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

148 paolo mancosu(‘It is not, then, the general proof which explains; it is the generalizableproof.’ Steiner (1978a); see Hafner and Mancosu (2005) for an extendeddiscussion)).5.5 ConclusionThe topic of mathematical explanation offers a vast and virgin territory toexploration. Most of the work remains to be done. We need to discuss andanalyze mathematical explanations in the sciences and mathematical explanationswithin pure mathematics. These case studies have then to be used totest a variety of theories of scientific explanation and theories of mathematicalexplanation. That in turn will be instrumental in the attempt of givingbroader and more encompassing theories of scientific explanation (or perhapsin showing that no such thing is to be had). Finally, all this work will havea major impact on broader philosophical problems such as, among others,accounting for mathematical applications and indispensability arguments inontology, and in providing a richer epistemology for mathematics.BibliographyBaker, Alan (2005), ‘Are there Genuine Mathematical Explanations of PhysicalPhenomena?’, Mind, 114, 223–238.Batterman,Robert(2001), The Devil in the Details (Oxford: Oxford University Press).Colyvan, Mark(2001), The Indispensability of Mathematics (Oxford: Oxford UniversityPress).(2002), ‘Mathematics and Aesthetic Considerations in Science’, Mind, 11, 69–78.Dummett, Michael (1978), ‘Platonism’, in Michael Dummett (ed.), Truth and OtherEnigmas (London: Duckworth) pp. 202–204.Feferman, Solomon (1964), ‘Systems of Predicative Analysis’, The Journal of SymbolicLogic, 29, 1–30.(2004), ‘Comments on ‘‘Predicativity as a Philosophical Position’’ by G. Hellman’,Revue Internationale de Philosophie, 229(3), 313–323.Hafner, Johannes and Mancosu, Paolo (2005), ‘The Varieties of MathematicalExplanation’, in P. Mancosu, K. Jørgensen, and S. Pedersen (eds.), Visualization,Explanation and Reasoning Styles in Mathematics (Dordrecht: Springer) pp. 215–250.Harari,Orna(2008), ‘Proclus’ Account of Explanatory Demonstrations in Mathematicsand its Context’, forthcoming in Archiv für Geschichte der Philosophie.