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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 2015-05-25
    Luca Bellotti (2013). A Neo-Kantian Approach in the Philosophy of Mathematics. In Margit Ruffing, Claudio La Rocca, Alfredo Ferrarin & Stefano Bacin (eds.), Kant Und Die Philosophie in Weltbürgerlicher Absicht: Akten des Xi. Kant-Kongresses 2010. De Gruyter. 3-6.
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  2. added 2015-05-15
    Philip A. Ebert (forthcoming). Richard G. Heck Jr. Reading Frege's Grundgesetze. Oxford: Oxford University Press, 2012. ISBN: 978-0-19-923370-0 ; 978-0-19-874437-5 ; 978-0-19-165535-7 . Pp. Xvii + 296. [REVIEW] Philosophia Mathematica:nkv015.
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  3. added 2015-05-14
    James S. J. Schwartz (forthcoming). Mathematical Structuralism, Modal Nominalism, and the Coherence Principle. Philosophia Mathematica:nkv013.
    According to Stewart Shapiro's coherence principle, structures exist whenever they can be coherently described. I argue that Shapiro's attempts to justify this principle are circular, as he relies on criticisms of modal nominalism which presuppose the coherence principle. I argue further that when the coherence principle is not presupposed, his reasoning more strongly supports modal nominalism than ante rem structuralism.
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  4. added 2015-05-07
    Uri D. Leibowitz & Neil Sinclair (eds.) (forthcoming). Explanation in Ethics and Mathematics. Oxford University Press.
    Contents: 1.'Introduction: Explanation in Ethics and Mathematics' Neil Sinclair & Uri D. Leibowitz. Part I: Evolutionary Debunking Arguments 2.'Genealogy and Reliability' Justin Clarke-Doane. 3.'Explaining the Reliability of Moral Beliefs' Folke Tersman. 4.'Genealogical Explanations of Chance and Morals' Toby Handfield. 5.'Evolutionary Debunking Arguments in Religion and Morality' Erik J. Wielenberg. 6.‘An Assumption of Extreme Significance’: Moore, Ross and Spencer on Ethics and Evolution' Hallvard Lillehammer. 7.'Reply: Confessions of a Modest Debunker' Richard Joyce. Part II: Indispensability Arguments. 8.'Moral Explanation for Moral Anti-Realism' (...)
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  5. added 2015-04-30
    Jeremy Heis (2014). Ernst Cassirer’s Substanzbegriff Und Funktionsbegriff. Hopos: The Journal of the International Society for the History of Philosophy of Science 4 (2):241-70.
    Ernst Cassirer’s book Substanzbegriff und Funktionsbegriff is a difficult book for contemporary readers to understand. Its topic, the theory of concept formation, engages with debates and authors that are largely unknown today. And its “historical” style violates the philosophical standards of clarity first propounded by early analytic philosophers. Cassirer, for instance, never says explicitly what he means by “substance-concept” and “function-concept.” In this article, I answer three questions: Why did Cassirer choose to focus on the topic of concept formation? What (...)
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  6. added 2015-04-29
    Christopher Pincock (2014). Sorin Bangu. The Applicability of Mathematics in Science: Indispensability and Ontology. Basingstoke: Palgrave Macmillan, 2012. ISBN 978-0-230-28520-0 . Pp. Xiii + 252. [REVIEW] Philosophia Mathematica 22 (3):401-412.
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  7. added 2015-04-29
    Christopher Pincock (2014). Sorin Bangu. The Applicability of Mathematics in Science: Indispensability and Ontology. Basingstoke: Palgrave Macmillan, 2012. ISBN 978-0-230-28520-0 . Pp. Xiii + 252. [REVIEW] Philosophia Mathematica 22 (3):401-412.
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  8. added 2015-04-29
    Roy T. Cook (2014). B. Jack Copeland, Carl J. Posy, and Oron Shagrir, Eds, Computability: Turing, Gödel, Church, and Beyond. Cambridge, Mass.: MIT Press, 2013. ISBN 978-0-262-01899-9. Pp. X + 362. [REVIEW] Philosophia Mathematica 22 (3):412-413.
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  9. added 2015-04-29
    Roy T. Cook (2014). B. Jack Copeland, Carl J. Posy, and Oron Shagrir, Eds, Computability: Turing, Gödel, Church, and Beyond. Cambridge, Mass.: MIT Press, 2013. ISBN 978-0-262-01899-9. Pp. X + 362. [REVIEW] Philosophia Mathematica 22 (3):412-413.
