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Mathematical Cultures: The London Meetings 2012-2014

Springer International Publishing (2016)

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  1. A Fresh Look at Research Strategies in Computational Cognitive Science: The Case of Enculturated Mathematical Problem Solving.Regina E. Fabry & Markus Pantsar - 2019 - Synthese 198 (4):3221-3263.
    Marr’s seminal distinction between computational, algorithmic, and implementational levels of analysis has inspired research in cognitive science for more than 30 years. According to a widely-used paradigm, the modelling of cognitive processes should mainly operate on the computational level and be targeted at the idealised competence, rather than the actual performance of cognisers in a specific domain. In this paper, we explore how this paradigm can be adopted and revised to understand mathematical problem solving. The computational-level approach applies methods from (...)
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  • The Material Reasoning of Folding Paper.Michael Friedman & Colin Jakob Rittberg - 2021 - Synthese 198 (S26):6333-6367.
    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 (...)
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  • Audience Role in Mathematical Proof Development.Zoe Ashton - 2020 - Synthese 198 (Suppl 26):6251-6275.
    The role of audiences in mathematical proof has largely been neglected, in part due to misconceptions like those in Perelman and Olbrechts-Tyteca which bar mathematical proofs from bearing reflections of audience consideration. In this paper, I argue that mathematical proof is typically argumentation and that a mathematician develops a proof with his universal audience in mind. In so doing, he creates a proof which reflects the standards of reasonableness embodied in his universal audience. Given this framework, we can better understand (...)
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  • Philosophy of Mathematical Practice: A Primer for Mathematics Educators.Yacin Hamami & Rebecca Morris - forthcoming - ZDM Mathematics Education.
    In recent years, philosophical work directly concerned with the practice of mathematics has intensified, giving rise to a movement known as the philosophy of mathematical practice . In this paper we offer a survey of this movement aimed at mathematics educators. We first describe the core questions philosophers of mathematical practice investigate as well as the philosophical methods they use to tackle them. We then provide a selective overview of work in the philosophy of mathematical practice covering topics including the (...)
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  • Enabling Mathematical Cultures: Introduction.Benedikt Löwe, Ursula Martin & Alison Pease - 2021 - Synthese 198 (Suppl 26):6225-6231.
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  • Extended Mathematical Cognition: External Representations with Non-Derived Content.Karina Vold & Dirk Schlimm - 2020 - Synthese 197 (9):3757-3777.
    Vehicle externalism maintains that the vehicles of our mental representations can be located outside of the head, that is, they need not be instantiated by neurons located inside the brain of the cogniser. But some disagree, insisting that ‘non-derived’, or ‘original’, content is the mark of the cognitive and that only biologically instantiated representational vehicles can have non-derived content, while the contents of all extra-neural representational vehicles are derived and thus lie outside the scope of the cognitive. In this paper (...)
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