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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 2014-11-23
    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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  2. added 2014-11-18
    Marvin R. G. Schiller (2011). Granularity Analysis for Tutoring Mathematical Proofs. Aka Verlag.
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  3. 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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  4. 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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  5. added 2014-11-16
    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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  6. added 2014-11-16
    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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  7. 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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  8. added 2014-11-12
    Shigeyuki Atarashi (forthcoming). Alison Walsh. Relations Between Logic and Mathematics in the Work of Benjamin and Charles S. Peirce. Boston: Docent Press, 2012. ISBN 978-098370046-3 (Pbk). Pp. X + 314. [REVIEW] Philosophia Mathematica:nku028.
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  9. added 2014-11-07
    Joongol Kim (forthcoming). The Sortal Resemblance Problem. Canadian Journal of Philosophy:1-18.
    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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  10. 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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  11. 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.
  12. 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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  13. 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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  14. added 2014-10-08
    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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