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From Euclidean Geometry to Knots and Nets

Larvor, Brendan (2017) From Euclidean Geometry to Knots and Nets. [Preprint]

Manders a model for modern maths--final submission.pdf

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this paper assumes the success of arguments against the view that informal mathematical proofs secure rational conviction in virtue of their relations with corresponding formal derivations. This assumption entails a need for an alternative account of the logic of informal mathematical proofs. Following examination of case studies by Manders, De Toffoli & Giardino, Leitgeb, Feferman and others, this paper proposes a framework for analysing those informal proofs that appeal to the perception or modification of diagrams or to the inspection or imaginative manipulation of mental models of mathematical phenomena. Proofs relying on diagrams can be rigorous if a) it is easy to draw a diagram that shares or otherwise indicates the structure of the mathematical object b) the information thus displayed is not metrical and c) it is possible to put the inferences into systematic mathematical relation with other mathematical inferential practices. Proofs that appeal to mental models can be rigorous if the mental models can be externalised as diagrammatic practice that satisfies these three conditions.

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Item Type: Preprint
Keywords: Proof; derivation; geometry; diagram
Subjects: Specific Sciences > Mathematics > Practice
Depositing User: Dr Brendan Larvor
Date Deposited: 08 Sep 2017 22:25
Last Modified: 08 Sep 2017 22:25
Item ID: 13403
Subjects: Specific Sciences > Mathematics > Practice
Date: September 2017

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