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Philosophy of Mathematics

Edited by Øystein Linnebo (Birkbeck College)
Assistant editor: Sam Roberts (Birkbeck College, University of Oslo)
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  1. added 2014-12-19
    Luca Incurvati (forthcoming). On the Concept of Finitism. Synthese.
    At the most general level, the concept of finitism is typically characterized by saying that finitistic mathematics is that part of mathematics which does not appeal to completed infinite totalities and is endowed with some epistemological property that makes it secure or privileged. This paper argues that this characterization can in fact be sharpened in various ways, giving rise to different conceptions of finitism. The paper investigates these conceptions and shows that they sanction different portions of mathematics as finitistic.
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  2. added 2014-12-18
    Steven M. Rosen (2014). How Can We Signify Being? Semiotics and Topological Self-Signification. Cosmos and History: The Journal of Natural and Social Philosophy 10 (2):250-277.
    The premise of this paper is that the goal of signifying Being central to ontological phenomenology has been tacitly subverted by the semiotic structure of conventional phenomenological writing. First it is demonstrated that the three components of the conventional sign as defined by C. S. Peirce—the sign-vehicle, object, and interpretant—bear an external relationship to each other. This is linked to the abstractness of alphabetic language, which objectifies nature and splits subject and object. It is the subject-object divide that phenomenology must (...)
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  3. added 2014-12-17
    Shay Logan (forthcoming). Category Theory is a Contentful Theory. Philosophia Mathematica:nku030.
    Linnebo and Pettigrew present some objections to category theory as an autonomous foundation. They do a commendable job making clear several distinct senses of ‘autonomous’ as it occurs in the phrase ‘autonomous foundation’. Unfortunately, their paper seems to treat the ‘categorist’ perspective rather unfairly. Several infelicities of this sort were addressed by McLarty. In this note I address yet another apparent infelicity.
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  4. added 2014-12-17
    Luca Incurvati & Julien Murzi (forthcoming). Maximally Consistent Sets of Instances of Naive Comprehension. Mind.
    Paul Horwich (1990) once suggested restricting the T-Schema to the maximal consistent set of its instances. But Vann McGee (1992) proved that there are multiple incompatible such sets, none of which, given minimal assumptions, is recursively axiomatizable. The analogous view for set theory---that Naïve Comprehension should be restricted according to consistency maxims---has recently been defended by Laurence Goldstein (2006; 2013). It can be traced back to W.V.O. Quine(1951), who held that Naïve Comprehension embodies the only really intuitive conception of set (...)
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  5. added 2014-12-12
    Axel Gelfert (2014). Applicability, Indispensability, and Underdetermination: Puzzling Over Wigner's 'Unreasonable Effectiveness of Mathematics'. Science and Education 23 (5):997-1009.
    In his influential 1960 paper ‘The Unreasonable Effectiveness of Mathematics in the Natural Sciences’, Eugene P. Wigner raises the question of why something that was developed without concern for empirical facts—mathematics—should turn out to be so powerful in explaining facts about the natural world. Recent philosophy of science has developed ‘Wigner’s puzzle’ in two different directions: First, in relation to the supposed indispensability of mathematical facts to particular scientific explanations and, secondly, in connection with the idea that aesthetic criteria track (...)
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  6. added 2014-12-09
    S. Centrone (2014). Mirja Hartimo Ed. Phenomenology and Mathematics. Phaenomenologia; 195. Dordrecht: Springer, 2010. ISBN 978-90-481-3728-2 ; 978-90-481-3728-2 ; 978-94-007-3196-7 . Pp. Xxv + 222. [REVIEW] Philosophia Mathematica 22 (1):126-129.
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  7. added 2014-12-08
    André Bazzoni (forthcoming). Hintikka on the Foundations of Mathematics: IF Logic and Uniformity Concepts. Journal of Philosophical Logic:1-10.
    The initial goal of the present paper is to reveal a mistake committed by Hintikka in a recent paper on the foundations of mathematics. His claim that independence-friendly logic (IFL) is the real logic of mathematics is supported in that article by an argument relying on uniformity concepts taken from real analysis. I show that the central point of his argument is a simple logical mistake. Second and more generally, I conclude, based on the previous remarks and on another standard (...)
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  8. added 2014-12-08
    Eva-Maria Engelen, Kurt Gödels mathematische Anschauung und John P. Burgess’ mathematische Intuition. XXIII Deutscher Kongress für Philosophie Münster 2014, Konferenzveröffentlichung.
  9. added 2014-12-08
    Barry Smith (2012). On Classifying Material Entities in Basic Formal Ontology. In Interdisciplinary Ontology. Proceedings of the Third Interdisciplinary Ontology Meeting. Keio University Press. 1-13.
    Basic Formal Ontology (BFO) was created in 2002 as an upper-level ontology to support the creation of consistent lower-level ontologies, initially in the subdomains of biomedical research, now also in other areas, including defense and security. BFO is currently undergoing revisions in preparation for the release of BFO version 2.0. We summarize some of the proposed revisions in what follows, focusing on BFO’s treatment of material entities, and specifically of the category object.
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  10. added 2014-12-07
    Shigeyuki Atarashi (forthcoming). Review of A. Walsh, Relations Between Logic and Mathematics in the Work of Benjamin and Charles S. Peirce. [REVIEW] Philosophia Mathematica:nku028.
