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Philosophy of Mathematics > Philosophy of Mathematics, Miscellaneous > Mathematical Practice

Mathematical Practice

Edited by Silvia De Toffoli (Princeton University)
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 2005, 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.
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  1. added 2019-03-30
    Evidence, Proofs, and Derivations.Andrew Aberdein - forthcoming - ZDM 51 (4).
    The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical practice. Nonetheless, evidence, proof, and derivation are closely intertwined. This paper seeks to tease these concepts apart. It emphasizes the role of argumentation as a context shared by evidence, proofs, and derivations. The utility of argumentation theory, in general, and argumentation schemes, in particular, (...)
  2. added 2019-03-30
    The Beauty (?) of Mathematical Proofs.Catarina Dutilh Novaes - 2019 - In Andrew Aberdein & Matthew Inglis (eds.), Advances in Experimental Philosophy of Logic and Mathematics. London: Bloomsbury Academic. pp. 63-93.
  3. added 2019-03-30
    Redefining Revolutions.Andrew Aberdein - 2018 - In Moti Mizrahi (ed.), The Kuhnian image of science: Time for a decisive transformation? London: Rowman & Littlefield. pp. 133–154.
    In their account of theory change in logic, Aberdein and Read distinguish 'glorious' from 'inglorious' revolutions--only the former preserves all 'the key components of a theory' [1]. A widespread view, expressed in these terms, is that empirical science characteristically exhibits inglorious revolutions but that revolutions in mathematics are at most glorious [2]. Here are three possible responses: 0. Accept that empirical science and mathematics are methodologically discontinuous; 1. Argue that mathematics can exhibit inglorious revolutions; 2. Deny that inglorious revolutions are (...)
  4. added 2019-03-28
    Can Diagrams Have Epistemic Value? The Case of Euclid.Jesse Norman - 2004 - In A. Blackwell, K. Marriott & A. Shimojima (eds.), Diagrammatic Representation and Inference. Springer. pp. 14--17.
  5. added 2019-03-26
    Making and Breaking Mathematical Sense.Roi Wagner - 2017 - Princeton, USA: Princeton University Press.
    In line with the emerging field of philosophy of mathematical practice, this book pushes the philosophy of mathematics away from questions about the reality and truth of mathematical entities and statements and toward a focus on what mathematicians actually do—and how that evolves and changes over time. How do new mathematical entities come to be? What internal, natural, cognitive, and social constraints shape mathematical cultures? How do mathematical signs form and reform their meanings? How can we model the cognitive processes (...)
  6. added 2019-03-25
    Mathematical Knowledge and the Interplay of Practices.Jose Ferreiros - 2016 - Princeton, USA: Princeton University Press.
    This book presents a new approach to the epistemology of mathematics by viewing mathematics as a human activity whose knowledge is intimately linked with practice. Charting an exciting new direction in the philosophy of mathematics, José Ferreirós uses the crucial idea of a continuum to provide an account of the development of mathematical knowledge that reflects the actual experience of doing math and makes sense of the perceived objectivity of mathematical results. -/- Describing a historically oriented, agent-based philosophy of mathematics, (...)
  7. added 2019-03-25
    The Impact of the Philosophy of Mathematical Practice on the Philosophy of Mathematics.Jean Paul Van Bendegem - 2014 - In Léna Soler, Sjoerd Zwart, Michael Lynch & Vincent Israel-Jost (eds.), Science After the Practice Turn in the Philosophy, History, and Social Studies of Science. New York, USA: Routledge. pp. 215-226.
  8. added 2019-03-25
    Perspectives on Mathematical Practices.Jean Paul Van Bendegem & Bart van Kerkhove (eds.) - 2007 - Springer.
    Philosophy of mathematics today has transformed into a very complex network of diverse ideas, viewpoints, and theories. Sometimes the emphasis is on the "classical" foundational work (often connected with the use of formal logical methods), sometimes on the sociological dimension of the mathematical research community and the "products" it produces, then again on the education of future mathematicians and the problem of how knowledge is or should be transmitted from one generation to the next. The editors of this book felt (...)
