ABSTRACT: The Epistemology of Mathematical Necessity

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’. This is a 3-page abstract for the DIAGRAMS2018 conference, summarising prior work in papers such as (“Things Unreasonably Compulsory”, Cognitio 15 (1): 89-112 (2014), and "The Hardness of the Iconic Must", Philosophia Mathematica 20 (1): 1-24 (2012)).