About this topic
Summary

Philosophy of mathematical practice is a branch of philosophy of mathematics starting with the assumption that mathematics is not only a body of eternal truths, but also a human activity with its specific dynamics of change and history.  By observing a wide range of mathematical practices, including advanced practices, questions beyond foundations and access to abstract objects arise. Examples of such questions are: Why do mathematicians reprove a theorem which already has an accepted proof?  When is a proof explanatory? What is mathematical understanding? What are the epistemic roles of diagrams and visualization in mathematics?  How did certain mathematical concepts evolve over time? These questions tend to admit localized answers, specific to certain contexts, rather than applying for all mathematics. In recent years, researchers have been accumulating detailed case studies to answer them.  Moreover, interdisciplinary endeavours have been pursued, bringing together not only philosophers and historians, but also cognitive scientists, sociologist, anthropologists, mathematics education researchers, and computer scientists.

Key works

The collection Mancosu 2008 contains an important sample of articles on the philosophy of mathematical practice.  For a more interdisciplinary collection, in which issues in sociology of mathematics and mathematical education are also included, see Van Bendegem & van Kerkhove 2007. Book length studies are Corfield 2003, Ferreiros 2016, and Wagner 2017.

Introductions

The introduction of Mancosu 2008 is very informative and clarifies the position of philosophy of mathematical practice in the landscape of philosophy of mathematics. For general descriptions of different approaches on mathematical practice, see Van Bendegem 2014. A recent survey article is Carter 2019.

Related categories

264 found
Order:
1 — 50 / 264
  1. added 2020-06-01
    Universal Intuitions of Spatial Relations in Elementary Geometry.Ineke J. M. Van der Ham, Yacin Hamami & John Mumma - 2017 - Journal of Cognitive Psychology 29 (3):269-278.
    Spatial relations are central to geometrical thinking. With respect to the classical elementary geometry of Euclid’s Elements, a distinction between co-exact, or qualitative, and exact, or metric, spatial relations has recently been advanced as fundamental. We tested the universality of intuitions of these relations in a group of Senegalese and Dutch participants. Participants performed an odd-one-out task with stimuli that in all but one case display a particular spatial relation between geometric objects. As the exact/co-exact distinction is closely related to (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  2. added 2020-05-22
    Cognitive Processing of Spatial Relations in Euclidean Diagrams.Yacin Hamami, Milan N. A. van der Kuil, Ineke J. M. van der Ham & John Mumma - 2020 - Acta Psychologica 205:1--10.
    The cognitive processing of spatial relations in Euclidean diagrams is central to the diagram-based geometric practice of Euclid's Elements. In this study, we investigate this processing through two dichotomies among spatial relations—metric vs topological and exact vs co-exact—introduced by Manders in his seminal epistemological analysis of Euclid's geometric practice. To this end, we carried out a two-part experiment where participants were asked to judge spatial relations in Euclidean diagrams in a visual half field task design. In the first part, we (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  3. added 2020-04-15
    Plans and Planning in Mathematical Proofs.Yacin Hamami & Rebecca Morris - forthcoming - Review of Symbolic Logic.
    In practice, mathematical proofs are most often the result of careful planning by the agents who produced them. As a consequence, each mathematical proof inherits a plan in virtue of the way it is produced, a plan which underlies its “architecture” or “unity”. This paper provides an account of plans and planning in the context of mathematical proofs. The approach adopted here consists in looking for these notions not in mathematical proofs themselves, but in the agents who produced them. The (...)
    Remove from this list  
    Translate
     
     
    Export citation  
     
    Bookmark   1 citation  
  4. added 2020-04-15
    Intellectual generosity and the reward structure of mathematics.Rebecca Lea Morris - forthcoming - Synthese:1-23.
    Prominent mathematician William Thurston was praised by other mathematicians for his intellectual generosity. But what does it mean to say Thurston was intellectually generous? And is being intellectually generous beneficial? To answer these questions I turn to virtue epistemology and, in particular, Roberts and Wood's (2007) analysis of intellectual generosity. By appealing to Thurston's own writings and interviewing mathematicians who knew and worked with him, I argue that Roberts and Wood's analysis nicely captures the sense in which he was intellectually (...)
    Remove from this list   Direct download (3 more)  
    Translate
     