  9. added 2019-03-23
    Imagination in Mathematics.Andrew Arana - 2016 - In Amy Kind (ed.), Routledge Handbook on the Philosophy of Imagination. Routledge. pp. 463-477.
    This article will consider imagination in mathematics from a historical point of view, noting the key moments in its conception during the ancient, modern and contemporary eras.
  10. added 2019-03-23
    What Philosophy of Mathematical Practice Can Teach Argumentation Theory About Diagrams and Pictures.Brendan Larvor - 2013 - In Andrew Aberdein & Ian J. Dove (eds.), The Argument of Mathematics. Springer. pp. 239--253.
  11. added 2019-03-23
    On the Relationship Between Plane and Solid Geometry.Andrew Arana & Paolo Mancosu - 2012 - Review of Symbolic Logic 5 (2):294-353.
    Traditional geometry concerns itself with planimetric and stereometric considerations, which are at the root of the division between plane and solid geometry. To raise the issue of the relation between these two areas brings with it a host of different problems that pertain to mathematical practice, epistemology, semantics, ontology, methodology, and logic. In addition, issues of psychology and pedagogy are also important here. To our knowledge there is no single contribution that studies in detail even one of the aforementioned areas.
  12. added 2019-03-23
    The Many Faces of Mathematical Constructivism.B. Kerkhove & J. P. Bendegem - 2012 - Constructivist Foundations 7 (2):97-103.
    Context: As one of the major approaches within the philosophy of mathematics, constructivism is to be contrasted with realist approaches such as Platonism in that it takes human mental activity as the basis of mathematical content. Problem: Mathematical constructivism is mostly identified as one of the so-called foundationalist accounts internal to mathematics. Other perspectives are possible, however. Results: The notion of “meaning finitism” is exploited to tie together internal and external directions within mathematical constructivism. The various contributions to this issue (...)
  13. added 2019-03-23
    Visual Thinking in Mathematics • by Marcus Giaquinto.Andrew Arana - 2009 - Analysis 69 (2):401-403.
    Our visual experience seems to suggest that no continuous curve can cover every point of the unit square, yet in the late 19th century Giuseppe Peano proved that such a curve exists. Examples like this, particularly in analysis received much attention in the 19th century. They helped to instigate what Hans Hahn called a ‘crisis of intuition’, wherein visual reasoning in mathematics came to be thought to be epistemically problematic. Hahn described this ‘crisis’ as follows : " Mathematicians had for (...)
  14. added 2019-03-23
    Review of D. Corfield's Toward A Philosophy Of Real Mathematics. [REVIEW]Andrew Arana - 2007 - Mathematical Intelligencer 29 (2).
    When mathematicians think of the philosophy of mathematics, they probably think of endless debates about what numbers are and whether they exist. Since plenty of mathematical progress continues to be made without taking a stance on either of these questions, mathematicians feel confident they can work without much regard for philosophical reflections. In his sharp–toned, sprawling book, David Corfield acknowledges the irrelevance of much contemporary philosophy of mathematics to current mathematical practice, and proposes reforming the subject accordingly.
  15. added 2019-03-23
    What is Dialectical Philosophy of Mathematics?Brendan Larvor - 2001 - Philosophia Mathematica 9 (2):212-229.
    The late Imre Lakatos once hoped to found a school of dialectical philosophy of mathematics. The aim of this paper is to ask what that might possibly mean. But Lakatos's philosophy has serious shortcomings. The paper elaborates a conception of dialectical philosophy of mathematics that repairs these defects and considers the work of three philosophers who in some measure fit the description: Yehuda Rav, Mary Leng and David Corfield.
  16. added 2019-03-22
    Explanation and Abstraction From a Backward-Error Analytic Perspective.Nicolas Fillion & Robert H. C. Moir - 2018 - European Journal for Philosophy of Science 8 (3):735-759.
    We argue that two powerful error-theoretic concepts provide a general framework that satisfactorily accounts for key aspects of the explanation of physical patterns. This method gives an objective criterion to determine which mathematical models in a class of neighboring models are just as good as the exact one. The method also emphasizes that abstraction is essential for explanation and provides a precise conceptual framework that determines whether a given abstraction is explanatorily relevant and justified. Hence, it increases our epistemological understanding (...)
