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  5.  65
    Diversity in Proof Appraisal.Matthew Inglis & Andrew Aberdein - 2016 - In Brendan Larvor (ed.), Mathematical Cultures: The London Meetings 2012--2014. Basel, Switzerland: pp. 163-179.
    We investigated whether mathematicians typically agree about the qualities of mathematical proofs. Between-mathematician consensus in proof appraisals is an implicit assumption of many arguments made by philosophers of mathematics, but to our knowledge the issue has not previously been empirically investigated. We asked a group of mathematicians to assess a specific proof on four dimensions, using the framework identified by Inglis and Aberdein (2015). We found widespread disagreement between our participants about the aesthetics, intricacy, precision and utility of the proof, (...)
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  6. On Mathematicians' Different Standards When Evaluating Elementary Proofs.Matthew Inglis, Juan Pablo Mejia-Ramos, Keith Weber & Lara Alcock - 2013 - Topics in Cognitive Science 5 (2):270-282.
    In this article, we report a study in which 109 research-active mathematicians were asked to judge the validity of a purported proof in undergraduate calculus. Significant results from our study were as follows: (a) there was substantial disagreement among mathematicians regarding whether the argument was a valid proof, (b) applied mathematicians were more likely than pure mathematicians to judge the argument valid, (c) participants who judged the argument invalid were more confident in their judgments than those who judged it valid, (...)
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  7.  20
    Sampling From the Mental Number Line: How Are Approximate Number System Representations Formed?Matthew Inglis & Camilla Gilmore - 2013 - Cognition 129 (1):63-69.
    Nonsymbolic comparison tasks are commonly used to index the acuity of an individual's Approximate Number System (ANS), a cognitive mechanism believed to be involved in the development of number skills. Here we asked whether the time that an individual spends observing numerical stimuli influences the precision of the resultant ANS representations. Contrary to standard computational models of the ANS, we found that the longer the stimulus was displayed, the more precise was the resultant representation. We propose an adaptation of the (...)
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  8.  60
    On the Persuasiveness of Visual Arguments in Mathematics.Matthew Inglis & Juan Pablo Mejía-Ramos - 2009 - Foundations of Science 14 (1-2):97-110.
    Two experiments are reported which investigate the factors that influence how persuaded mathematicians are by visual arguments. We demonstrate that if a visual argument is accompanied by a passage of text which describes the image, both research-active mathematicians and successful undergraduate mathematics students perceive it to be significantly more persuasive than if no text is given. We suggest that mathematicians’ epistemological concerns about supporting a claim using visual images are less prominent when the image is described in words. Finally we (...)
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  9. Introduction.Andrew Aberdein & Matthew Inglis - 2019 - In Andrew Aberdein & Matthew Inglis (eds.), Advances in Experimental Philosophy of Logic and Mathematics. Bloomsbury Academic. pp. 1-13.
    There has been little overt discussion of the experimental philosophy of logic or mathematics. So it may be tempting to assume that application of the methods of experimental philosophy to these areas is impractical or unavailing. This assumption is undercut by three trends in recent research: a renewed interest in historical antecedents of experimental philosophy in philosophical logic; a “practice turn” in the philosophies of mathematics and logic; and philosophical interest in a substantial body of work in adjacent disciplines, such (...)
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  10.  23
    Intelligence and Negation Biases on the Conditional Inference Task: A Dual-Processes Analysis.Nina Attridge & Matthew Inglis - 2014 - Thinking and Reasoning 20 (4):454-471.
    We examined a large set of conditional inference data compiled from several previous studies and asked three questions: How is normative performance related to intelligence? Does negative conclusion bias stem from Type 1 or Type 2 processing? Does implicit negation bias stem from Type 1 or Type 2 processing? Our analysis demonstrated that rejecting denial of the antecedent and affirmation of the consequent inferences was positively correlated with intelligence, while endorsing modus tollens inferences was not; that the occurrence of negative (...)
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  11.  18
    Are Aesthetic Judgements Purely Aesthetic? Testing the Social Conformity Account.Matthew Inglis & Andrew Aberdein - 2020 - ZDM 52 (6):1127-1136.
    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 (...)
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  12.  18
    Is the ANS Linked to Mathematics Performance?Matthew Inglis, Sophie Batchelor, Camilla Gilmore & Derrick G. Watson - 2017 - Behavioral and Brain Sciences 40.
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