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1 — 50 / 65
  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 (...)
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  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 (...)
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  3. added 2020-02-11
    The Iconic Logic of Peirce's Graphs.Jesse Norman - 2004 - Mind 113 (452):783-787.
  4. added 2020-01-18
    Self-Graphing Equations.Samuel Alexander - manuscript
    Can you find an xy-equation that, when graphed, writes itself on the plane? This idea became internet-famous when a Wikipedia article on Tupper’s self-referential formula went viral in 2012. Under scrutiny, the question has two flaws: it is meaningless (it depends on fonts) and it is trivial. We fix these flaws by formalizing the problem.
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  5. 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.
  6. 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 (...)
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  7. 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. (...)
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  8. added 2019-04-30
    What is a Logical Diagram?Catherine Legg - 2013 - In Sun-Joo Shin & Amirouche Moktefi (eds.), Visual Reasoning with Diagrams. Springer. pp. 1-18.
    Robert Brandom’s expressivism argues that not all semantic content may be made fully explicit. This view connects in interesting ways with recent movements in philosophy of mathematics and logic (e.g. Brown, Shin, Giaquinto) to take diagrams seriously - as more than a mere “heuristic aid” to proof, but either proofs themselves, or irreducible components of such. However what exactly is a diagram in logic? Does this constitute a semiotic natural kind? The paper will argue that such a natural kind does (...)
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  9. added 2019-04-30
    The Hardness of the Iconic Must: Can Peirce’s Existential Graphs Assist Modal Epistemology.C. Legg - 2012 - Philosophia Mathematica 20 (1):1-24.
    Charles Peirce's diagrammatic logic — the Existential Graphs — is presented as a tool for illuminating how we know necessity, in answer to Benacerraf's famous challenge that most ‘semantics for mathematics’ do not ‘fit an acceptable epistemology’. It is suggested that necessary reasoning is in essence a recognition that a certain structure has the particular structure that it has. This means that, contra Hume and his contemporary heirs, necessity is observable. One just needs to pay attention, not merely to individual (...)
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  10. added 2019-04-26
    Visual Thinking in Mathematics: An Epistemological Study.Marcus Giaquinto - 2007 - Oxford University Press.
    Visual thinking -- visual imagination or perception of diagrams and symbol arrays, and mental operations on them -- is omnipresent in mathematics. Is this visual thinking merely a psychological aid, facilitating grasp of what is gathered by other means? Or does it also have epistemological functions, as a means of discovery, understanding, and even proof? By examining the many kinds of visual representation in mathematics and the diverse ways in which they are used, Marcus Giaquinto argues that visual thinking in (...)
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  11. added 2019-03-28
    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*, (...)
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  12. added 2019-03-28
    The Twofold Role of Diagrams in Euclid’s 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 (...)
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  13. added 2019-03-28
    Pictures and Pedagogy: The Role of Diagrams in Feynman's Early Lectures.Ari Gross - 2012 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 43 (3):184-194.
    This paper aims to give a substantive account of how Feynman used diagrams in the first lectures in which he explained his new approach to quantum electrodynamics. By critically examining unpublished lecture notes, Feynman’s use and interpretation of both "Feynman diagrams" and other visual representations will be illuminated. This paper discusses how the morphology of Feynman’s early diagrams were determined by both highly contextual issues, which molded his images to local needs and particular physical characterizations, and an overarching common diagrammatic (...)
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  14. added 2019-03-28
    And so On...: Reasoning with Infinite Diagrams.Solomon Feferman - 2012 - Synthese 186 (1):371 - 386.
    This paper presents examples of infinite diagrams (as well as infinite limits of finite diagrams) whose use is more or less essential for understanding and accepting various proofs in higher mathematics. The significance of these is discussed with respect to the thesis that every proof can be formalized, and a "pre" form of this thesis that every proof can be presented in everyday statements-only form.
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  15. 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.
  16. added 2019-03-28
    Words, Proofs and Diagrams.David Barker-Plummer, David I. Beaver, Johan van Benthem & Patrick Scotto di Luzio (eds.) - 2002 - Center for the Study of Language and Inf.