  17. added 2019-03-22
    The ‘Miracle’ of Applicability? The Curious Case of the Simple Harmonic Oscillator.Sorin Bangu & Robert H. C. Moir - 2018 - Foundations of Physics 48 (5):507-525.
    The paper discusses to what extent the conceptual issues involved in solving the simple harmonic oscillator model fit Wigner’s famous point that the applicability of mathematics borders on the miraculous. We argue that although there is ultimately nothing mysterious here, as is to be expected, a careful demonstration that this is so involves unexpected difficulties. Consequently, through the lens of this simple case we derive some insight into what is responsible for the appearance of mystery in more sophisticated examples of (...)
  18. added 2019-03-04
    Acceptable Gaps in Mathematical Proofs.Line Edslev Andersen - forthcoming - Synthese.
  19. added 2019-03-04
    Epistemic Injustice in Mathematics.Colin Jakob Rittberg, Fenner Stanley Tanswell & Jean Paul Van Bendegem - forthcoming - Synthese:1-30.
    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, (...)
  20. added 2019-03-04
    Philosophy of Mathematical Practice — Motivations, Themes and Prospects.Jessica Carter - 2019 - Philosophia Mathematica 27 (1):1-32.
    ABSTRACT A number of examples of studies from the field ‘The Philosophy of Mathematical Practice’ 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.
  21. added 2019-03-04
    Manipulative Imagination: How to Move Things Around in Mathematics.Valeria Giardino - 2018 - Theoria : An International Journal for Theory, History and Fundations of Science 33 (2):345-360.
    In the first part of the paper, previous work about embodied mathematics and the practice of topology will be presented. According to the proposed view, in order to become experts, topologists have to learn how to use manipulative imagination: representations are cognitive tools whose functioning depends from pre-existing cognitive abilities and from specific training. In the second part of the paper, the notion of imagination as “make-believe” is discussed to give an account of cognitive tools in mathematics as props; to (...)
  22. added 2019-03-04
    Roi Wagner. Making and Breaking Mathematical Sense: Histories and Philosophies of Mathematical Practice. [REVIEW]José Ferreirós - 2018 - Philosophia Mathematica 26 (1):131-136.
    © The Authors [2018]. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: [email protected] mathematics a reflection of some already-given realm? It would not matter whether we are talking about the empirical world in a Millian way, or the domain of a priori truths in Leibnizian or maybe Kantian style, or some world of analytical truths à la Carnap. Or perhaps — could mathematics be something more, or something less, than such a reflection? Might it be human, (...)
  23. added 2019-03-04
    Mathematical Knowledge and the Interplay of Practices. [REVIEW]María de Paz - 2018 - Philosophical Quarterly 68 (271):406-408.
    Mathematical Knowledge and the Interplay of Practices. By Ferreirós José.
  24. added 2019-03-04
    Tools for Thought: The Case of Mathematics.Valeria Giardino - 2018 - Endeavour 2 (42):172-179.
    The objective of this article is to take into account the functioning of representational cognitive tools, and in particular of notations and visualizations in mathematics. In order to explain their functioning, formulas in algebra and logic and diagrams in topology will be presented as case studies and the notion of manipulative imagination as proposed in previous work will be discussed. To better characterize the analysis, the notions of material anchor and representational affordance will be introduced.
  25. added 2019-03-04
    On Frege’s Begriffsschrift Notation for Propositional Logic: Design Principles and Trade-Offs.Dirk Schlimm - 2018 - History and Philosophy of Logic 39 (1):53-79.
    Well over a century after its introduction, Frege's two-dimensional Begriffsschrift notation is still considered mainly a curiosity that stands out more for its clumsiness than anything else. This paper focuses mainly on the propositional fragment of the Begriffsschrift, because it embodies the characteristic features that distinguish it from other expressively equivalent notations. In the first part, I argue for the perspicuity and readability of the Begriffsschrift by discussing several idiosyncrasies of the notation, which allow an easy conversion of logically equivalent (...)