  11. added 2014-12-06
    Peter Simons (forthcoming). Guillermo E. Rosado Haddock. Against the Current: Selected Philosophical Papers. Frankfurt: Ontos, 2012. ISBN: 9783868381481 . Pp. Xii + 456. [REVIEW] Philosophia Mathematica:nku032.
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  12. added 2014-12-06
    Roy T. Cook (2013). Appendix: How to Read Grundgesetze. In Gottlob Frege (ed.), Basic Laws of Arithmetic, Derived Using Concept-Script: Volumes I & Ii. Oxford University Press.
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  13. added 2014-12-06
    Philip A. Ebert & Marcus Rossberg (2013). Translator's Introduction. In Gottlob Frege (ed.), Basic Laws of Arithmetic, Derived Using Concept-Script: Volumes I & Ii. Oxford University Press.
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  14. added 2014-12-05
    Paolo Mancosu (forthcoming). William Ewald and Wilfried Sieg, Eds, David Hilbert's Lectures on the Foundations of Arithmetic and Logic, 1917–1933. Heidelberg: Springer, 2013. ISBN: 978-3-540-69444-1 ; 978-3-540-20578-4 . Pp. Xxv + 1062. [REVIEW] Philosophia Mathematica:nku031.
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  15. added 2014-11-24
    Audrey Yap (forthcoming). Dedekind and Cassirer on Mathematical Concept Formation. Philosophia Mathematica:nku029.
    Dedekind's major work on the foundations of arithmetic employs several techniques that have left him open to charges of psychologism, and through this, to worries about the objectivity of the natural-number concept he defines. While I accept that Dedekind takes the foundation for arithmetic to lie in certain mental powers, I will also argue that, given an appropriate philosophical background, this need not make numbers into subjective mental objects. Even though Dedekind himself did not provide that background, one can nevertheless (...)
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  16. added 2014-11-18
    Marvin R. G. Schiller (2011). Granularity Analysis for Tutoring Mathematical Proofs. Aka Verlag.
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  17. added 2014-11-16
    Crispin Wright (2013). Foreword. In Gottlob Frege (ed.), Basic Laws of Arithmetic, Derived Using Concept-Script: Volumes I & Ii. Oxford University Press.
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  18. added 2014-11-16
    Gottlob Frege (2013). Basic Laws of Arithmetic, Derived Using Concept-Script: Volumes I & Ii. Oxford University Press.
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  19. added 2014-11-16
    Jakub Sirovátka (ed.) (2012). Endlichkeit Und Transzendenz: Perspektiven Einer Grundbeziehung. Meiner.
    Weder soll die Endlichkeit in ihrer Eigenständigkeit aufgelöst noch die Transzendenz aufgehoben werden. Das Absolute ist sowohl in seiner radikalen Transzendenz als auch in der Beziehung zum Menschen zu denken.
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  20. added 2014-11-08
    Joongol Kim (2014). The Sortal Resemblance Problem. Canadian Journal of Philosophy 44 (3-4):407-424.
    Is it possible to characterize the sortal essence of Fs for a sortal concept F solely in terms of a criterion of identity C for F? That is, can the question ‘What sort of thing are Fs?’ be answered by saying that Fs are essentially those things whose identity can be assessed in terms of C? This paper presents a case study supporting a negative answer to these questions by critically examining the neo-Fregean suggestion that cardinal numbers can be fully (...)
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  21. added 2014-11-04
    Mark Zelcer (2014). Review of Noson Yanofsky, The Outer Limits of Reason: What Science, Mathematics and Logic Cannot Tell Us. [REVIEW] Philosophical Quarterly 64:383-385.
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  22. added 2014-11-04
    Mark Zelcer (2014). Review of E. Brian Davies, Why Beliefs Matter: Reflections on the Nature of Science. [REVIEW] Science, Religion and Culture 1 (3):141-143.
  23. added 2014-10-16
    Cian Dorr (2014). Review of The Construction of Logical Space by Agustín Rayo. [REVIEW] Notre Dame Philosophical Reviews 201406.
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  24. added 2014-10-10
    Emanuele Serrelli (forthcoming). Evolutionary Genetics and Cultural Traits in a 'Body of Theory' Perspective. In Fabrizio Panebianco & Emanuele Serrelli (eds.), Understanding cultural traits. A multidisciplinary perspective on cultural diversity. Springer.
    The chapter explains why evolutionary genetics – a mathematical body of theory developed since the 1910s – eventually got to deal with culture: the frequency dynamics of genes like “the lactase gene” in populations cannot be correctly modeled without including social transmission. While the body of theory requires specific justifications, for example meticulous legitimations of describing culture in terms of traits, the body of theory is an immensely valuable scientific instrument, not only for its modeling power but also for the (...)
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  25. added 2014-10-09
    Marion Haemmerli & Achille C. Varzi (2014). Adding Convexity to Mereotopology. In Pawel Garbacz & Oliver Kutz (eds.), Formal Ontology in Information Systems. Proceedings of the Eighth International Conference. IOS Press. 65–78.
    Convexity predicates and the convex hull operator continue to play an important role in theories of spatial representation and reasoning, yet their first-order axiomatization is still a matter of controversy. In this paper, we present a new approach to adding convexity to mereotopological theory with boundary elements by specifying first-order axioms for a binary segment operator s. We show that our axioms yields a convex hull operator h that supports, not only the basic properties of convex regions, but also complex (...)
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