     
    Export citation  
     
    Bookmark  
  5. added 2020-04-15
    Philosophy of Mathematical Practice: A Primer for Mathematics Educators.Yacin Hamami & Rebecca Morris - forthcoming - ZDM Mathematics Education.
    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 (...)
    Remove from this list   Direct download (2 more)  
    Translate
     
     
    Export citation  
     
    Bookmark  
  6. added 2020-04-11
    Are Aesthetic Judgements Purely Aesthetic? Testing the Social Conformity Account.Matthew Inglis & Andrew Aberdein - forthcoming - ZDM.
    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 (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  7. added 2020-02-14
    Proving Quadratic Reciprocity: Explanation, Disagreement, Transparency and Depth.William D'Alessandro - 2020 - Synthese:1-44.
    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 geometric interpretation, due to Gauss (...)
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  8. added 2020-01-21
    Reliability of Mathematical Inference.Jeremy Avigad - forthcoming - Synthese:1-23.
    Of all the demands that mathematics imposes on its practitioners, one of the most fundamental is that proofs ought to be correct. It has been common since the turn of the twentieth century to take correctness to be underwritten by the existence of formal derivations in a suitable axiomatic foundation, but then it is hard to see how this normative standard can be met, given the differences between informal proofs and formal derivations, and given the inherent fragility and complexity of (...)
    Remove from this list   Direct download (6 more)  
    Translate
     
     
    Export citation  
     
    Bookmark  
  9. added 2019-11-12
    Motivated Proofs: What They Are, Why They Matter and How to Write Them.Rebecca Lea Morris - 2020 - Review of Symbolic Logic 13 (1):23-46.
    Mathematicians judge proofs to possess, or lack, a variety of different qualities, including, for example, explanatory power, depth, purity, beauty and fit. Philosophers of mathematical practice have begun to investigate the nature of such qualities. However, mathematicians frequently draw attention to another desirable proof quality: being motivated. Intuitively, motivated proofs contain no "puzzling" steps, but they have received little further analysis. In this paper, I begin a philosophical investigation into motivated proofs. I suggest that a proof is motivated if and (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  10. added 2019-10-13
    Last Bastion of Reason. [REVIEW]James Franklin - 2000 - New Criterion 18 (9):74-78.
    Attacks the irrationalism of Lakatos's Proofs and Refutations and defends mathematics as a "last bastion" of reason against postmodernist and deconstructionist currents.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  11. added 2019-09-28
    Tools of Reason: The Practice of Scientific Diagramming From Antiquity to the Present.Greg Priest, Silvia De Toffoli & Paula Findlen - 2018 - Endeavour 42 (2-3):49-59.
  12. added 2019-09-24
    Formal Semantics and Applied Mathematics: An Inferential Account.Ryan M. Nefdt - 2020 - Journal of Logic, Language and Information 29 (2):221-253.
    In this paper, I utilise the growing literature on scientific modelling to investigate the nature of formal semantics from the perspective of the philosophy of science. Specifically, I incorporate the inferential framework proposed by Bueno and Colyvan : 345–374, 2011) in the philosophy of applied mathematics to offer an account of how formal semantics explains and models its data. This view produces a picture of formal semantic models as involving an embedded process of inference and representation applying indirectly to linguistic (...)
    Remove from this list   Direct download (2 more)  
    Translate
     
     
    Export citation  
     
    Bookmark  
  13. added 2019-09-23
    À Maneira de Um Colar de Pérolas?André Porto - 2017 - Revista Portuguesa de Filosofia 73 (3-4):1381-1404.
    This paper offers an overview of various alternative formulations for Analysis, the theory of Integral and Differential Calculus, and its diverging conceptions of the topological structure of the continuum. We pay particularly attention to Smooth Analysis, a proposal created by William Lawvere and Anders Kock based on Grothendieck’s work on a categorical algebraic geometry. The role of Heyting’s logic, common to all these alternatives is emphasized.
    Remove from this list   Direct download (3 more)  
    Translate
     
     
    Export citation  
     
    Bookmark  
  14. added 2019-08-09
    Teaching and Learning Guide For: Explanation in Mathematics: Proofs and Practice.William D'Alessandro - 2019 - Philosophy Compass 14 (11).
    This is a teaching and learning guide to accompany "Explanation in Mathematics: Proofs and Practice".
    Remove from this list   Direct download (6 more)  
     
