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Philosophical Relevance of Category Theory

In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford, England: Oxford University Press (2008)

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  1. Proof, Explanation, and Justification in Mathematical Practice.Moti Mizrahi - 2020 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 51 (4):551-568.
    In this paper, I propose that applying the methods of data science to “the problem of whether mathematical explanations occur within mathematics itself” (Mancosu 2018) might be a fruitful way to shed new light on the problem. By carefully selecting indicator words for explanation and justification, and then systematically searching for these indicators in databases of scholarly works in mathematics, we can get an idea of how mathematicians use these terms in mathematical practice and with what frequency. The results of (...)
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  • The twofold role of diagrams in Euclid’s plane geometry.Marco Panza - 2012 - Synthese 186 (1):55-102.
    Proposition I.1 is, by far, the most popular example used to justify the thesis that many of Euclid’s geometric arguments are diagram-based. Many scholars have recently articulated this thesis in different ways and argued for it. My purpose is to reformulate it in a quite general way, by describing what I take to be the twofold role that diagrams play in Euclid’s plane geometry (EPG). Euclid’s arguments are object-dependent. They are about geometric objects. Hence, they cannot be diagram-based unless diagrams (...)
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  • Mathematical structuralism today.Julian C. Cole - 2010 - Philosophy Compass 5 (8):689-699.
    Two topics figure prominently in recent discussions of mathematical structuralism: challenges to the purported metaphysical insight provided by sui generis structuralism and the significance of category theory for understanding and articulating mathematical structuralism. This article presents an overview of central themes related to these topics.
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