1. Schopenhauer on Diagrammatic Proof
- Author
-
Michael J. Bevan
- Subjects
Philosophy of mathematics ,Diagrammatic reasoning ,Philosophy ,Subject (philosophy) ,Context (language use) ,Proposition ,Mathematical proof ,Set (psychology) ,Legitimacy ,Epistemology - Abstract
The present paper discusses the treatment of diagrammatic proof in Schopenhauer’s philosophy of mathematics. ‘Picture proofs’ have been the subject of some scattered contemporary debate, and my aim here is to see whether Schopenhauer’s treatment might prove fruitful in the context of recent discussion. In particular I argue that Schopenhauer’s remarks on diagrammatic proof, though few and far between, might be able to provide conceptual tools adequate to meet some of the broader challenges facing the legitimacy of such proof. In § 1 the notion of a picture proof is introduced and two general objections to its legitimacy are formulated. In § 2 I set out what I take to be the substance of Schopenhauer’s advocacy of picture proofs and in § 3 I formulate replies to these challenges based on the Schopenhauerian distinction between a proposition’s ground of knowledge (Erkenntnisgrund) and its ground of being (Seynsgrund).
- Published
- 2020
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