The material reasoning of folding paper

Synthese 198 (S26):6333-6367 (2021)
  Copy   BIBTEX

Abstract

This paper inquires the ways in which paper folding constitutes a mathematical practice and may prompt a mathematical culture. To do this, we first present and investigate the common mathematical activities shared by this culture, i.e. we present mathematical paper folding as a material reasoning practice. We show that the patterns of mathematical activity observed in mathematical paper folding are, at least since the end of the nineteenth century, sufficiently stable to be considered as a practice. Moreover, we will argue that this practice is material. The permitted inferential actions when reasoning by folding are controlled by the physical realities of paper-like material, whilst claims to generality of some reasoning operations are supported by arguments from other mathematical idioms. The controlling structure provided by this material side of the practice is tight enough to allow for non-textual shared standards of argument and wide enough to provide sufficiently many problems for a practice to form. The upshot is that mathematical paper folding is a non-propositional and non-diagrammatic reasoning practice that adds to our understanding of the multi-faceted nature of the epistemic force of mathematical proof. We then draw on what we have learned from our contemplations about paper folding to highlight some lessons about what a study of mathematical cultures entails.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,923

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

The parallel structure of mathematical reasoning.Andrew Aberdein - 2012 - In Alison Pease & Brendan Larvor (eds.), Proceedings of the Symposium on Mathematical Practice and Cognition Ii: A Symposium at the Aisb/Iacap World Congress 2012. Society for the Study of Artificial Intelligence and the Simulation of Behaviour. pp. 7--14.
Mathematical reasoning: induction, deduction and beyond.David Sherry - 2006 - Studies in History and Philosophy of Science Part A 37 (3):489-504.
Towards a theory of mathematical argument.Ian J. Dove - 2009 - Foundations of Science 14 (1-2):136-152.
Mathematical arguments in context.Jean Paul Van Bendegem & Bart Van Kerkhove - 2009 - Foundations of Science 14 (1-2):45-57.
Prolegomena to a cognitive investigation of Euclidean diagrammatic reasoning.Yacin Hamami & John Mumma - 2013 - Journal of Logic, Language and Information 22 (4):421-448.
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.

Analytics

Added to PP
2019-03-05

Downloads
55 (#297,704)

6 months
14 (#200,610)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Citations of this work

Experimenting with Triangles.Valeria Giardino - 2022 - Axiomathes 32 (1):55-77.

Add more citations

References found in this work

The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History.Reviel Netz - 1999 - Cambridge and New York: Cambridge University Press.
The Philosophy of Mathematical Practice.Paolo Mancosu (ed.) - 2008 - Oxford, England: Oxford University Press.
The Euclidean Diagram.Kenneth Manders - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford University Press. pp. 80--133.

View all 19 references / Add more references