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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 2015-04-21
    Izabella Bondecka-Krzykowska & Roman Murawski (2006). 2. Remarks On The Structuralistic Epistemology Of Mathematics. Logique Et Analyse 49:85-93.
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  2. added 2015-04-21
    Alan Baker (2002). Maximizing Principles and Mathematical Methodology. Logique Et Analyse 45.
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  3. added 2015-04-21
    E. Bencivenga (1988). Incompleteness of a Free Arithmetic. Logique Et Analyse 31 (21):79.
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  4. added 2015-04-21
    E. Bencivenga (1983). Société Mathématique de Belgique - Belgisch Wiskundig Genootschap. Logique Et Analyse:247.
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  5. 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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  6. 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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  7. added 2015-04-16
    John Bell (1976). ECH, T. J.: "The Axiom of Choice". [REVIEW] British Journal for the Philosophy of Science 27:187.
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  8. added 2015-04-16
    J. L. Bell (1975). FRAENKEL, A. A., BARHILLEL, Y. And LEVY, A. "Foundations of Set Theory". [REVIEW] British Journal for the Philosophy of Science 26:165.
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  9. 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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  10. added 2015-04-07
    Karel Berka (1981). Bernard Bolzano. Horizont.
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  11. added 2015-04-06
    Maria Teresa de la Garza, Christina Slade & Marie-France Daniel (unknown). Philosophy of Mathematics in the Classroom. Analytic Teaching and Philosophical Praxis 20 (2):88-104.
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  12. added 2015-04-06
    Louise Lafortune, Marie-France Daniel, Richard Pallascio & Michael Schleifer (unknown). Evolution of Pupil’s Attitudes to Mathematics When Using a Philosophical Approach. Analytic Teaching and Philosophical Praxis 20 (1):46-63.
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  13. 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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  14. 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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  15. 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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  16. added 2015-04-06
    Domenico Zambella (forthcoming). Elementary Classes of Finite VC-Dimension. Archive for Mathematical Logic.
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  17. 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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  18. 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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  19. 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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  20. 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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  21. 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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  22. 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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  23. 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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  24. 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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  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
    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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  27. 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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  28. 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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  29. 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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  30. 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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  31. 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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  32. 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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  33. 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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  34. 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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  35. 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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  36. 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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  37. 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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  38. added 2015-04-06
    Sebastian Tomasz Kołodziejczyk (2013). Towards Graham Priest. Polish Journal of Philosophy 7 (2):5-6.
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  39. 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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  40. 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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  41. added 2015-04-06
    Andrew Aberdein, Commentary On: Michel Dufour's "Argument and Explanation in Mathematics.
  42. added 2015-04-06
    Steven W. Patterson, Are Arguments Abstract Objects?
    Geoff Goddu's 2010 paper "Is 'Argument' subject to the process/product ambiguity?" and Paul Simard-Smith and Andrei Moldovan's 2011 paper “Arguments as abstract objects” have revived the dialogue about what might be called the "metaphysics of argument". Both papers are important. Both also seem to me to be open to significant objections. In this paper I will lay out some of these objections and give, in rough outline, the kernel of an alternative approach.
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  43. added 2015-04-06
    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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  44. 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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  45. added 2015-04-06
    Anna Pietryga (2013). Graham Priest and His P-Scheme. Polish Journal of Philosophy 7 (2):37-51.
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  46. added 2015-04-06
    Nuno Ornelas Martins (2012). Mathematics, Science and the Cambridge Tradition. Economic Thought.
    In this paper the use of mathematics in economics will be discussed, by comparing two approaches to mathematics, a Cartesian approach, and a Newtonian approach. I will argue that while mainstream economics is underpinned by a Cartesian approach which led to a divorce between mathematics and reality, the contributions of key authors of the Cambridge tradition, like Marshall, Keynes and Sraffa, are characterised by a Newtonian approach to mathematics, where mathematics is aimed at a study of reality. Marshall was influenced (...)
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  47. added 2015-04-06
    Richard Foley (2012). Chapter 12. The Lottery and Preface. In , When is True Belief Knowledge? Princeton University Press. 70-72.
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  48. added 2015-04-06
    David Kary & Sheldon Wein, When is an Exercise in Logic Also a Logic Game?
    This paper looks to Bernard Suits’s analysis of games and game playing for at least a partial answer to the question in its title. It applies Suits’s analysis to Sudoku, a popular logic puzzle, and to Ana-lytical Reasoning, a question type in standardized assessments. The purpose is both to test Suits’s analysis in a novel domain and to give educators and test developers useful insight into the relationship between logic exercises and games.
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  49. added 2015-04-06
    Trudy Govier, Commentary on Belanger, Hilbert & Goodnight.
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  50. added 2015-04-06
    Ivor Grattan-Guinness (2008). Foundations of Mathematics and Logicism. In Michel Weber (ed.), Handbook of Whiteheadian Process Thought. De Gruyter. 97-104.
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