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

introduction 13and epistemological problems are worthy of investigation she has decided tofocus on an aspect of the methodology of mathematics completely ignoredin previous analytic philosophy of mathematics. This is a large subject areaconcerning the sort of arguments that are brought to bear in the decision infavor or against certain new axioms in set theory. Previous analytic philosophyof mathematics would have relegated this to the ‘context of discovery’ and assuch not worthy or suitable for rigorous investigation. Maddy counters thatthese decisions are rational and can be accounted for by a naturalistic modelthat spells out the principles and maxims directing the practice. Maddy’s projectcan be seen as a contribution to the general problem of how evidence andjustification functions in mathematics. This can be seen as related to a study of‘heuristics’, although this has to be taken in the appropriate sense as her casestudies cannot be confused with, or reduced to, traditional studies on ‘problemsolving’. Another feature of Maddy’s work that ties her approach to that ofthe mavericks is the appeal to the history of logic and mathematics as a centralcomponent in her naturalized account. This is not surprising: mathematicalpractice is embodied in the concrete work of mathematicians and that work hastaken place in history. Although Maddy, unlike Kitcher 1984, is not proposingan encompassing account of the rationality in the changes in mathematicalpractice, or a theory of mathematical growth, the case studies she investigatedhave led her to consider portions of the history of analysis and of set theory.The history of set theory (up to its present state) is the ‘laboratory’ for thedistillation of the naturalistic model of the practice. Finally, a major differencein attitude between Maddy and the ‘mavericks’ is the lack on Maddy’s partof any polemic against logic and foundations. Rather, her ambition is one ofmaking sense of the inner rationality of foundational work in set theory.4 This collectionThe rather stark contrast used to present different directions of philosophicalwork on mathematical practice in Sections 2 and 3 would not be appropriateto characterize some of the most recent contributions in this area, inwhich a variety of approaches often coexist together. This is especially trueof the volumes ‘Perspectives on Mathematical Practices’ (van Kerkhove andvan Bengedem 2002 and 2007) which contain a variety of contributions,some of which find their inspiration in the maverick tradition and others inMaddy’s work, while others yet point the way to independent developments.Similar considerations apply to Mancosu et al. (2005), although in contrast