28 found
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  1. 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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  2. An Inquiry into the Practice of Proving in Low-Dimensional Topology.Silvia De Toffoli & Valeria Giardino - 2014 - In Giorgio Venturi, Marco Panza & Gabriele Lolli (eds.), From Logic to Practice: Italian Studies in the Philosophy of Mathematics. Cham: 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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  3. Envisioning Transformations – The Practice of Topology.Silvia De Toffoli & Valeria Giardino - 2016 - In Brendan Larvor (ed.), Mathematical Cultures: The London Meetings 2012-2014. Springer International Publishing. 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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  4.  75
    Introduction: Varieties of Iconicity.Valeria Giardino & Gabriel Greenberg - 2015 - Review of Philosophy and Psychology 6 (1):1-25.
    This introduction aims to familiarize readers with basic dimensions of variation among pictorial and diagrammatic representations, as we understand them, in order to serve as a backdrop to the articles in this volume. Instead of trying to canvas the vast range of representational kinds, we focus on a few important axes of difference, and a small handful of illustrative examples. We begin in Section 1 with background: the distinction between pictures and diagrams, the concept of systems of representation, and that (...)
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  5. 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.
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  6.  59
    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 (...)
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  7. Intuition and visualization in mathematical problem solving.Valeria Giardino - 2010 - Topoi 29 (1):29-39.
    In this article, I will discuss the relationship between mathematical intuition and mathematical visualization. I will argue that in order to investigate this relationship, it is necessary to consider mathematical activity as a complex phenomenon, which involves many different cognitive resources. I will focus on two kinds of danger in recurring to visualization and I will show that they are not a good reason to conclude that visualization is not reliable, if we consider its use in mathematical practice. Then, I (...)
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  8.  42
    The Practice of Mathematics: Cognitive Resources and Conceptual Content.Valeria Giardino - 2023 - Topoi 42 (1):259-270.
    In the past 10 years, contemporary philosophy of mathematics has seen the development of a trend that conceives mathematics as first and foremost a human activity and in particular as a kind of practice. However, only recently the need for a general framework to account for the target of the so-called philosophy of mathematical practice has emerged. The purpose of the present article is to make progress towards the definition of a more precise general framework for the philosophy of mathematical (...)
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  9.  6
    Diagrammatic Proofs in Mathematics: (Almost) 20 Years of Research.Valeria Giardino - 2024 - In Bharath Sriraman (ed.), Handbook of the History and Philosophy of Mathematical Practice. Cham: Springer. pp. 2045-2067.
    The objective of this chapter is to introduce some of the views that have been put forward in almost 20 years of research on diagrammatic proofs in the philosophy of mathematical practice. In Sect. 1, some contextual elements will be presented on the reasons why diagrammatic proofs have attracted so much philosophical attention in the past years. In Sect. 2, the “first wave” in the research on diagrammatic proofs based on the analysis of case studies will be described: this is (...)
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  10. Mettere a Fuoco Il Mondo. Conversazioni sulla Filosofia di Achille Varzi (Special Issue of Isonomia – Epistemologica).Elena Casetta, Valeria Giardino, Andrea Borghini, Patrizia Pedrini, Francesco Calemi, Daniele Santoro, Giuliano Torrengo, Claudio Calosi, Pierluigi Graziani & Achille C. Varzi (eds.) - 2014 - ISONOMIA – Epistemologica. University of Urbino.
    Achille Varzi è uno dei maggiori metafisici viventi. Nel corso degli anni ha scritto testi fondamentali di logica, metafisica, mereologia, filosofia del linguaggio. Ha sconfinato nella topologia, nella geografia, nella matematica, ha ragionato di mostri e confini, percezione e buchi, viaggi nel tempo, nicchie, eventi e ciambelle; e non ha disdegnato di dialogare con gli abitanti di Flatlandia, con Neo e con Terminator. Tra le sue opere principali: Holes and Other Superficialities e Parts and Places. The Structures of Spatial Representation, (...)