    Export citation  
     
    Bookmark  
  15. added 2019-08-06
    Explanation in Mathematics: Proofs and Practice.William D'Alessandro - 2019 - Philosophy Compass 14 (11).
    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 (...)
    Remove from this list   Direct download (7 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  16. added 2019-06-10
    Mathematical Cultures: The London Meetings 2012--2014.Brendan Larvor (ed.) - 2016 - Springer International Publishing.
  17. added 2019-06-10
    Why the Naïve Derivation Recipe Model Cannot Explain How Mathematicians’ Proofs Secure Mathematical Knowledge.Brendan Larvor - 2016 - Philosophia Mathematica 24 (3):401-404.
    The view that a mathematical proof is a sketch of or recipe for a formal derivation requires the proof to function as an argument that there is a suitable derivation. This is a mathematical conclusion, and to avoid a regress we require some other account of how the proof can establish it.
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  18. added 2019-06-10
    Tales of Wonder: Ian Hacking: Why is There Philosophy of Mathematics at All? Cambridge University Press, 2014, 304pp, $80 HB.Brendan Larvor - 2015 - Metascience 24 (3):471-478.
    Why is there Philosophy of Mathematics at all? Ian Hacking. in Metascience (2015).
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  19. added 2019-06-10
    Albert Lautman, ou la dialectique dans les mathématiques.Brendan Larvor - 2010 - Philosophiques 37 (1):75-94.
    Dans cet article, j’explore dans un premier temps la conception que se fait Lautman de la dialectique en examinant ses références à Platon et Heidegger. Je compare ensuite les structures dialectiques identifiées par Lautman dans les mathématiques contemporaines avec celles qui émergent de ses sources philosophiques. Enfin, je soutiens que les structures qu’il a découvertes dans les mathématiques sont plus riches que le suggère son modèle platonicien, et que la distinction « ontologique » de Heidegger est moins utile que semblait (...)
    Remove from this list   Direct download (6 more)  
    Translate
     
     
    Export citation  
     
    Bookmark   1 citation  
  20. added 2019-06-08
    The Semantics of Social Constructivism.Shay Allen Logan - 2015 - Synthese 192 (8):2577-2598.
    This essay will examine some rather serious trouble confronting claims that mathematicalia might be social constructs. Because of the clarity with which he makes the case and the philosophical rigor he applies to his analysis, our exemplar of a social constructivist in this sense is Julian Cole, especially the work in his 2009 and 2013 papers on the topic. In a 2010 paper, Jill Dieterle criticized the view in Cole’s 2009 paper for being unable to account for the atemporality of (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  21. added 2019-06-08
    Category Theory is a Contentful Theory.Shay Logan - 2015 - Philosophia Mathematica 23 (1):110-115.
    Linnebo and Pettigrew present some objections to category theory as an autonomous foundation. They do a commendable job making clear several distinct senses of ‘autonomous’ as it occurs in the phrase ‘autonomous foundation’. Unfortunately, their paper seems to treat the ‘categorist’ perspective rather unfairly. Several infelicities of this sort were addressed by McLarty. In this note I address yet another apparent infelicity.
    Remove from this list   Direct download (6 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  22. added 2019-06-06
    The Growth of Mathematical Knowledge—Introduction of Convex Bodies.Tinne Hoff Kjeldsen & Jessica Carter - 2012 - Studies in History and Philosophy of Science Part A 43 (2):359-365.
  23. added 2019-06-06
    Early Modern Mathematical Practice in the Round. [REVIEW]Richard J. Oosterhoff - 2012 - Studies in History and Philosophy of Science Part A 43 (1):224-227.
  24. added 2019-06-06
    Crossing Curves: A Limit to the Use of Diagrams in Proofs†: Articles.Marcus Giaquinto - 2011 - Philosophia Mathematica 19 (3):281-307.
    This paper investigates the following question: when can one reliably infer the existence of an intersection point from a diagram presenting crossing curves or lines? Two cases are considered, one from Euclid's geometry and the other from basic real analysis. I argue for the acceptability of such an inference in the geometric case but against in the analytic case. Though this question is somewhat specific, the investigation is intended to contribute to the more general question of the extent and limits (...)
    Remove from this list   Direct download (8 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  25. added 2019-06-06
    Paolo Mancosu, Ed. The Philosophy of Mathematical Practice. Oxford: Oxford University Press, 2008. ISBN 978-0-19-929645-3. Pp. Xi &Plus; 447: Critical Studies/Book Reviews. [REVIEW]Brendan Larvor - 2010 - Philosophia Mathematica 18 (3):350-360.
    (No abstract is available for this citation).
    Remove from this list   Direct download (8 more)  
     
