Show simple item record

Files in this item


Item metadata

dc.contributor.advisorCotnoir, A. J.
dc.contributor.advisorGreenough, Patrick
dc.contributor.authorTanswell, Fenner Stanley
dc.coverage.spatial212 p.en_US
dc.description.abstractThis thesis is about the nature of proofs in mathematics as it is practiced, contrasting the informal proofs found in practice with formal proofs in formal systems. In the first chapter I present a new argument against the Formalist-Reductionist view that informal proofs are justified as rigorous and correct by corresponding to formal counterparts. The second chapter builds on this to reject arguments from Gödel's paradox and incompleteness theorems to the claim that mathematics is inherently inconsistent, basing my objections on the complexities of the process of formalisation. Chapter 3 looks into the relationship between proofs and the development of the mathematical concepts that feature in them. I deploy Waismann's notion of open texture in the case of mathematical concepts, and discuss both Lakatos and Kneebone's dialectical philosophies of mathematics. I then argue that we can apply work from conceptual engineering to the relationship between formal and informal mathematics. The fourth chapter argues for the importance of mathematical knowledge-how and emphasises the primary role of the activity of proving in securing mathematical knowledge. In the final chapter I develop an account of mathematical knowledge based on virtue epistemology, which I argue provides a better view of proofs and mathematical rigour.en_US
dc.description.sponsorshipFunded by the Caroline Elder PG Scholarship and a SASP scholarship, and with travel funded by the Indo-European Research Training Network in Logic and the Arché Travel Fund.en
dc.publisherUniversity of St Andrews
dc.subjectVirtue epistemologyen_US
dc.subjectOpen textureen_US
dc.subjectMathematical practiceen_US
dc.subjectGödel's theoremsen_US
dc.subjectConceptual engineeringen_US
dc.subjectPhilosophy of mathematicsen_US
dc.subject.lcshVirtue epistemologyen
dc.subject.lcshProof theoryen
dc.titleProof, rigour and informality : a virtue account of mathematical knowledgeen_US
dc.contributor.sponsorCaroline Elder Scholarshipen_US
dc.contributor.sponsorSt Andrews and Stirling Graduate Programme in Philosophy (SASP)en_US
dc.contributor.sponsorIndo-European Research and Training Network in Logic (IERTNiL)en_US
dc.contributor.sponsorArché Travel Funden_US
dc.type.qualificationnamePhD Doctor of Philosophyen_US
dc.publisher.institutionThe University of St Andrewsen_US
dc.publisher.departmentUniversity of Stirlingen_US

This item appears in the following Collection(s)

Show simple item record