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  11. Geometria, ragionamento e scommesse.Valeria Giardino - 2014 - In University of Urbino © Isonomia – Epistemologica (ed.), Mettere a fuoco il mondo. pp. 36-46.
    Poiché i miei interessi di ricerca si concentrano sul rapporto tra spazio e rappresentazione, nel presente articolo commenterò un lavoro di Achille C. Varzi pubblicato nel 2008 e intitolato, nella sua versione italiana, «Configurazioni, regole e inferenze». Accennerò anche a un secondo articolo scritto da Varzi e Massimo Warglien e pubblicato nel 2003, intitolato «The Geometry of Negation». Mi rivolgerò poi alla psicologia sperimentale, collegando alcuni aspetti delle osservazioni di Varzi a un articolo di Johnson- Laird del 2005 intitolato «The (...)
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  12.  33
    Experimenting with Triangles.Valeria Giardino - 2022 - Axiomathes 32 (1):55-77.
    Is there anything like an experiment in mathematics? And if this is the case, what would distinguish a mathematical experiment from a mathematical thought experiment? In the present paper, a framework for the practice of mathematics will be put forward, which will consider mathematics as an experimenting activity and as a proving activity. The relationship between these two activities will be explored and more importantly a distinction between thought-experiments, real experiments, quasi experiments and proofs in pure mathematics will be provided. (...)
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  13.  12
    Introduction: From Practice to Results in Mathematics and Logic.Valeria Giardino, Amirouche Moktefi, Sandra Mois & Jean Van Bendegem - 2012 - Philosophia Scientiae 16 (1):5-11.
    1 Mathematical practice: a short overview This volume is a collection of essays that discuss the relationships between the practices deployed by logicians and mathematicians, either as individuals or as members of research communities, and the results from their research. We are interested in exploring the concept of 'practices' in the formal sciences. Though common in the history, philosophy and sociology of science, this concept has surprisingly thus far been little reflected upon in logic...
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  14.  12
    Introduction: From Practice to Results in Mathematics and Logic.Valeria Giardino, Amirouche Moktefi, Sandra Mois & Jean Paul Van Bendegem - 2012 - Philosophia Scientiae 16:5-11.
    1 Mathematical practice: a short overview This volume is a collection of essays that discuss the relationships between the practices deployed by logicians and mathematicians, either as individuals or as members of research communities, and the results from their research. We are interested in exploring the concept of 'practices' in the formal sciences. Though common in the history, philosophy and sociology of science, this concept has surprisingly thus far been little reflected upon in logic...
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  15.  40
    Introduction: From Practice to Results in Mathematics and Logic.Valeria Giardino, Amirouche Moktefi, Sandra Mois & Jean Paul Van Bendegem - 2012 - Philosophia Scientiae 16:5-11.
    1 Mathematical practice: a short overview This volume is a collection of essays that discuss the relationships between the practices deployed by logicians and mathematicians, either as individuals or as members of research communities, and the results from their research. We are interested in exploring the concept of 'practices' in the formal sciences. Though common in the history, philosophy and sociology of science, this concept has surprisingly thus far been little reflected upon in logic...
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  16. An Inquiry into the Practice of Proving in Low-Dimensional Topology.Valeria Giardino & Silvia Toffoli - 2014 - In Giorgio Venturi, Marco Panza & Gabriele Lolli (eds.), From Logic to Practice: Italian Studies in the Philosophy of Mathematics. Cham: Springer International Publishing.
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  17.  5
    Diagrammatic Representation and Inference. 13th International Conference, Diagrams 2022, Rome, Italy, September 14–16, 2022, Proceedings.Valeria Giardino, Sven Linker, Tony Burns, Francesco Bellucci, J. M. Boucheix & Diego Viana (eds.) - 2022 - Springer.