    Export citation  
     
    Bookmark  
  26. added 2019-06-06
    Indispensability and Practice.Penelope Maddy - 1992 - Journal of Philosophy 89 (6):275.
  27. added 2019-06-06
    Philosophical Theory and Mathematical Practice in the Seventeenth Century.Douglas M. Jesseph - 1989 - Studies in History and Philosophy of Science Part A 20 (2):215.
    It is argued that, contrary to the standard accounts of the development of infinitesimal mathematics, the leading mathematicians of the seventeenth century were deeply concerned with the rigor of their methods. examples are taken from the work of cavalieri and leibniz, with further material drawn from guldin, barrow, and wallis.
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  28. added 2019-06-05
    Problems in the Philosophy of Mathematics. Imre Lakatos. [REVIEW]Edward A. Maziarz - 1969 - Philosophy of Science 36 (3):324-326.
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  29. added 2019-06-04
    “Always Mixed Together”: Notation, Language, and the Pedagogy of Frege's Begriffsschrift.David E. Dunning - forthcoming - Modern Intellectual History:1-33.
    Gottlob Frege is considered a founder of analytic philosophy and mathematical logic, but the traditions that claim Frege as a forebear never embraced his Begriffsschrift, or “conceptual notation”—the invention he considered his most important accomplishment. Frege believed that his notation rendered logic visually observable. Rejecting the linearity of written language, he claimed Begriffsschrift exhibited a structure endogenous to logic itself. But Frege struggled to convince others to use his notation, as his frustrated pedagogical efforts at the University of Jena illustrate. (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  30. added 2019-06-03
    Canonical Maps.Jean-Pierre Marquis - 2018 - In Elaine Landry (ed.), Categories for the Working Philosophers. Oxford, UK: pp. 90-112.
    Categorical foundations and set-theoretical foundations are sometimes presented as alternative foundational schemes. So far, the literature has mostly focused on the weaknesses of the categorical foundations. We want here to concentrate on what we take to be one of its strengths: the explicit identification of so-called canonical maps and their role in mathematics. Canonical maps play a central role in contemporary mathematics and although some are easily defined by set-theoretical tools, they all appear systematically in a categorical framework. The key (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  31. added 2019-06-03
    Conceptual Engineering for Mathematical Concepts.Fenner Stanley Tanswell - 2018 - Inquiry: An Interdisciplinary Journal of Philosophy 61 (8):881-913.
    ABSTRACTIn this paper I investigate how conceptual engineering applies to mathematical concepts in particular. I begin with a discussion of Waismann’s notion of open texture, and compare it to Shapiro’s modern usage of the term. Next I set out the position taken by Lakatos which sees mathematical concepts as dynamic and open to improvement and development, arguing that Waismann’s open texture applies to mathematical concepts too. With the perspective of mathematics as open-textured, I make the case that this allows us (...)
    Remove from this list   Direct download (8 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  32. added 2019-06-03
    Saving Proof From Paradox: Gödel’s Paradox and the Inconsistency of Informal Mathematics.Fenner Stanley Tanswell - 2016 - In Peter Verdee & Holger Andreas (eds.), Logical Studies of Paraconsistent Reasoning in Science and Mathematics. Springer. pp. 159-173.
    In this paper I shall consider two related avenues of argument that have been used to make the case for the inconsistency of mathematics: firstly, Gödel’s paradox which leads to a contradiction within mathematics and, secondly, the incompatibility of completeness and consistency established by Gödel’s incompleteness theorems. By bringing in considerations from the philosophy of mathematical practice on informal proofs, I suggest that we should add to the two axes of completeness and consistency a third axis of formality and informality. (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  33. added 2019-06-03
    The Exact (Up to Infinitesimals) Infinite Perimeter of the Koch Snowflake and its Finite Area.Yaroslav Sergeyev - 2016 - Communications in Nonlinear Science and Numerical Simulation 31 (1-3):21–29.
    The Koch snowflake is one of the first fractals that were mathematically described. It is interesting because it has an infinite perimeter in the limit but its limit area is finite. In this paper, a recently proposed computational methodology allowing one to execute numerical computations with infinities and infinitesimals is applied to study the Koch snowflake at infinity. Numerical computations with actual infinite and infinitesimal numbers can be executed on the Infinity Computer being a new supercomputer patented in USA and (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  34. added 2019-06-03
    Proof, Rigour and Informality : A Virtue Account of Mathematical Knowledge.Fenner Stanley Tanswell - 2016 - St Andrews Research Repository Philosophy Dissertations.
    This thesis is about the nature of proofs in mathematics as it is practiced, contrasting the informal proofs found in practice with formal proofs in formal systems. In the first chapter I present a new argument against the Formalist-Reductionist view that informal proofs are justified as rigorous and correct by corresponding to formal counterparts. The second chapter builds on this to reject arguments from Gödel's paradox and incompleteness theorems to the claim that mathematics is inherently inconsistent, basing my objections on (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   3 citations  
  35. added 2019-06-03
    A Problem with the Dependence of Informal Proofs on Formal Proofs.Fenner Tanswell - 2015 - Philosophia Mathematica 23 (3):295-310.
    Derivationists, those wishing to explain the correctness and rigour of informal proofs in terms of associated formal proofs, are generally held to be supported by the success of the project of translating informal proofs into computer-checkable formal counterparts. I argue, however, that this project is a false friend for the derivationists because there are too many different associated formal proofs for each informal proof, leading to a serious worry of overgeneration. I press this worry primarily against Azzouni's derivation-indicator account, but (...)
    Remove from this list   Direct download (6 more)  
     