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  10. added 2015-04-29
    Thomas Donaldson (2014). A Trivialist's Travails†. [REVIEW] Philosophia Mathematica 22 (3):380-401.
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  11. added 2015-04-29
    Thomas Donaldson (2014). A Trivialist's Travails†. [REVIEW] Philosophia Mathematica 22 (3):380-401.
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  12. added 2015-04-29
    Donald Gillies (2014). Timothy Childers. Philosophy and Probability. Oxford: Oxford University Press, 2013. ISBN: 978-0-19-966182-4 ; 978-0-19-966183-1 . Pp. Xviii + 194. [REVIEW] Philosophia Mathematica 22 (3):413-417.
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  13. added 2015-04-29
    Donald Gillies (2014). Timothy Childers. Philosophy and Probability. Oxford: Oxford University Press, 2013. ISBN: 978-0-19-966182-4 ; 978-0-19-966183-1 . Pp. Xviii + 194. [REVIEW] Philosophia Mathematica 22 (3):413-417.
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  14. added 2015-04-29
    Oran Magal (2014). Wilfried Sieg. Hilbert's Programs and Beyond. Oxford: Oxford University Press, 2013. ISBN 978-0-19-537222-9 ; 978-0-19-970715-7 . Pp. Xii + 439†. [REVIEW] Philosophia Mathematica 22 (3):417-423.
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  15. added 2015-04-29
    Oran Magal (2014). Wilfried Sieg. Hilbert's Programs and Beyond. Oxford: Oxford University Press, 2013. ISBN 978-0-19-537222-9 ; 978-0-19-970715-7 . Pp. Xii + 439†. [REVIEW] Philosophia Mathematica 22 (3):417-423.
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  16. added 2015-04-27
    Michael Rescorla (forthcoming). The Representational Foundations of Computation. Philosophia Mathematica:nkv009.
    Turing computation over a non-linguistic domain presupposes a notation for the domain. Accordingly, computability theory studies notations for various non-linguistic domains. It illuminates how different ways of representing a domain support different finite mechanical procedures over that domain. Formal definitions and theorems yield a principled classification of notations based upon their computational properties. To understand computability theory, we must recognize that representation is a key target of mathematical inquiry. We must also recognize that computability theory is an intensional enterprise: it (...)
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  17. added 2015-04-18
    Simon Hewitt (forthcoming). When Do Some Things Form a Set? Philosophia Mathematica:nkv010.
    This paper raises the question under what circumstances a plurality forms a set, parallel to the Special Composition Question for mereology. The range of answers that have been proposed in the literature are surveyed and criticised. I argue that there is good reason to reject both the view that pluralities never form sets and the view that pluralities always form sets. Instead, we need to affirm restricted set formation. Casting doubt on the availability of any informative principle which will settle (...)
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  18. added 2015-04-17
    Max Jones (forthcoming). James Franklin. An Aristotelian Realist Philosophy of Mathematics. New York: Palgrave Macmillan, 2014. ISBN: 978-1-137-40072-7 ; 978-1-137-40073-4 ; 978-1-137-40074-1 . Pp. X + 308. [REVIEW] Philosophia Mathematica:nkv011.
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  19. added 2015-04-14
    Jody Azzouni & Otávio Bueno (forthcoming). True Nominalism: Referring Versus Coding. British Journal for the Philosophy of Science:axv004.
    One major motivation for nominalism, at least according to Hartry Field, is the desirability of intrinsic explanations: explanations that don’t invoke objects that are causally irrelevant to the phenomena being explained. There is something right about the search for such explanations. But that search must be carefully implemented. Nothing is gained if, to avoid a certain class of objects, one only introduces other objects and relations that are just as nominalistically questionable. We will argue that this is the case for (...)
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  20. added 2015-04-08
    Adam Tamas Tuboly (2014). Unifying Historical Perspectives. [REVIEW] The Berlin Review of Books 2014.
    Greg Frost-Arnold’s book is a highly elegant edition and commentary of Carnap’s notes, claiming just as much as he is warranted on the basis of the manuscript and other relevant texts, and formulating his scholarly assumptions very carefully. Along the way he tries to unify the three historiographical strategies: narrative, argumentative and micro-historical.