    8 chapters are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
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  18.  32
    Giaquinto, Marcus. Visual Thinking in Mathematics: An Epistemological Study.Valeria Giardino - 2012 - Review of Metaphysics 66 (1):148-150.
  19.  16
    Introduction: From Practice to Results in Mathematics and Logic.Valeria Giardino, Amirouche Moktefi, Sandra Mols & Jean Paul Van Bendegem - 2012 - Philosophia Scientiae 16:5-11.
    1 Mathematical practice: a short overview This volume is a collection of essays that discuss the relationships between the practices deployed by logicians and mathematicians, either as individuals or as members of research communities, and the results from their research. We are interested in exploring the concept of 'practices' in the formal sciences. Though common in the history, philosophy and sociology of science, this concept has surprisingly thus far been little reflected upon in logic...
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  20.  1
    New Perspectives: An Introduction.Valeria Giardino - 2024 - In Bharath Sriraman (ed.), Handbook of the History and Philosophy of Mathematical Practice. Cham: Springer. pp. 2785-2792.
    In this short Introduction to the present section, I will first briefly point out the reasons why the chapters collected here present original research in the context of the philosophy of the practice of mathematics, and open even newer perspectives. It is important to note that one crucial issue for future research will be to explore the connections within these chapters and with other chapters included in other sections – in particular, but not exclusively, the sections on Proof, on “Experimental” (...)
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  21.  11
    Sperimentare con i triangoli.Valeria Giardino - 2009 - Rivista di Estetica 42:39-54.
    It is possible to argue that the only ‘genuine’ experiments in mathematics are in fact thought experiments. Nevertheless, one preliminary question is to ask what genuine mathematica experiments are, and whether the activity of experimentation is a proper mathematical activity. In this article, I will consider which kind of conception of mathematics allows for the existence of experiments in mathematics and I will present the constraints these experiments are subject to. Then, I will discuss three examples to arrive at a (...)
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  22. Diagrammatic Representation and Inference. Diagrams 2020. Lecture Notes in Computer Science, vol 12169.Ahti Veikko Pietarinen, P. Chapman, Leonie Bosveld-de Smet, Valeria Giardino, James Corter & Sven Linker (eds.) - 2020
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  23. Diagrammatic Representation and Inference. Diagrams 2020. Lecture Notes in Computer Science, vol 12169. 2020.Ahti Veikko Pietarinen, Peter Chapman, Leonie Bosveld-de Smet, Valeria Giardino, James Corter & Sven Linker (eds.) - 2020
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  24. On the completeness of spider diagrams augmented with constands / Gem Stapleton...[et al.]. A practice-based approach to diagrams. [REVIEW]Valeria Giardino - 2013 - In Sun-Joo Shin & Amirouche Moktefi (eds.), Visual Reasoning with Diagrams. Basel: Birkhaüser.
     
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  25.  52
    Arturo Carsetti • seeing, thinking and knowing: Meaning and self-organisation in visual cognition and thought • dordrecht, the netherlands: Kluwer academic publishers, • 2004 • hardback £97.00 • isbn: 1402020805. [REVIEW]Valeria Giardino - 2006 - British Journal for the Philosophy of Science 57 (3):623-625.
  26.  28
    Review of M. Giaquinto, Visual Thinking in Mathematics: An Epistemological Study[REVIEW]Valeria Giardino - 2012 - Review of Metaphysics 66 (1):148-150.
  27.  56
    Mohan Matthen seeing, doing and knowing: A philosophical theory of sense perception oxford: Oxford university press, 2005 hardback £40.00 ISBN: 0199268509. [REVIEW]Valeria Giardino - 2006 - British Journal for the Philosophy of Science 57 (4):781-783.
  28.  29
    Review of Frederik Stjernfelt, Diagrammatology: An Investigation on the Borderlines of Phenomenology, Ontology and Semiotics[REVIEW]Valeria Giardino - 2008 - Notre Dame Philosophical Reviews 2008 (7).
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