Forms and Roles of Diagrams in Knot Theory

Erkenntnis 79 (4):829-842 (2014)
Download Edit this record How to cite View on PhilPapers
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
Keywords
No keywords specified (fix it)
ISBN(s)
PhilPapers/Archive ID
DETFAR
Upload history
Archival date: 2017-08-23
View other versions
Added to PP index
2013-11-02

Total views
519 ( #10,369 of 58,741 )

Recent downloads (6 months)
83 ( #8,219 of 58,741 )

How can I increase my downloads?

Downloads since first upload
This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.