# The Epistemology of Mathematical Necessity

In Peter Chapman, Gem Stapleton, Amirouche Moktefi, Sarah Perez-Kriz & Francesco Bellucci (eds.),

*Diagrammatic Representation and Inference10th International Conference, Diagrams 2018, Edinburgh, UK, June 18-22, 2018, Proceedings*. Berlin: Springer-Verlag. pp. 810-813 (2018)**Abstract**

It seems possible to know that a mathematical claim is necessarily true by inspecting a diagrammatic proof. Yet how does this work, given that human perception seems to just
(as Hume assumed) ‘show us particular objects in front of us’? I draw on Peirce’s account of perception to answer this question. Peirce considered mathematics as experimental a science as physics. Drawing on an example, I highlight the existence of a primitive constraint or blocking function in our thinking which we might call ‘the hardness of the mathematical must’.

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References found in this work BETA

The Hardness of the Iconic Must: Can Peirce’s Existential Graphs Assist Modal Epistemology.C. Legg - 2012 -

*Philosophia Mathematica*20 (1):1-24.Perceiving Necessity.Catherine Legg & James Franklin - 2017 -

*Pacific Philosophical Quarterly*98 (3).What is a Logical Diagram?Catherine Legg - 2013 - In Sun-Joo Shin & Amirouche Moktefi (eds.),

*Visual Reasoning with Diagrams*. Springer. pp. 1-18.
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