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  1. True Beauty.Ryan P. Doran - forthcoming - British Journal of Aesthetics.
    What is the nature of the concept BEAUTY? Does it differ fundamentally from nearby concepts such as PRETTINESS? It is argued that BEAUTY, but not PRETTINESS, is a dual-character concept. Across a number of contexts, it is proposed that BEAUTY has a descriptive sense that is characterised by, inter alia, having intrinsically pleasing appearances; and a normative sense associated with deeply-held values. This account is supported across two, pre-registered, studies (N=500), and by drawing on analysis of corpus data. It is (...)
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  • Do Mathematicians Agree about Mathematical Beauty?Rentuya Sa, Lara Alcock, Matthew Inglis & Fenner Stanley Tanswell - 2024 - Review of Philosophy and Psychology 15 (1):299-325.
    Mathematicians often conduct aesthetic judgements to evaluate mathematical objects such as equations or proofs. But is there a consensus about which mathematical objects are beautiful? We used a comparative judgement technique to measure aesthetic intuitions among British mathematicians, Chinese mathematicians, and British mathematics undergraduates, with the aim of assessing whether judgements of mathematical beauty are influenced by cultural differences or levels of expertise. We found aesthetic agreement both within and across these demographic groups. We conclude that judgements of mathematical beauty (...)
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  • Virtue theory of mathematical practices: an introduction.Andrew Aberdein, Colin Jakob Rittberg & Fenner Stanley Tanswell - 2021 - Synthese 199 (3-4):10167-10180.
    Until recently, discussion of virtues in the philosophy of mathematics has been fleeting and fragmentary at best. But in the last few years this has begun to change. As virtue theory has grown ever more influential, not just in ethics where virtues may seem most at home, but particularly in epistemology and the philosophy of science, some philosophers have sought to push virtues out into unexpected areas, including mathematics and its philosophy. But there are some mathematicians already there, ready to (...)
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  • Mathematizing as a virtuous practice: different narratives and their consequences for mathematics education and society.Deborah Kant & Deniz Sarikaya - 2020 - Synthese 199 (1-2):3405-3429.
    There are different narratives on mathematics as part of our world, some of which are more appropriate than others. Such narratives might be of the form ‘Mathematics is useful’, ‘Mathematics is beautiful’, or ‘Mathematicians aim at theorem-credit’. These narratives play a crucial role in mathematics education and in society as they are influencing people’s willingness to engage with the subject or the way they interpret mathematical results in relation to real-world questions; the latter yielding important normative considerations. Our strategy is (...)
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  • Prolegomena to virtue-theoretic studies in the philosophy of mathematics.James V. Martin - 2020 - Synthese 199 (1-2):1409-1434.
    Additional theorizing about mathematical practice is needed in order to ground appeals to truly useful notions of the virtues in mathematics. This paper aims to contribute to this theorizing, first, by characterizing mathematical practice as being epistemic and “objectual” in the sense of Knorr Cetina The practice turn in contemporary theory, Routledge, London, 2001). Then, it elaborates a MacIntyrean framework for extracting conceptions of the virtues related to mathematical practice so understood. Finally, it makes the case that Wittgenstein’s methodology for (...)
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  • Proof, Explanation, and Justification in Mathematical Practice.Moti Mizrahi - 2020 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 51 (4):551-568.
    In this paper, I propose that applying the methods of data science to “the problem of whether mathematical explanations occur within mathematics itself” (Mancosu 2018) might be a fruitful way to shed new light on the problem. By carefully selecting indicator words for explanation and justification, and then systematically searching for these indicators in databases of scholarly works in mathematics, we can get an idea of how mathematicians use these terms in mathematical practice and with what frequency. The results of (...)
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  • 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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  • Зеркало Клио: Метафизическое Постижение Истории.Алексей Владиславович Халапсис - 2017 - Днипро, Днепропетровская область, Украина, 49000:
    В монографии представлены несколько смысловых блоков, связанных с восприятием и интерпретацией человеком исторического бытия. Ранние греческие мыслители пытались получить доступ к исходникам (началам) бытия, и эти интенции легли в основу научного знания, а также привели к появлению метафизики. В классической (и в неклассической) метафизике за основу была принята догма Пифагора и Платона о неизменности подлинной реальности, из чего следовало отрицание бытийного характера времени. Автор монографии отказывается от этой догмы и предлагает стратегию обновления метафизики и перехода ее к новому — постнеклассическому (...)
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  • (1 other version)Teaching and Learning Guide for: Explanation in Mathematics: Proofs and Practice.William D'Alessandro - 2019 - Philosophy Compass 14 (11):e12629.
    This is a teaching and learning guide to accompany "Explanation in Mathematics: Proofs and Practice".
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  • (1 other version)Explanation in mathematics: Proofs and practice.William D'Alessandro - 2019 - Philosophy Compass 14 (11):e12629.
