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  1.  9
    Ian Hacking. Why Is There Philosophy of Mathematics At All?Michael Detlefsen - 2017 - Philosophia Mathematica 25 (3):407-412.
    © The Author [2017]. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.comThe author makes clear that he does not see this book as a contribution to the philosophy of mathematics as traditionally understood. He takes it instead to be an essay about the philosophy of mathematics, one whose purpose is to explain its existence and to make clear the limited extent to which its current and past forms are properly regarded as philosophies of mathematics per (...)
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  2.  2
    Emily Rolfe Grosholz. Starry Reckoning: Reference and Analysis in Mathematics and Cosmology.Gandon Sébastien - 2017 - Philosophia Mathematica 25 (3):419-422.
    © The Authors [2017]. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com...Emily Grosholz is interested in the growth of knowledge: what happens when reasoning not only orders what we already know, but adds to what we know? In her previous works, especially in her [2007], Grosholz insisted on the fact that working scientists and mathematicians, when they add to what we know, often combine different ‘modes of representation’, taking advantage of the ambiguity that arises when (...)
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  3.  16
    Further Into the Abyss: Graham Priest’s Towards Non-Being.Bob Hale - 2017 - Philosophia Mathematica 25 (3):394-406.
    PriestGraham. Towards Non-Being: The Logic and Metaphysics of Intentionality. Oxford University Press, 2016. 2nd ed. ISBN 978-0-19-878359-6 ; 978-0-19-878360-2. Pp. xxxvi + 368.
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  4.  5
    Richard Lane Tieszen, 1951–2017.Charles Parsons - 2017 - Philosophia Mathematica 25 (3):390-391.
    Richard Tieszen, professor of philosophy at San José State University and a member of the editorial board of Philosophia Mathematica, died March 28, 2017 in Zen Hospice in San Francisco. He had been diagnosed with cancer eight years before and had had some radical treatments, but by the beginning of March his options had run out.
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  5.  3
    Carlo Cellucci. Rethinking Knowledge: The Heuristic View.Stephen Pollard - 2017 - Philosophia Mathematica 25 (3):413-418.
    CarloCellucci. Rethinking Knowledge: The Heuristic View. Cham, Switzerland: Springer International Publishing, 2017. ISBN 978-3-319-53236-3, 978-3-319-53237-0. Pp. xx + 428††.
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  6.  7
    Introduction to Special Issue: Dedekind and the Philosophy of Mathematics.Erich Reck - 2017 - Philosophia Mathematica 25 (3):287-291.
    © The Author [2017]. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.comRichard Dedekind was a contemporary of Bernhard Riemann, Georg Cantor, and Gottlob Frege, among others. Together, they revolutionized mathematics and logic in the second half of the nineteenth century. Dedekind had an especially strong influence on David Hilbert, Ernst Zermelo, Emmy Noether, and Nicolas Bourbaki, who completed that revolution in the twentieth century. With respect to mainstream mathematics, he is best known for his contributions (...)
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  7.  5
    Dedekind and Cassirer on Mathematical Concept Formation†.Audrey Yap - 2017 - Philosophia Mathematica 25 (3):369-389.
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  8.  18
    Computing with Numbers and Other Non-Syntactic Things: De Re Knowledge of Abstract Objects.Stewart Shapiro - 2017 - Philosophia Mathematica 25 (2):268-281.
    ABSTRACT Michael Rescorla has argued that it makes sense to compute directly with numbers, and he faulted Turing for not giving an analysis of number-theoretic computability. However, in line with a later paper of his, it only makes sense to compute directly with syntactic entities, such as strings on a given alphabet. Computing with numbers goes via notation. This raises broader issues involving de re propositional attitudes towards numbers and other non-syntactic abstract entities.
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  9.  12
    Mohan Ganesalingam. The Language of Mathematics: A Linguistic and Philosophical Investigation. FoLLI Publications on Logic, Language and Information. [REVIEW]Andrew Aberdein - 2017 - Philosophia Mathematica 25 (1):143–147.
  10.  4
    Referring to Mathematical Objects Via Definite Descriptions.Stefan Buijsman - 2017 - Philosophia Mathematica 25 (1):128-138.
    Linsky and Zalta try to explain how we can refer to mathematical objects by saying that this happens through definite descriptions which may appeal to mathematical theories. I present two issues for their account. First, there is a problem of finding appropriate pre-conditions to reference, which are currently difficult to satisfy. Second, there is a problem of ensuring the stability of the resulting reference. Slight changes in the properties ascribed to a mathematical object can result in a shift of reference (...)
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  11.  8
    Introduction.Salvatore Florio - 2017 - Philosophia Mathematica 25 (1):1-2.
    Introduction to a special issue on abstraction principles.
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  12.  10
    Categories for the Neologicist.Shay Allen Logan - 2017 - Philosophia Mathematica 25 (1):26-44.
    Abstraction principles provide implicit definitions of mathematical objects. In this paper, an abstraction principle defining categories is proposed. It is unsatisfiable and inconsistent in the expected ways. Two restricted versions of the principle which are consistent are presented.
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  13.  22
    The Psychology and Philosophy of Natural Numbers.Oliver R. Marshall - 2017 - Philosophia Mathematica:nkx002.
    ABSTRACT I argue against both neuropsychological and cognitive accounts of our grasp of numbers. I show that despite the points of divergence between these two accounts, they face analogous problems. Both presuppose too much about what they purport to explain to be informative, and also characterize our grasp of numbers in a way that is absurd in the light of what we already know from the point of view of mathematical practice. Then I offer a positive methodological proposal about the (...)
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