Use this URL to cite or link to this record in EThOS:  http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.703474 
Title:  Proof, rigour and informality : a virtue account of mathematical knowledge  
Author:  Tanswell, Fenner Stanley 
ISNI:
0000 0004 6061 8697


Awarding Body:  University of St Andrews  
Current Institution:  University of St Andrews  
Date of Award:  2017  
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Abstract:  
This 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 FormalistReductionist 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 knowledgehow 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.


Supervisor:  Cotnoir, A. J. ; Greenough, Patrick  Sponsor:  Caroline Elder Scholarship ; St Andrews and Stirling Graduate Programme in Philosophy (SASP) ; IndoEuropean Research and Training Network in Logic (IERTNiL) ; Arché Travel Fund  
Qualification Name:  Thesis (Ph.D.)  Qualification Level:  Doctoral  
EThOS ID:  uk.bl.ethos.703474  DOI:  Not available  
Keywords:  Proof ; Rigour ; Formalisation ; Mathematics ; Virtue epistemology ; Open texture ; Knowinghow ; Mathematical practice ; Lakatos ; Paradox ; Gödel's theorems ; Incompleteness ; Conceptual engineering ; Philosophy of mathematics ; QA9.54T2 ; MathematicsPhilosophy ; Proof theory  
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