Erkenntnis 79 (4):829-842 (2014)
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Abstract |
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 develop a specific form of enhanced manipulative imagination, in order to draw inferences from knot diagrams by performing epistemic actions. Moreover, it will be argued that knot diagrams not only can promote discovery, but also provide evidence. This case study is an experimentation ground to evaluate the role of space and action in making inferences by reasoning diagrammatically.
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DOI | 10.1007/s10670-013-9568-7 |
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References found in this work BETA
On Distinguishing Epistemic From Pragmatic Action.David Kirsh & Paul Maglio - 1994 - Cognitive Science 18 (4):513-49.
The Philosophy of Mathematical Practice.Paolo Mancosu (ed.) - 2008 - Oxford, England: Oxford University Press.
Visual Thinking in Mathematics: An Epistemological Study.Marcus Giaquinto - 2007 - Oxford, England: Oxford University Press.
Visual Thinking in Mathematics: An Epistemological Study.Marcus Giaquinto - 2007 - Oxford, England: Oxford University Press.
View all 15 references / Add more references
Citations of this work BETA
‘Chasing’ the Diagram—the Use of Visualizations in Algebraic Reasoning.Silvia de Toffoli - 2017 - Review of Symbolic Logic 10 (1):158-186.
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.
View all 20 citations / Add more citations
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