    Export citation  
     
    Bookmark   11 citations  
  36. added 2019-06-03
    Mathematical Abstraction, Conceptual Variation and Identity.Jean-Pierre Marquis - 2014 - In Peter Schroeder-Heister, Gerhard Heinzmann, Wilfred Hodges & Pierre Edouard Bour (eds.), Logic, Methodology and Philosophy of Science, Proceedings of the 14th International Congress. London, UK: pp. 299-322.
    One of the key features of modern mathematics is the adoption of the abstract method. Our goal in this paper is to propose an explication of that method that is rooted in the history of the subject.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  37. added 2019-05-07
    La scoperta scientifica: la ricerca di un metodo e il suo smarrimento.Emiliano Ippoliti - 2019 - In Stefano Velotti & Luigi Conti (eds.), Strumenti del Pensiero. Vol. 2. Rome: Laterza. pp. 935-964.
    (ENG) The paper examines the first attempts put forward in ancient Greek to build a method for scientific discovery and how they have been progressively neglected. -/- (ITA) L'articolo esamina i primi tentativi effettuati nell'antica grecia di costruire un metodo della scoperta scientifica, e analizza le ragioni che hanno portato al suo progessivo abbandono.
    Remove from this list  
    Translate
     
     
    Export citation  
     
    Bookmark  
  38. added 2019-05-07
    La Scoperta Scientifica: Rinascita e Raffinamento dei Metodi.Emiliano Ippoliti - 2019 - In Stefano Velotti & Luigi Conti (eds.), Gli strumenti del Pensier. Rome: Laterza. pp. 935-964.
    (ENG) The paper examines the main approaches developed in the XIX and XX century to account for the way scientific discover unfolds. -/- (ITA) L'articolo esamina le principali teorie filosofico-scientifiche elaborate nell'800 e nle '900 per render conto dei processi di scoperta scientifica.
    Remove from this list  
    Translate
     
