6 found
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  1.  66
    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.  5
    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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  3.  81
    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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  4.  34
    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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  5.  17
    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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  6. Advances in Experimental Philosophy of Logic and Mathematics.Andrew Aberdein & Matthew Inglis (eds.) - forthcoming - London: Bloomsbury Press.