    The past twenty years have witnessed extensive collaborative research between computer scientists, logicians, linguists, philosophers, and psychologists. These interdisciplinary studies stem from the realization that researchers drawn from all fields are studying the same problem. Specifically, a common concern amongst researchers today is how logic sheds light on the nature of information. Ancient questions concerning how humans communicate, reason and decide, and modern questions about how computers should communicate, reason and decide are of prime interest to researchers in various disciplines. (...)
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  17. added 2019-03-18
    Prolegomena to a Cognitive Investigation of Euclidean Diagrammatic Reasoning.Yacin Hamami & John Mumma - 2013 - Journal of Logic, Language and Information 22 (4):421-448.
    Euclidean diagrammatic reasoning refers to the diagrammatic inferential practice that originated in the geometrical proofs of Euclid’s Elements. A seminal philosophical analysis of this practice by Manders (‘The Euclidean diagram’, 2008) has revealed that a systematic method of reasoning underlies the use of diagrams in Euclid’s proofs, leading in turn to a logical analysis aiming to capture this method formally via proof systems. The central premise of this paper is that our understanding of Euclidean diagrammatic reasoning can be fruitfully advanced (...)
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  18. added 2019-03-07
    Seeing is Reasoning.Kathryn Mann & James Robert Brown - 2007 - Metascience 16 (1):131-135.
  19. 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 (...)
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  20. added 2019-02-27
    The Epistemology of Mathematical Necessity.Cathy Legg - 2018 - In Peter Chapman, Gem Stapleton, Amirouche Moktefi, Sarah Perez-Kriz & Francesco Bellucci (eds.), Diagrammatic Representation and Inference10th International Conference, Diagrams 2018, Edinburgh, UK, June 18-22, 2018, Proceedings. Berlin: Springer-Verlag. pp. 810-813.
    It seems possible to know that a mathematical claim is necessarily true by inspecting a diagrammatic proof. Yet how does this work, given that human perception seems to just (as Hume assumed) ‘show us particular objects in front of us’? I draw on Peirce’s account of perception to answer this question. Peirce considered mathematics as experimental a science as physics. Drawing on an example, I highlight the existence of a primitive constraint or blocking function in our thinking which we might (...)
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  21. added 2018-11-08
    A Priori Concepts in Euclidean Proof.Peter Fisher Epstein - 2018 - Proceedings of the Aristotelian Society 118 (3):407-417.
    With the discovery of consistent non-Euclidean geometries, the a priori status of Euclidean proof was radically undermined. In response, philosophers proposed two revisionary interpretations of the practice: some argued that Euclidean proof is a purely formal system of deductive logic; others suggested that Euclidean reasoning is empirical, employing concepts derived from experience. I argue that both interpretations fail to capture the true nature of our geometrical thought. Euclidean proof is not a system of pure logic, but one in which our (...)
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  22. added 2018-01-18
    A Perceptual Account of Symbolic Reasoning.David Landy, Colin Allen & Carlos Zednik - 2014 - Frontiers in Psychology 5.
    People can be taught to manipulate symbols according to formal mathematical and logical rules. Cognitive scientists have traditionally viewed this capacity—the capacity for symbolic reasoning—as grounded in the ability to internally represent numbers, logical relationships, and mathematical rules in an abstract, amodal fashion. We present an alternative view, portraying symbolic reasoning as a special kind of embodied reasoning in which arithmetic and logical formulae, externally represented as notations, serve as targets for powerful perceptual and sensorimotor systems. Although symbolic reasoning often (...)
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  23. added 2017-12-14
    Forms and Roles of Diagrams in Knot Theory.Silvia De Toffoli & Valeria Giardino - 2014 - Erkenntnis 79 (4):829-842.
    The aim of this article is to explain why knot diagrams are an effective notation in topology. Their cognitive features and epistemic roles will be assessed. First, it will be argued that different interpretations of a figure give rise to different diagrams and as a consequence various levels of representation for knots will be identified. Second, it will be shown that knot diagrams are dynamic by pointing at the moves which are commonly applied to them. For this reason, experts must (...)
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  24. added 2017-10-30
    A Diagrammatic Representation for Entities and Mereotopological Relations in Ontologies.José M. Parente de Oliveira & Barry Smith - 2017 - In CEUR, vol. 1908.