  26. added 2019-03-04
    José Ferreirós. Mathematical Knowledge and the Interplay of Practices. [REVIEW]Dirk Schlimm - 2017 - Philosophia Mathematica 25 (1):139-143.
  27. added 2019-03-04
    Modularity in Mathematics.Jeremy Avigad - 2017 - Review of Symbolic Logic:1-33.
    In a wide range of fields, the word "modular" is used to describe complex systems that can be decomposed into smaller systems with limited interactions between them. This essay argues that mathematical knowledge can fruitfully be understood as having a modular structure, and explores the ways in which modularity in mathematics is epistemically advantageous.
  28. added 2019-03-04
    From Euclidean Geometry to Knots and Nets.Brendan Larvor - 2017 - Synthese:1-22.
    This paper assumes the success of arguments against the view that informal mathematical proofs secure rational conviction in virtue of their relations with corresponding formal derivations. This assumption entails a need for an alternative account of the logic of informal mathematical proofs. Following examination of case studies by Manders, De Toffoli and Giardino, Leitgeb, Feferman and others, this paper proposes a framework for analysing those informal proofs that appeal to the perception or modification of diagrams or to the inspection or (...)
  29. added 2019-03-04
    Mathematical Knowledge and the Interplay of Practices. [REVIEW]Madeline Muntersbjorn - 2017 - History and Philosophy of Logic 38 (1):89-92.
  30. added 2019-03-04
    Ways of Advancing Knowledge. A Lesson From Knot Theory and Topology.Emiliano Ippoliti - 2016 - In Emiliano Ippoliti, Fabio Sterpetti & Thomas Nickles (eds.), Models and Inferences in Science. Springer. pp. 147--172.
  31. added 2019-03-04
    Character and Object.Rebecca Morris & Jeremy Avigad - 2016 - Review of Symbolic Logic 9 (3):480-510.
    In 1837, Dirichlet proved that there are infinitely many primes in any arithmetic progression in which the terms do not all share a common factor. Modern presentations of the proof are explicitly higher-order, in that they involve quantifying over and summing over Dirichlet characters, which are certain types of functions. The notion of a character is only implicit in Dirichlet’s original proof, and the subsequent history shows a very gradual transition to the modern mode of presentation. In this essay, we (...)
  32. added 2019-03-04
    Rebutting and Undercutting in Mathematics.Kenny Easwaran - 2015 - Philosophical Perspectives 29 (1):146-162.
    In my () I argued that a central component of mathematical practice is that published proofs must be “transferable” — that is, they must be such that the author's reasons for believing the conclusion are shared directly with the reader, rather than requiring the reader to essentially rely on testimony. The goal of this paper is to explain this requirement of transferability in terms of a more general norm on defeat in mathematical reasoning that I will call “convertibility”. I begin (...)
  33. added 2019-03-04
    That We See That Some Diagrammatic Proofs Are Perfectly Rigorous.Jody Azzouni - 2013 - Philosophia Mathematica 21 (3):323-338.
    Mistaken reasons for thinking diagrammatic proofs aren't rigorous are explored. The main result is that a confusion between the contents of a proof procedure (what's expressed by the referential elements in a proof procedure) and the unarticulated mathematical aspects of a proof procedure (how that proof procedure is enabled) gives the impression that diagrammatic proofs are less rigorous than language proofs. An additional (and independent) factor is treating the impossibility of naturally generalizing a diagrammatic proof procedure as an indication of (...)
  34. added 2019-03-04
    Diagrammatic Reasoning in Frege’s Begriffsschrift.Danielle Macbeth - 2012 - Synthese 186 (1):289-314.
    In Part III of his 1879 logic Frege proves a theorem in the theory of sequences on the basis of four definitions. He claims in Grundlagen that this proof, despite being strictly deductive, constitutes a real extension of our knowledge, that it is ampliative rather than merely explicative. Frege furthermore connects this idea of ampliative deductive proof to what he thinks of as a fruitful definition, one that draws new lines. My aim is to show that we can make good (...)
  35. added 2019-03-04
    Constructive Geometrical Reasoning and Diagrams.John Mumma - 2012 - Synthese 186 (1):103-119.
