Philosophy of Mathematics

Edited by Øystein Linnebo (Birkbeck College)
Assistant editor: Sam Roberts (Birkbeck College, University of Oslo)
153 found
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1 — 50 / 153
  1. added 2017-04-21
    A Process Oriented Definition of Number.Rolfe David - manuscript
    In this paper Russell’s definition of number is criticized. Russell’s assertion that a number is a particular kind of set implies that number has the properties of a set. It is argued that this would imply that a number contains elements and that this does not conform to our intuitive notion of number. An alternative definition is presented in which number is not seen as an object, but rather as a process and is related to the act of counting and (...)
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  2. added 2017-04-18
    Contradictions Inherent in Special Relativity: Space Varies.Kim Joosoak - manuscript
    Special relativity has changed the fundamental view on space and time since Einstein introduced it in 1905. It substitutes four dimensional spacetime for the absolute space and time of Newtonian mechanics. It is believed that the validities of Lorentz invariants are fully confirmed empirically for the last one hundred years and therefore its status are canonical underlying all physical principles. However, spacetime metric is a geometric approach on nature when we interpret the natural phenomenon. A geometric flaw on this will (...)
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  3. added 2017-04-15
    What is the Infinite?Øystein Linnebo - 2013 - The Philosophers' Magazine 61:42-47.
    The paper discusses some different conceptions of the infinity, from Aristotle to Georg Cantor (1845-1918) and beyond. The ancient distinction between actual and potential infinity is explained, along with some arguments against the possibility of actually infinite collections. These arguments were eventually rejected by most philosophers and mathematicians as a result of Cantor’s elegant and successful theory of actually infinite collections.
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  4. added 2017-04-13
    Mathematics and Aesthetics in Kantian Perspectives.Wenzel Christian Helmut - 2016 - In Peter Cassaza, Steven G. Krantz & Randi R. Ruden (eds.), I, Mathematician II. Further Introspections on the Mathematical Life. The Consortium of Mathematics and its Applications. pp. 93-106.
    This essay will inform the reader about Kant’s views on mathematics and aesthetics. It will also critically discuss these views and offer further suggestions and personal opinions from the author’s side. Kant (1724-1804) was not a mathematician, nor was he an artist. One must even admit that he had little understanding of higher mathematics and that he did not have much of a theory that could be called a “philosophy of mathematics” either. But he formulated a very influential aesthetic theory (...)
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  5. added 2017-04-11
    Fitting Feelings and Elegant Proofs: On the Psychology of Aesthetic Evaluation in Mathematics.Todd Cain - forthcoming - Philosophia Mathematica:nkx007.
    ABSTRACT This paper explores the role of aesthetic judgements in mathematics by focussing on the relationship between the epistemic and aesthetic criteria employed in such judgements, and on the nature of the psychological experiences underpinning them. I claim that aesthetic judgements in mathematics are plausibly understood as expressions of what I will call ‘aesthetic-epistemic feelings’ that serve a genuine cognitive and epistemic function. I will then propose a naturalistic account of these feelings in terms of sub-personal processes of representing and (...)
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  6. added 2017-04-06
    The Beautiful Art of Mathematics.Adam Rieger - forthcoming - Philosophia Mathematica:nkx006.
    ABSTRACT Mathematicians frequently use aesthetic vocabulary and sometimes even describe themselves as engaged in producing art. Yet aestheticians, in so far as they have discussed this at all, have often downplayed the ascriptions of aesthetic properties as metaphorical. In this paper I argue firstly that the aesthetic talk should be taken literally, and secondly that it is at least reasonable to classify some mathematics as art.
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  7. added 2017-04-03
    Hájek’s Faulty Discussion of Philosophical Heuristics.Danny Frederick - manuscript
    I point out some logical errors and infelicities in Hájek’s discussion of philosophical heuristics.
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  8. added 2017-03-31
    The Epistemic Lightness of Truth: Deflationism and its Logic.Cezary Cieśliński - forthcoming - Cambridge University Press.