    In the graphical representation of ontologies, it is customary to use graph theory as the representational background. We claim here that the standard graph-based approach has a number of limitations. We focus here on a problem in the graph-based representation of ontologies in complex domains such as biomedical, engineering and manufacturing: lack of mereotopological representation. Based on such limitation, we proposed a diagrammatic way to represent an entity’s structure and various forms of mereotopological relationships between the entities.
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  25. added 2017-08-23
    ‘Chasing’ the Diagram—the Use of Visualizations in Algebraic Reasoning.Silvia de Toffoli - 2017 - Review of Symbolic Logic 10 (1):158-186.
    The aim of this article is to investigate the roles of commutative diagrams (CDs) in a specific mathematical domain, and to unveil the reasons underlying their effectiveness as a mathematical notation; this will be done through a case study. It will be shown that CDs do not depict spatial relations, but represent mathematical structures. CDs will be interpreted as a hybrid notation that goes beyond the traditional bipartition of mathematical representations into diagrammatic and linguistic. It will be argued that one (...)
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  26. added 2017-08-23
    Envisioning Transformations – The Practice of Topology.Silvia De Toffoli & Valeria Giardino - 2016 - In Brendan Larvor (ed.), Mathematical Cultures: The London Meetings 2012--2014. Zurich, Switzerland: Birkhäuser. pp. 25-50.
    The objective of this article is twofold. First, a methodological issue is addressed. It is pointed out that even if philosophers of mathematics have been recently more and more concerned with the practice of mathematics, there is still a need for a sharp definition of what the targets of a philosophy of mathematical practice should be. Three possible objects of inquiry are put forward: (1) the collective dimension of the practice of mathematics; (2) the cognitives capacities requested to the practitioners; (...)
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  27. added 2017-08-23
    An Inquiry Into the Practice of Proving in Low-Dimensional Topology.Silvia De Toffoli & Valeria Giardino - 2015 - In Gabriele Lolli, Giorgio Venturi & Marco Panza (eds.), From Logic to Practice. Zurich, Switzerland: Springer International Publishing. pp. 315-336.
    The aim of this article is to investigate specific aspects connected with visualization in the practice of a mathematical subfield: low-dimensional topology. Through a case study, it will be established that visualization can play an epistemic role. The background assumption is that the consideration of the actual practice of mathematics is relevant to address epistemological issues. It will be shown that in low-dimensional topology, justifications can be based on sequences of pictures. Three theses will be defended. First, the representations used (...)
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  28. added 2017-07-21
    The Advantages of Bringing Infinity to a Finite Place: Penrose Diagrams as Objects of Intuition.Aaron Sidney Wright - 2014 - Historical Studies in the Natural Sciences 44 (2):99-139.
  29. added 2017-03-25
    The Psychology and Philosophy of Natural Numbers.Oliver R. Marshall - 2017 - Philosophia Mathematica (1):nkx002.
    ABSTRACT I argue against both neuropsychological and cognitive accounts of our grasp of numbers. I show that despite the points of divergence between these two accounts, they face analogous problems. Both presuppose too much about what they purport to explain to be informative, and also characterize our grasp of numbers in a way that is absurd in the light of what we already know from the point of view of mathematical practice. Then I offer a positive methodological proposal about the (...)
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  30. added 2017-02-17
    Visual Reasoning with Diagrams.Sun-Joo Shin & Amirouche Moktefi (eds.) - 2013 - Basel: Birkhaüser.
  31. added 2017-02-13
    Exploiting the Potential of Diagrams in Guiding Hardware Reasoning.Kathryn Fisler - 1996 - In Gerard Allwein & Jon Barwise (eds.), Logical Reasoning with Diagrams. Oxford University Press. pp. 225--256.
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  32. added 2017-02-10
    Mathematical Diagrams in Practice: An Evolutionary Account.Iulian D. Toader - 2002 - Logique Et Analyse 179:341-355.
  33. added 2017-01-26
    Toward the Rigorous Use of Diagrams in Reasoning About Hardware.Steven D. Johnson, Jon Barwise & Gerard Allwein - 1996 - In Gerard Allwein & Jon Barwise (eds.), Logical Reasoning with Diagrams. Oxford University Press.