    Modern formal accounts of the constructive nature of elementary geometry do not aim to capture the intuitive or concrete character of geometrical construction. In line with the general abstract approach of modern axiomatics, nothing is presumed of the objects that a geometric construction produces. This study explores the possibility of a formal account of geometric construction where the basic geometric objects are understood from the outset to possess certain spatial properties. The discussion is centered around Eu , a recently developed (...)
  36. added 2019-03-04
    How to Think About Informal Proofs.Brendan Larvor - 2012 - Synthese 187 (2):715-730.
    It is argued in this study that (i) progress in the philosophy of mathematical practice requires a general positive account of informal proof; (ii) the best candidate is to think of informal proofs as arguments that depend on their matter as well as their logical form; (iii) articulating the dependency of informal inferences on their content requires a redefinition of logic as the general study of inferential actions; (iv) it is a decisive advantage of this conception of logic that it (...)
  37. added 2019-03-04
    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.
  38. added 2019-03-04
    The Twofold Role of Diagrams in Euclids Plane Geometry.Marco Panza - 2012 - Synthese 186 (1):55-102.
    Proposition I.1 is, by far, the most popular example used to justify the thesis that many of Euclid’s geometric arguments are diagram-based. Many scholars have recently articulated this thesis in different ways and argued for it. My purpose is to reformulate it in a quite general way, by describing what I take to be the twofold role that diagrams play in Euclid’s plane geometry (EPG). Euclid’s arguments are object-dependent. They are about geometric objects. Hence, they cannot be diagram-based unless diagrams (...)
  39. added 2019-03-04
    To Diagram, to Demonstrate: To Do, To See, and To Judge in Greek Geometry.Philip Catton & Cemency Montelle - 2012 - Philosophia Mathematica 20 (1):25-57.
    Not simply set out in accompaniment of the Greek geometrical text, the diagram also is coaxed into existence manually (using straightedge and compasses) by commands in the text. The marks that a diligent reader thus sequentially produces typically sum, however, to a figure more complex than the provided one and also not (as it is) artful for being synoptically instructive. To provide a figure artfully is to balance multiple desiderata, interlocking the timelessness of insight with the temporality of construction. Our (...)
  40. added 2019-03-04
    Seeing How It Goes: Paper-and-Pencil Reasoning in Mathematical Practice.Danielle Macbeth - 2012 - Philosophia Mathematica 20 (1):58-85.
    Throughout its long history, mathematics has involved the use ofsystems of written signs, most notably, diagrams in Euclidean geometry and formulae in the symbolic language of arithmetic and algebra in the mathematics of Descartes, Euler, and others. Such systems of signs, I argue, enable one to embody chains of mathematical reasoning. I then show that, properly understood, Frege’s Begriffsschrift or concept-script similarly enables one to write mathematical reasoning. Much as a demonstration in Euclid or in early modern algebra does, a (...)
  41. added 2019-03-04
    Diagrams as Sketches.Brice Halimi - 2012 - Synthese 186 (1):387-409.
    This article puts forward the notion of “evolving diagram” as an important case of mathematical diagram. An evolving diagram combines, through a dynamic graphical enrichment, the representation of an object and the representation of a piece of reasoning based on the representation of that object. Evolving diagrams can be illustrated in particular with category-theoretic diagrams (hereafter “diagrams*”) in the context of “sketch theory,” a branch of modern category theory. It is argued that sketch theory provides a diagrammatic* theory of diagrams*, (...)
  42. added 2019-03-04
    Proof and Understanding in Mathematical Practice.Danielle Macbeth - 2012 - Philosophia Scientiae 16 (1):29-54.
    Prouver des théorèmes est une pratique mathématique qui semble clairement améliorer notre compréhension mathématique. Ainsi, prouver et reprouver des théorèmes en mathématiques, vise à apporter une meilleure compréhension. Cependant, comme il est bien connu, les preuves mathématiques totalement formalisées sont habituellement inintelligibles et, à ce titre, ne contribuent pas à notre compréhension mathématique. Comment, alors, comprendre la relation entre prouver des théorèmes et améliorer notre compréhension mathématique. J'avance ici que nous avons d'abord besoin d'une notion différente de preuve , qui (...)