    This book analyses and defends the deflationist claim that there is nothing deep about our notion of truth. According to this view, truth is a 'light' and innocent concept, devoid of any essence which could be revealed by scientific inquiry. Cezary Cieśliński considers this claim in light of recent formal results on axiomatic truth theories, which are crucial for understanding and evaluating the philosophical thesis of the innocence of truth. Providing an up-to-date discussion and original perspectives on this central and (...)
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  9. added 2017-03-29
    Introduction: Scientific Explanation Beyond Causation.Alexander Reutlinger & Juha Saatsi - 2017 - In Alexander Reutlinger & Juha Saatsi (eds.), Explanation Beyond Causation: Philosophical Perspectives on Non-Causal Explanations. Oxford: Oxford University Press.
    This is an introduction to the volume "Explanation Beyond Causation: Philosophical Perspectives on Non-Causal Explanations", edited by A. Reutlinger and J. Saatsi (OUP, forthcoming in 2017). -/- Explanations are very important to us in many contexts: in science, mathematics, philosophy, and also in everyday and juridical contexts. But what is an explanation? In the philosophical study of explanation, there is long-standing, influential tradition that links explanation intimately to causation: we often explain by providing accurate information about the causes of the (...)
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  10. added 2017-03-25
    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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  11. added 2017-03-23
    On Deductionism.Dan Bruiger - manuscript
    Deductionism assimilates nature to conceptual artifacts (models, equations), and tacitly holds that real physical systems are such artifacts. Some physical concepts represent properties of deductive systems rather than of nature. Properties of mathematical or deductive systems can thereby sometimes falsely be ascribed to natural systems.
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  12. added 2017-03-22
    How Mathematics Can Make a Difference.Sam Baron, Mark Colyvan & David Ripley - 2017 - Philosophers' Imprint 17 (3).
    Standard approaches to counterfactuals in the philosophy of explanation are geared toward causal explanation. We show how to extend the counterfactual theory of explanation to non-causal cases, involving extra-mathematical explanation: the explanation of physical facts by mathematical facts. Using a structural equation framework, we model impossible perturbations to mathematics and the resulting differences made to physical explananda in two important cases of extra-mathematical explanation. We address some objections to our approach.
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  13. added 2017-03-20
    Minimal Type Theory (MTT).Pete Olcott - manuscript
    Minimal Type Theory (MTT) is based on type theory in that it is agnostic about Predicate Logic level and expressly disallows the evaluation of incompatible types. It is called Minimal because it has the fewest possible number of fundamental types, and has all of its syntax expressed entirely as the connections in a directed acyclic graph.
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  14. added 2017-03-20
    Introduction to Abstractionism.Philip A. Ebert & Marcus Rossberg - 2016 - In Philip A. Ebert & Marcus Rossberg (eds.), Abstractionism. Oxford: Oxford University Press. pp. 3-33.
  15. added 2017-03-20
    Ebert.A. Philip - 2016 - In Philip A. Ebert & Marcus Rossberg (eds.), Abstractionism. Oxford: Oxford University Press. pp. 133--160.
  16. added 2017-03-20
    Dummett’s Criticism of the Context Principle.A. Ebert Philip - 2015 - Grazer Philosophische Studien 92:23-51.
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  17. added 2017-03-11
    The Idea of Infinity in its Physical and Spiritual Meanings.Graham Nicholson - manuscript
    Abstract -/- The concept of infinity is of ancient origins and has puzzled deep thinkers ever since up to the present day. Infinity remains somewhat of a mystery in a physical world in which our comprehension is largely framed around the concept of boundaries. This is partly because we live in a physical world that is governed by certain dimensions or limits – width, breadth, depth, mass, space, age and time. To our ordinary understanding, it is a seemingly finite world (...)
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  18. added 2017-03-11
    In Defense of Mathematical Inferentialism.Seungbae Park - 2017 - Analysis and Metaphysics 16:70-83.