     
    Export citation  
     
    Bookmark  
  39. added 2019-04-29
    Exploring the Boundaries of Conceptual Evaluation.Christopher Pincock - 2010 - Philosophia Mathematica 18 (1):106-121.
    This is a critical notice of Mark Wilson's Wandering Significance.
    Remove from this list   Direct download (8 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  40. added 2019-04-28
    Mathematical Models of Abstract Systems: Knowing Abstract Geometric Forms.Jean-Pierre Marquis - 2013 - Annales de la Faculté des Sciences de Toulouse 22 (5):969-1016.
    Scientists use models to know the world. It i susually assumed that mathematicians doing pure mathematics do not. Mathematicians doing pure mathematics prove theorems about mathematical entities like sets, numbers, geometric figures, spaces, etc., they compute various functions and solve equations. In this paper, I want to exhibit models build by mathematicians to study the fundamental components of spaces and, more generally, of mathematical forms. I focus on one area of mathematics where models occupy a central role, namely homotopy theory. (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  41. added 2019-04-28
    Mathematical Engineering and Mathematical Change.Jean‐Pierre Marquis - 1999 - International Studies in the Philosophy of Science 13 (3):245 – 259.
    In this paper, I introduce and examine the notion of “mathematical engineering” and its impact on mathematical change. Mathematical engineering is an important part of contemporary mathematics and it roughly consists of the “construction” and development of various machines, probes and instruments used in numerous mathematical fields. As an example of such constructions, I briefly present the basic steps and properties of homology theory. I then try to show that this aspect of contemporary mathematics has important consequences on our conception (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  42. added 2019-04-26
    Explanation in Mathematical Conversations: An Empirical Investigation.Alison Pease, Andrew Aberdein & Ursula Martin - 2019 - Philosophical Transactions of the Royal Society A 377.
    Analysis of online mathematics forums can help reveal how explanation is used by mathematicians; we contend that this use of explanation may help to provide an informal conceptualization of simplicity. We extracted six conjectures from recent philosophical work on the occurrence and characteristics of explanation in mathematics. We then tested these conjectures against a corpus derived from online mathematical discussions. To this end, we employed two techniques, one based on indicator terms, the other on a random sample of comments lacking (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  43. added 2019-04-26
    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 (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  44. added 2019-04-26
    A Study of Mathematical Determination Through Bertrand’s Paradox.Davide Rizza - 2018 - Philosophia Mathematica 26 (3):375-395.
    Certain mathematical problems prove very hard to solve because some of their intuitive features have not been assimilated or cannot be assimilated by the available mathematical resources. This state of affairs triggers an interesting dynamic whereby the introduction of novel conceptual resources converts the intuitive features into further mathematical determinations in light of which a solution to the original problem is made accessible. I illustrate this phenomenon through a study of Bertrand’s paradox.
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  45. added 2019-04-26
    Reconstruction in Philosophy of Mathematics.Davide Rizza - 2018 - Dewey Studies 2 (2):31-53.
    Throughout his work, John Dewey seeks to emancipate philosophical reflection from the influence of the classical tradition he traces back to Plato and Aristotle. For Dewey, this tradition rests upon a conception of knowledge based on the separation between theory and practice, which is incompatible with the structure of scientific inquiry. Philosophical work can make progress only if it is freed from its traditional heritage, i.e. only if it undergoes reconstruction. In this study I show that implicit appeals to the (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  46. added 2019-04-26
    Mohan Ganesalingam. The Language of Mathematics: A Linguistic and Philosophical Investigation. FoLLI Publications on Logic, Language and Information. [REVIEW]Andrew Aberdein - 2017 - Philosophia Mathematica 25 (1):143–147.
  47. added 2019-04-26
    Stairway to Heaven: The Abstract Method and Levels of Abstraction in Mathematics.Jean Pierre Marquis & Jean-Pierre Marquis - 2016 - The Mathematical Intelligencer 38 (3):41-51.
    In this paper, following the claims made by various mathematicians, I try to construct a theory of levels of abstraction. I first try to clarify the basic components of the abstract method as it developed in the first quarter of the 20th century. I then submit an explication of the notion of levels of abstraction. In the final section, I briefly explore some of main philosophical consequences of the theory.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  48. added 2019-04-26
    Divergent Mathematical Treatments in Utility Theory.Davide Rizza - 2016 - Erkenntnis 81 (6):1287-1303.
    In this paper I study how divergent mathematical treatments affect mathematical modelling, with a special focus on utility theory. In particular I examine recent work on the ranking of information states and the discounting of future utilities, in order to show how, by replacing the standard analytical treatment of the models involved with one based on the framework of Nonstandard Analysis, diametrically opposite results are obtained. In both cases, the choice between the standard and nonstandard treatment amounts to a selection (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  49. added 2019-04-26
    The Applicability of Mathematics: Beyond Mapping Accounts.Davide Rizza - 2013 - Philosophy of Science 80 (3):398-412.
  50. added 2019-04-26
    Commentary On: Michel Dufour's "Argument and Explanation in Mathematics".Andrew Aberdein - 2013 - In Dima Mohammed & Marcin Lewinski (eds.), Virtues of argumentation: Proceedings of the 10th International Conference of the Ontario Society for the Study of Argumentation (OSSA), May 22–25, 2013. OSSA.
1 — 50 / 264