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  34. added 2017-01-20
    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 (...)
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  35. added 2016-12-08
    On the Norms of Visual Argument: A Case for Normative Non-Revisionism.David Godden - 2017 - Argumentation 31 (2):395-431.
    Visual arguments can seem to require unique, autonomous evaluative norms, since their content seems irreducible to, and incommensurable with, that of verbal arguments. Yet, assertions of the ineffability of the visual, or of visual-verbal incommensurability, seem to preclude counting putatively irreducible visual content as functioning argumentatively. By distinguishing two notions of content, informational and argumentative, I contend that arguments differing in informational content can have equivalent argumentative content, allowing the same argumentative norms to be rightly applied in their evaluation.
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  36. added 2016-12-05
    Perceiving Necessity.Catherine Legg & James Franklin - 2017 - Pacific Philosophical Quarterly 98 (3).
    In many diagrams one seems to perceive necessity – one sees not only that something is so, but that it must be so. That conflicts with a certain empiricism largely taken for granted in contemporary philosophy, which believes perception is not capable of such feats. The reason for this belief is often thought well-summarized in Hume's maxim: ‘there are no necessary connections between distinct existences’. It is also thought that even if there were such necessities, perception is too passive or (...)
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  37. added 2016-06-03
    Diagrams of the Past: How Timelines Can Aid the Growth of Historical Knowledge.Marc Champagne - 2016 - Cognitive Semiotics 9 (1):11-44.
    Historians occasionally use timelines, but many seem to regard such signs merely as ways of visually summarizing results that are presumably better expressed in prose. Challenging this language-centered view, I suggest that timelines might assist the generation of novel historical insights. To show this, I begin by looking at studies confirming the cognitive benefits of diagrams like timelines. I then try to survey the remarkable diversity of timelines by analyzing actual examples. Finally, having conveyed this (mostly untapped) potential, I argue (...)
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  38. added 2015-06-14
    Proof: Its Nature and Significance.Michael Detlefsen - 2008 - In Bonnie Gold & Roger A. Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy. Mathematical Association of America. pp. 1.
    I focus on three preoccupations of recent writings on proof. -/- I. The role and possible effects of empirical reasoning in mathematics. Do recent developments (specifically, the computer-assisted proof of the 4CT) point to something essentially new as regards the need for and/or effects of using broadly empirical and inductive reasoning in mathematics? In particular, should we see such things as the computer-assisted proof of the 4CT as pointing to the existence of mathematical truths of which we cannot have a (...)
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  39. added 2014-10-08
    The Euclidean Diagram.Kenneth Manders - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford University Press. pp. 80--133.
    This chapter gives a detailed study of diagram-based reasoning in Euclidean plane geometry (Books I, III), as well as an exploration how to characterise a geometric practice. First, an account is given of diagram attribution: basic geometrical claims are classified as exact (equalities, proportionalities) or co-exact (containments, contiguities); exact claims may only be inferred from prior entries in the demonstration text, but co-exact claims may be asserted based on what is seen in the diagram. Diagram control by constructions is necessary (...)
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  40. added 2014-06-09
    Mind and Sign: Method and the Interpretation of Mathematics in Descartes's Early Work.Amy M. Schmitter - 2000 - Canadian Journal of Philosophy 30 (3):371-411.
    Method may be second only to substance-dualism as the best-known among Descartes's enthusiasms. But knowing that Descartes wants to promote good method is one thing; knowing what exactly he wants to promote is another. Two views seem fairly widespread. The first rests on the claim that Descartes endorses a purely procedural picture of reason, so that right reasoning is a matter of proprieties of operation, rather than respect for its objects. On this view, a method for regulating our reason would (...)
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  41. added 2014-05-30
    “Things Unreasonably Compulsory”: A Peircean Challenge to a Humean Theory of Perception, Particularly With Respect to Perceiving Necessary Truths.Catherine Legg - 2014 - Cognitio 15 (1):89-112.