    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 explanatory proofs, and if so, how do (...)
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  • Diversity in proof appraisal.Matthew Inglis & Andrew Aberdein - 2016 - In Brendan Larvor (ed.), Mathematical Cultures: The London Meetings 2012-2014. Springer International Publishing. 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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  • The Aesthetics of Theory Selection and the Logics of Art.Ian O’Loughlin & Kate McCallum - 2018 - Philosophy of Science (2):325-343.
    Philosophers of science discuss whether theory selection depends on aesthetic judgments or criteria, and whether these putatively aesthetic features are genuinely extra-epistemic. As examples, judgments involving criteria such as simplicity and symmetry are often cited. However, other theory selection criteria, such as fecundity, coherence, internal consistency, and fertility, more closely match those criteria used in art contexts and by scholars working in aesthetics. Paying closer attention to the way these criteria are used in art contexts allows us to understand some (...)
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  • Introduction to Special Issue: Aesthetics in Mathematics†.Angela Breitenbach & Davide Rizza - 2018 - Philosophia Mathematica 26 (2):153-160.
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  • Fitting Feelings and Elegant Proofs: On the Psychology of Aesthetic Evaluation in Mathematics.Cain Todd - 2017 - Philosophia Mathematica:nkx007.
    ABSTRACT This paper explores the role of aesthetic judgements in mathematics by focussing on the relationship between the epistemic and aesthetic criteria employed in such judgements, and on the nature of the psychological experiences underpinning them. I claim that aesthetic judgements in mathematics are plausibly understood as expressions of what I will call ‘aesthetic-epistemic feelings’ that serve a genuine cognitive and epistemic function. I will then propose a naturalistic account of these feelings in terms of sub-personal processes of representing and (...)
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  • Explanations in the wild.Justin Sulik, Jeroen van Paridon & Gary Lupyan - 2023 - Cognition 237 (C):105464.
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  • Entering the valley of formalism: trends and changes in mathematicians’ publication practice—1885 to 2015.Mikkel Willum Johansen & Josefine Lomholt Pallavicini - 2022 - Synthese 200 (3):1-23.
    Over the last century, there have been considerable variations in the frequency of use and types of diagrams used in mathematical publications. In order to track these changes, we developed a method enabling large-scale quantitative analysis of mathematical publications to investigate the number and types of diagrams published in three leading mathematical journals in the period from 1885 to 2015. The results show that diagrams were relatively common at the beginning of the period under investigation. However, beginning in 1910, they (...)
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  • Paradoxes and structural rules from a dialogical perspective.Catarina Dutilh Novaes & Rohan French - 2018 - Philosophical Issues 28 (1):129-158.
    In recent years, substructural approaches to paradoxes have become quite popular. But whatever restrictions on structural rules we may want to enforce, it is highly desirable that such restrictions be accompanied by independent philosophical motivation, not directly related to paradoxes. Indeed, while these recent developments have shed new light on a number of issues pertaining to paradoxes, it seems that we now have even more open questions than before, in particular two very pressing ones: what (independent) motivations do we have (...)
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  • Three Roles of Empirical Information in Philosophy: Intuitions on Mathematics do Not Come for Free.Deniz Sarikaya, José Antonio Pérez-Escobar & Deborah Kant - 2021 - Kriterion – Journal of Philosophy 35 (3):247-278.
    This work gives a new argument for ‘Empirical Philosophy of Mathematical Practice’. It analyses different modalities on how empirical information can influence philosophical endeavours. We evoke the classical dichotomy between “armchair” philosophy and empirical/experimental philosophy, and claim that the latter should in turn be subdivided in three distinct styles: Apostate speculator, Informed analyst, and Freeway explorer. This is a shift of focus from the source of the information towards its use by philosophers. We present several examples from philosophy of mind/science (...)
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  • Mathematicians’ Assessments of the Explanatory Value of Proofs.Juan Pablo Mejía Ramos, Tanya Evans, Colin Rittberg & Matthew Inglis - 2021 - Axiomathes 31 (5):575-599.
    The literature on mathematical explanation contains numerous examples of explanatory, and not so explanatory proofs. In this paper we report results of an empirical study aimed at investigating mathematicians’ notion of explanatoriness, and its relationship to accounts of mathematical explanation. Using a Comparative Judgement approach, we asked 38 mathematicians to assess the explanatory value of several proofs of the same proposition. We found an extremely high level of agreement among mathematicians, and some inconsistencies between their assessments and claims in the (...)
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  • Functional Beauty, Pleasure, and Experience.Panos Paris - 2020 - Australasian Journal of Philosophy 98 (3):516-530.
    I offer a set of sufficient conditions for beauty, drawing on Parsons and Carlson’s account of ‘functional beauty’. First, I argue that their account is flawed, whilst falling short of...
