TY - JOUR

T1 - The material reasoning of folding paper

AU - Friedman, Michael

AU - Rittberg, Colin Jakob

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Diagrammatic reasoning

KW - Material reasoning

KW - Mathematical culture

KW - Mathematical practice

KW - Paper folding

KW - Visual reasoning

UR - http://www.scopus.com/inward/record.url?scp=85065546547&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85065546547&partnerID=8YFLogxK

U2 - 10.1007/s11229-019-02131-x

DO - 10.1007/s11229-019-02131-x

M3 - Article

AN - SCOPUS:85065546547

VL - 198

SP - 6333

EP - 6367

JO - Synthese

JF - Synthese

SN - 0039-7857

ER -