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  21. added 2015-04-06
    Colleen E. Crangle, Adolfo García de la Sienra & Helen E. Longino (eds.) (forthcoming). Foundations and Methods From Mathematics to Neuroscience. CSLI Publications.
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  22. added 2015-04-06
    Robert Knowles & David Liggins (forthcoming). Good Weasel Hunting. Synthese:1-16.
    The ‘indispensability argument’ for the existence of mathematical objects appeals to the role mathematics plays in science. In a series of publications, Joseph Melia has offered a distinctive reply to the indispensability argument. The purpose of this paper is to clarify Melia’s response to the indispensability argument and to advise Melia and his critics on how best to carry forward the debate. We will begin by presenting Melia’s response and diagnosing some recent misunderstandings of it. Then we will discuss four (...)
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  23. added 2015-04-06
    Domenico Zambella (forthcoming). Elementary Classes of Finite VC-Dimension. Archive for Mathematical Logic.
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  24. added 2015-04-06
    Josh Hunt (forthcoming). Indispensability and the Problem of Compatible Explanations. Synthese:1-17.
    Alan Baker’s enhanced indispensability argument supports mathematical platonism through the explanatory role of mathematics in science. Busch and Morrison defend nominalism by denying that scientific realists use inference to the best explanation to directly establish ontological claims. In response to Busch and Morrison, I argue that nominalists can rebut the EIA while still accepting Baker’s form of IBE. Nominalists can plausibly require that defenders of the EIA establish the indispensability of a particular mathematical entity. Next, I argue that IBE cannot (...)
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  25. added 2015-04-06
    Emil Jeřábek (2015). Open Induction in a Bounded Arithmetic for TC0. Archive for Mathematical Logic 54 (3-4):359-394.
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  26. added 2015-04-06
    Ilkka Niiniluoto (2015). Constructive Realism in Mathematics. [REVIEW] In Andrés Villaveces, Roman Kossak, Juha Kontinen & Åsa Hirvonen (eds.), Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics. De Gruyter. 339-354.
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  27. added 2015-04-06
    Philipp Werner (2015). 10 Das Axiom Φ L. In David Lewis Und Seine Mereologische Interpretation der Zermelo-Fraenkelschen Mengenlehre: Eine Rekonstruktion. De Gruyter. 59-102.
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  28. added 2015-04-06
    Andrés Villaveces, Roman Kossak, Juha Kontinen & Åsa Hirvonen, Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics.
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  29. added 2015-04-06
    Pierre Matet (2015). Ideals on $${P_{\Kappa}}$$ P Κ Associated with Games of Uncountable Length. Archive for Mathematical Logic 54 (3-4):291-328.
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  30. added 2015-04-06
    Tapani Hyttinen (2015). Counting Measure and Forking in Finite Models. [REVIEW] In Andrés Villaveces, Roman Kossak, Juha Kontinen & Åsa Hirvonen (eds.), Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics. De Gruyter. 265-280.
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  31. added 2015-04-06
    Ilkka Niiniluoto (2015). Constructive Realism in Mathematics. In Andrés Villaveces, Roman Kossak, Juha Kontinen & Åsa Hirvonen (eds.), Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics. De Gruyter. 339-354.
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  32. added 2015-04-06
    Carl Mummert, Alaeddine Saadaoui & Sean Sovine (2015). The Modal Logic of Reverse Mathematics. Archive for Mathematical Logic 54 (3-4):425-437.
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  33. added 2015-04-06
    Xavier Caicedo (2015). Lindström’s Theorem for Positive Logics, a Topological View. [REVIEW] In Andrés Villaveces, Roman Kossak, Juha Kontinen & Åsa Hirvonen (eds.), Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics. De Gruyter. 73-90.
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  34. added 2015-04-06
    Carlos Augusto Di Prisco (2015). Some Aspects of the Ramsey Theory of Real Numbers. [REVIEW] In Andrés Villaveces, Roman Kossak, Juha Kontinen & Åsa Hirvonen (eds.), Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics. De Gruyter. 115-138.
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  35. added 2015-04-06
    Michal Garlík (2015). A New Proof of Ajtai’s Completeness Theorem for Nonstandard Finite Structures. Archive for Mathematical Logic 54 (3-4):413-424.