  43. added 2019-03-04
    From Practice to New Concepts: Geometric Properties of Groups.Irena Starikova - 2012 - Philosophia Scientiae 16 (1):129-151.
    Cet article cherche à montrer comment la pratique mathématique, particulièrement celle admettant des représentations visuelles, peut conduire à de nouveaux résultats mathématiques. L'argumentation est basée sur l'étude du cas d'un domaine des mathématiques relativement récent et prometteur: la théorie géométrique des groupes. L'article discute comment la représentation des groupes par les graphes de Cayley rendit possible la découverte de nouvelles propriétés géométriques de groupes.The paper aims to show how mathematical practice, in particular with visual representations, can lead to new mathematical (...)
  44. added 2019-03-04
    Crossing Curves: A Limit to the Use of Diagrams in Proofs.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 (...)
  45. added 2019-03-04
    Understanding, Formal Verification, and the Philosophy of Mathematics.Jeremy Avigad - 2010 - Journal of the Indian Council of Philosophical Research 27:161-197.
    The philosophy of mathematics has long been concerned with deter- mining the means that are appropriate for justifying claims of mathemat- ical knowledge, and the metaphysical considerations that render them so. But, as of late, many philosophers have called attention to the fact that a much broader range of normative judgments arise in ordinary math- ematical practice; for example, questions can be interesting, theorems important, proofs explanatory, concepts powerful, and so on. The as- sociated values are often loosely classied as (...)
  46. added 2019-03-04
    Diagrams and Proofs in Analysis.Jessica Carter - 2010 - International Studies in the Philosophy of Science 24 (1):1 – 14.
    This article discusses the role of diagrams in mathematical reasoning in the light of a case study in analysis. In the example presented certain combinatorial expressions were first found by using diagrams. In the published proofs the pictures were replaced by reasoning about permutation groups. This article argues that, even though the diagrams are not present in the published papers, they still play a role in the formulation of the proofs. It is shown that they play a role in concept (...)
  47. added 2019-03-04
    Diagrammatic Reasoning in Euclid’s Elements.Danielle Macbeth - 2010 - In Bart van Kerkhove, Jean Paul van Bendegem & Jonas de Vuyst (eds.), Philosophical Perspectives on Mathematical Practice 12. College Publications. pp. 235-267.
  48. added 2019-03-04
    Paolo Mancosu, Ed. The Philosophy of Mathematical Practice. Oxford: Oxford University Press, 2008. ISBN 978-0-19-929645-3. Pp. Xi + 447. [REVIEW]B. Larvor - 2010 - Philosophia Mathematica 18 (3):350-360.
    (No abstract is available for this citation).
  49. added 2019-03-04
    Probabilistic Proofs and Transferability.Kenny Easwaran - 2009 - Philosophia Mathematica 17 (3):341-362.
    In a series of papers, Don Fallis points out that although mathematicians are generally unwilling to accept merely probabilistic proofs, they do accept proofs that are incomplete, long and complicated, or partly carried out by computers. He argues that there are no epistemic grounds on which probabilistic proofs can be rejected while these other proofs are accepted. I defend the practice by presenting a property I call ‘transferability’, which probabilistic proofs lack and acceptable proofs have. I also consider what this (...)
  50. added 2019-03-04
    Marcus Giaquinto. Visual Thinking in Mathematics: An Epistemological Study. [REVIEW]Jeremy Avigad - 2009 - Philosophia Mathematica 17 (1):95-108.
    Published in 1891, Edmund Husserl's first book, Philosophie der Arithmetik, aimed to ‘prepare the scientific foundations for a future construction of that discipline’. His goals should seem reasonable to contemporary philosophers of mathematics: "…through patient investigation of details, to seek foundations, and to test noteworthy theories through painstaking criticism, separating the correct from the erroneous, in order, thus informed, to set in their place new ones which are, if possible, more adequately secured. 1"But the ensuing strategy for grounding mathematical knowledge (...)
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