Mancosu - Philosophy of Mathematical Practice (Oxford, 2008).pdf

understanding proofs 351Mathematics guides our thought in deep and powerful ways, and deserves aphilosophy that recognizes that fact. When we focus on particular features ofmathematical practice, metaphysical concerns often seem petty and irrelevant,and we find, instead, a rich assortment of issues that have concrete bearingupon what we do and say about the subject. Our task is to develop a conceptualframework in which we can fruitfully begin to address these issues, and tonarrow our focus to the point where discernible progress can be made. I hopethe present chapter serves as encouragement.Added in Proof. After the article had been sent to the publisher, I came acrosswork by Jody Azzouni which bears directly on many of the issues raised here.Although, I cannot explore the points of agreement and disagreement now,the reader may wish to compare my views to those of Azzouni (2005) andAzzoumi (2006).BibliographyAigner,MartinandZiegler,Günter M. (2001), Proofs from The Book, 2nd edn (Berlin:Springer-Verlag).Avigad, Jeremy (2006), ‘Mathematical method and proof’, Synthese, 153, 105–159.Avigad, Jeremy, Donnelly, Kevin, Gray, David, and Raff, Paul(2007) ‘A formallyverified proof of the prime number theorem’, ACM Transactions on ComputationalLogic, 9(1:2).Avigad, Jeremy and Friedman, Harvey(2006), ‘Combining decision procedures forthe reals’, Logical Methods in Computer Science, 2(4:4).Azzoumi, Jody(2005), ‘Is there a sense in which mathematics can have foundations?’In G. Sica (ed.), Essays in the Foundations of Mathematics and Logic, 9–47 (Monza:Polimetrica).(2006), Tracking Reason: Proof, Consequence, and Truth (Oxford: OxfordUniversity Press).Ballarin, Clemens(2006), ‘Interpretation of locales in Isabelle: theories and proofcontexts’, in J. M. Borwein and W. M. Farmer (eds.), Mathematical Knowledge Management:Proceedings of the Fifth International Conference, MKM 2006, 31–43 (Berlin:Springer-Verlag).Beeson, Michael (1998), ‘Design principles of Mathpert: software to support educationin algebra and calculus’, in N. Kajler (ed.), Computer—Human Interaction in SymbolicComputation, 89–115 (Berlin: Springer-Verlag).Bertot, YvesandCastéran, Pierre (2004), Interactive Theorem Proving and ProgramDevelopment: Coq’art: the Calculus of Inductive Constructions (Berlin: Springer-Verlag).Bos, HenkJ.M.(2000), Redefining Geometrical Exactness: Descartes’ Transformation of theEarly Modern Concept of Construction (New York: Springer-Verlag).