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  36. added 2015-04-06
    Philipp Werner (2015). 8 Das Axiom Φ B. In David Lewis Und Seine Mereologische Interpretation der Zermelo-Fraenkelschen Mengenlehre: Eine Rekonstruktion. De Gruyter. 41-48.
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  37. added 2015-04-06
    M. Leng (2015). Truth Through Proof: A Formalist Foundation for Mathematics. Philosophical Quarterly 65 (259):288-292.
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  38. added 2015-04-06
    Laura Celani, Logic in Theory and in Practice : The Normative Status of Logic.
    In my thesis, I address the question ʽWhat normative status does logic have?', to argue that logical normativity is of a weak sort, and that its constraining power is similar to that of recommendations. The thesis first discusses the notion of logical validity and logical formality, then asks whether logic is a priori and whether it can provide a priori norms for thinking. Subsequently, the issue of the bridge principles linking formal logic to informal reasoning is addressed, jointly with a (...)
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  39. added 2015-04-06
    Åsa Hirvonen, Juha Kontinen, Roman Kossak & Andrés Villaveces (eds.) (2015). Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics. De Gruyter.
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  40. added 2015-04-06
    Miloš Adžić & Miloš Arsenijević (2014). Gunkology and Pointilism: Two Mutually Supervening Models of the Region–Based and the Point-Based Theory of the Infinite Twodimensional Continuum. In Giovanni Macchia, Francesco Orilia & Vincenzo Fano (eds.), Space and Time: A Priori and a Posteriori Studies. De Gruyter. 137-170.
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  41. added 2015-04-06
    Nicholas Rescher (2014). 9. Logic and the Interconnection of Philosophical Issues. In Logical Inquiries: Basic Issues in Philosophical Logic. De Gruyter. 128-138.
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  42. added 2015-04-06
    Victor Selivanov & Peter Hertling (2014). Complexity Issues for Preorders on Finite Labeled Forests. In Dieter Spreen, Hannes Diener & Vasco Brattka (eds.), Logic, Computation, Hierarchies. De Gruyter. 165-190.
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  43. added 2015-04-06
    Nicholas Rescher (2014). 8. Provability Incompleteness in Gödel and Leibniz. In Logical Inquiries: Basic Issues in Philosophical Logic. De Gruyter. 107-127.
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  44. added 2015-04-06
    Brigitte Weingart (2014). Contact at a Distance The Topology of Fascination. In Julia Weber & Rüdiger Campe (eds.), Rethinking Emotion: Interiority and Exteriority in Premodern, Modern, and Contemporary Thought. De Gruyter. 72-100.
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  45. added 2015-04-06
    Pierluigi Graziani (2014). A Structural and Foundational Analysis of Euclid’s Plane Geometry: The Case Study of Continuity. In Giovanni Macchia, Francesco Orilia & Vincenzo Fano (eds.), Space and Time: A Priori and a Posteriori Studies. De Gruyter. 63-106.
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  46. added 2015-04-06
    Hans-Peter A. Künzi, Paulus Haihambo & Collins Amburo Agyingi (2014). Tight Extensions of T0-Quasi-Metric Spaces. In Dieter Spreen, Hannes Diener & Vasco Brattka (eds.), Logic, Computation, Hierarchies. De Gruyter. 9-22.
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  47. added 2015-04-06
    Joanna Odrowąż-Sypniewska (2013). Paraconsistent Vs. Contextual Solutions to Sorites. Polish Journal of Philosophy 7 (2):21-36.
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  48. added 2015-04-06
    Andrew Aberdein, Commentary On: Begoῆa Carrascal's "The Practice of Arguing and the Arguments: Examples From Mathematics.
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  49. added 2015-04-06
    Piotr Warzoszczak (2013). Remarks on Graham Priest’s Views on Transworld Identity. Polish Journal of Philosophy 7 (2):79-91.
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  50. added 2015-04-06
    Michel Dufour, Argument and Explanation in Mathematics.
    Are there arguments in mathematics? Are there explanations in mathematics? Are there any connections between argument, proof and explanation? Highly controversial answers and arguments are reviewed. The main point is that in the case of a mathematical proof, the pragmatic criterion used to make a distinction between argument and explanation is likely to be insufficient for you may grant the conclusion of a proof but keep on thinking that the proof is not explanatory.
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