Friedman, Michael and Rittberg, Colin Jakob (2019) The Material Reasoning of Folding Paper. [Preprint]
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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 paperlike 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 nontextual 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 nonpropositional and nondiagrammatic reasoning practice that adds to our understanding of the multifaceted 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.
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Item Type:  Preprint  

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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://philsciarchive.pitt.edu/id/eprint/15797 
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The Material Reasoning of Folding Paper. (deposited 25 Feb 2019 21:44)
 The Material Reasoning of Folding Paper. (deposited 05 Mar 2019 16:08) [Currently Displayed]
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