    Much mainstream analytic epistemology is built around a sceptical treatment of modality which descends from Hume. The roots of this scepticism are argued to lie in Hume’s (nominalist) theory of perception, which is excavated, studied and compared with the very different (realist) theory of perception developed by Peirce. It is argued that Peirce’s theory not only enables a considerably more nuanced and effective epistemology, it also (unlike Hume’s theory) does justice to what happens when we appreciate a proof in mathematics.
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  42. added 2014-04-02
    Review of M. Giaquinto, Visual Thinking in Mathematics: An Epistemological Study[REVIEW]Valeria Giardino - 2012 - Review of Metaphysics 66 (1):148-150.
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  43. added 2014-04-02
    Basic Moral Decisions and Alternative Concepts of Rationality.John C. Harsanyi - 1983 - Social Theory and Practice 9 (2/3):231-244.
  44. added 2014-03-20
    Perceiving the Infinite and the Infinitesimal World: Unveiling and Optical Diagrams in Mathematics. [REVIEW]Lorenzo Magnani & Riccardo Dossena - 2005 - Foundations of Science 10 (1):7-23.
    Many important concepts of the calculus are difficult to grasp, and they may appear epistemologically unjustified. For example, how does a real function appear in “small” neighborhoods of its points? How does it appear at infinity? Diagrams allow us to overcome the difficulty in constructing representations of mathematical critical situations and objects. For example, they actually reveal the behavior of a real function not “close to” a point (as in the standard limit theory) but “in” the point. We are interested (...)
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  45. added 2014-03-14
    Thought Experiments in Science, Philosophy, and Mathematics.James Robert Brown - 2007 - Croatian Journal of Philosophy 7 (1):3-27.
    Most disciplines make use of thought experiments, but physics and philosophy lead the pack with heavy dependence upon them. Often this is for conceptual clarification, but occasionally they provide real theoretical advances. In spite of their importance, however, thought experiments have received rather little attention as a topic in their own right until recently. The situation has improved in the past few years, but a mere generation ago the entire published literature on thought experiments could have been mastered in a (...)
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  46. added 2014-03-10
    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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  47. added 2014-03-10
    The Role of Diagrams in Mathematical Arguments.David Sherry - 2008 - Foundations of Science 14 (1-2):59-74.
    Recent accounts of the role of diagrams in mathematical reasoning take a Platonic line, according to which the proof depends on the similarity between the perceived shape of the diagram and the shape of the abstract object. This approach is unable to explain proofs which share the same diagram in spite of drawing conclusions about different figures. Saccheri’s use of the bi-rectangular isosceles quadrilateral in Euclides Vindicatus provides three such proofs. By forsaking abstract objects it is possible to give a (...)
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  48. added 2014-03-09
    Review of P. Mancosu, K. F. Jørgensen, and S. A. Pedersen (Eds.), Visualization, Explanation and Reasoning Styles in Mathematics[REVIEW]Jean Paul Van Bendegem - 2006 - Philosophia Mathematica 14 (3):378-391.
    What is philosophy of mathematics and what is it about? The most popular answer, I suppose, to this question would be that philosophers should provide a justification for our presently most cherished mathematical theories and for the most important tool to develop such theories, namely logico-mathematical proof. In fact, it does cover a large part of the activity of philosophers that think about mathematics. Discussions about the merits and faults of classical logic versus one or other ‘deviant’ logics as the (...)
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  49. added 2014-01-10
    Visual Reasoning in Euclid's Geometry: An Epistemology of Diagrams.Alexander Jesse Norman - unknown
    Philosophy of Mathematics, Epistemology & Methodology.
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  50. added 2014-01-09
    Review of J. Norman, After Euclid: Visual Reasoning and the Epistemology of Diagrams[REVIEW]F. Janet - 2007 - Philosophia Mathematica 15 (1):116-121.
    This monograph treats the important topic of the epistemology of diagrams in Euclidean geometry. Norman argues that diagrams play a genuine justificatory role in traditional Euclidean arguments, and he aims to account for these roles from a modified Kantian perspective. Norman considers himself a semi-Kantian in the following broad sense: he believes that Kant was right that ostensive constructions are necessary in order to follow traditional Euclidean proofs, but he wants to avoid appealing to Kantian a priori intuition as the (...)
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