PhilSci Archive

The Material Reasoning of Folding Paper

Friedman, Michael and Rittberg, Colin Jakob (2019) The Material Reasoning of Folding Paper. [Preprint]

This is the latest version of this item.

[img]
Preview
Text
The Material Reasoning of Folding Paper (pre-print).pdf

Download (462kB) | Preview

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 19th 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.


Export/Citation: EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL
Social Networking:
Share |

Item Type: Preprint
Creators:
CreatorsEmailORCID
Friedman, Michael
Rittberg, Colin Jakob0000-0002-9470-6981
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > History
Specific Sciences > Mathematics > Practice
Specific Sciences > Mathematics > Proof
General Issues > Models and Idealization
Depositing User: Dr. Colin Jakob Rittberg
Date Deposited: 05 Mar 2019 16:08
Last Modified: 05 Mar 2019 16:08
Item ID: 15797
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > History
Specific Sciences > Mathematics > Practice
Specific Sciences > Mathematics > Proof
General Issues > Models and Idealization
Date: 2019
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/15797

Available Versions of this Item

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Actions (login required)

View Item View Item