Skip to Main content Skip to Navigation
New interface
Journal articles

Forms and Roles of Diagrams in Knot Theory

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.
Document type :
Journal articles
Complete list of metadata
Contributor : Admin UL Connect in order to contact the contributor
Submitted on : Wednesday, September 5, 2018 - 12:17:44 PM
Last modification on : Thursday, March 17, 2022 - 10:08:22 AM



Silvia de Toffoli, Valeria Giardino. Forms and Roles of Diagrams in Knot Theory. Erkenntnis, 2014, 79 (4), pp.829 - 842. ⟨10.1007/s10670-013-9568-7⟩. ⟨hal-01868295⟩



Record views