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  • Philosophy of Mathematical Practice — Motivations, Themes and Prospects†.Jessica Carter - 2019 - Philosophia Mathematica 27 (1):1-32.
    A number of examples of studies from the field ‘The Philosophy of Mathematical Practice’ (PMP) are given. To characterise this new field, three different strands are identified: an agent-based, a historical, and an epistemological PMP. These differ in how they understand ‘practice’ and which assumptions lie at the core of their investigations. In the last part a general framework, capturing some overall structure of the field, is proposed.
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  • Epistemic injustice in mathematics.Colin Jakob Rittberg, Fenner Stanley Tanswell & Jean Paul Van Bendegem - 2020 - Synthese 197 (9):3875-3904.
    We investigate how epistemic injustice can manifest itself in mathematical practices. We do this as both a social epistemological and virtue-theoretic investigation of mathematical practices. We delineate the concept both positively—we show that a certain type of folk theorem can be a source of epistemic injustice in mathematics—and negatively by exploring cases where the obstacles to participation in a mathematical practice do not amount to epistemic injustice. Having explored what epistemic injustice in mathematics can amount to, we use the concept (...)
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  • The Nature and Experience of Mathematical Beauty.Raman-Sundström Manya, Öhman Lars-Daniel & Sinclair Nathalie - 2016 - Journal of Humanistic Mathematics 6 (1):3-7.
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  • Intuitive credit attribution and the priority rule.Mia Karabegovic, Tristin Blatt, Pascal Boyer & Hugo Mercier - forthcoming - Philosophical Psychology.
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  • Fitting Feelings and Elegant Proofs: On the Psychology of Aesthetic Evaluation in Mathematics.Cain Todd - 2018 - Philosophia Mathematica 26 (2):211-233.
    This paper explores the role of aesthetic judgements in mathematics by focussing on the relationship between the epistemic and aesthetic criteria employed in such judgements, and on the nature of the psychological experiences underpinning them. I claim that aesthetic judgements in mathematics are plausibly understood as expressions of what I will call ‘aesthetic-epistemic feelings’ that serve a genuine cognitive and epistemic function. I will then propose a naturalistic account of these feelings in terms of sub-personal processes of representing and assessing (...)
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  • Indeterminacy, coincidence, and “Sourcing Newness” in mathematical research.James V. Martin - 2022 - Synthese 200 (1):1-23.
    Far from being unwelcome or impossible in a mathematical setting, indeterminacy in various forms can be seen as playing an important role in driving mathematical research forward by providing “sources of newness” in the sense of Hutter and Farías :434–449, 2017). I argue here that mathematical coincidences, phenomena recently under discussion in the philosophy of mathematics, are usefully seen as inducers of indeterminacy and as put to work in guiding mathematical research. I suggest that to call a pair of mathematical (...)
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  • Philosophy of mathematical practice: A primer for mathematics educators.Yacin Hamami & Rebecca Morris - 2020 - ZDM Mathematics Education 52:1113–1126.
    In recent years, philosophical work directly concerned with the practice of mathematics has intensified, giving rise to a movement known as the philosophy of mathematical practice . In this paper we offer a survey of this movement aimed at mathematics educators. We first describe the core questions philosophers of mathematical practice investigate as well as the philosophical methods they use to tackle them. We then provide a selective overview of work in the philosophy of mathematical practice covering topics including the (...)
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  • Intuitions about mathematical beauty: A case study in the aesthetic experience of ideas.Samuel G. B. Johnson & Stefan Steinerberger - 2019 - Cognition 189 (C):242-259.
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  • Beauty Is Not All There Is to Aesthetics in Mathematics.R. S. D. Thomas - 2017 - Philosophia Mathematica 25 (1):116–127.
    Aesthetics in philosophy of mathematics is too narrowly construed. Beauty is not the only feature in mathematics that is arguably aesthetic. While not the highest aesthetic value, being interesting is a sine qua non for publishability. Of the many ways to be interesting, being explanatory has recently been discussed. The motivational power of what is interesting is important for both directing research and stimulating education. The scientific satisfaction of curiosity and the artistic desire for beautiful results are complementary but both (...)
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  • Getting Out in Front of the Owl of Minerva Problem.David Godden - 2021 - Argumentation 36 (1):35-60.
    Our meta-argumentative vocabulary supplies the conceptual tools used to reflectively analyse, regulate, and evaluate our argumentative performances. Yet, this vocabulary is susceptible to misunderstanding and abuse in ways that make possible new discursive mistakes and pathologies. Thus, our efforts to self-regulate our reason-transacting practices by articulating their norms makes possible new ways to violate and flout those very norms. Scott Aikin identifies the structural possibility of this vicious feedback loop as the Owl of Minerva Problem. In the spirit of a (...)
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