    I defend a new position in philosophy of mathematics that I call mathematical inferentialism. It holds that a mathematical sentence can perform the function of facilitating deductive inferences from some concrete sentences to other concrete sentences, that a mathematical sentence is true if and only if all of its concrete consequences are true, that the abstract world does not exist, and that we acquire mathematical knowledge by confirming concrete sentences. Mathematical inferentialism has several advantages over mathematical realism and fictionalism.
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  19. added 2017-03-10
    Tomáš Akvinský instrumentalistou v matematice?Lukáš Novák - 2016 - Studia Neoaristotelica 13 (4):41-66.
    P. Sousedík and D. Svoboda, in their paper “Různá pojetí matematiky u vybraných autorů od antiky po raný novověk: Je matematika teoretická věda nebo pouhá technika?”, proposed an interpretation of Aquinas’s understanding of the nature of mathematics which the author regards as unsatisfactory. The purpose of this review article is to point out its problems and to suggest in its stead an adequate interpretation of Aquinas’s mind, on the basis of a detailed analysis of his texts. The author shows that (...)
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  20. added 2017-03-06
    Modal Objectivity.Clarke-Doane Justin - manuscript
    It is widely held that the intelligibility of modal metaphysics has been vindicated. Quine’s arguments to the contrary supposedly confused analyticity with metaphysical necessity, and rigid with non-rigid designators. But even if modal metaphysics is intelligible, it could be misconceived. It could be that metaphysical necessity is not absolute necessity – the strictest “non-epistemic” (non-deontic) notion of necessity – and that no proposition of traditional metaphysical interest is necessary in every non-epistemic sense. If there were nothing otherwise “uniquely metaphysically significant” (...)
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  21. added 2017-03-06
    The Inaccuracy of Partial Truth in Yablovian If-Thenism.Joseph Ulatowski - forthcoming - Australasian Philosophical Review 2.
    Yablo has argued for an alternative form of if-thenism that is more conducive with his figurative fictionalism. This commentary sets out to challenge whether the remainder, ρ, tends to be an inaccurate representation of the conditions that are supposed to complete the enthymeme from φ to Ψ. Whilst by some accounts the inaccuracies shouldn't set off any alarm bells, the truth of ρ is too inexact. The content of ρ, a partial truth, must display a sensitivity to the contextual background (...)
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  22. added 2017-03-06
    Forms of Mathematization.Sophie Roux - 2010 - Early Science and Medicine 15 (4-5):319-337.
  23. added 2017-03-03
    Strategic Value Recognition.Zoltán Tóth László - manuscript
    Everything has mathematically expressible value. -/- The null hypothesis is that nothing, zero is a physical reality based mathematical conception which we can perceive as an energy, matter, information, space, time free state. Revealing as our common physical, mathematical, philosophical origin, a physical reality based mathematical reference point. I state that in proportion to this physical reality based sense(conception) everything has some kind of mathematically expressible value. Space, time, information, energy, matter.
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  24. added 2017-03-03
    A New Theorem Introduced by Piyush Goel with Four Proof(Piyush Theorem).Goel Piyush - 2016 - Edupediapublications 3:1-5.
    Abstract -/- Mathematics for Piyush is a Passion from his childhood he was so passionate about Mathematics used to play with Numbers draw figures and try to get sides distance one day I draw a AP SERIES Right Angle Triangle (thinking that the distance between the point of intersection of median & altitude at the base must be sum of rest sides that was in My Mind). And at last Piyush Succeed. This new Theorem proved with Four Proof (Trigonometry/Co-ordinates Geometry/Acute (...)
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  25. added 2017-03-03
    Aristotelianism in the Philosophy of Mathematics: A Journal of Analytic Scholasticism.James Franklin - 2011 - Studia Neoaristotelica 8 (1):3-15.
    Modern philosophy of mathematics has been dominated by Platonism and nominalism, to the neglect of the Aristotelian realist option. Aristotelianism holds that mathematics studies certain real properties of the world – mathematics is neither about a disembodied world of “abstract objects”, as Platonism holds, nor it is merely a language of science, as nominalism holds. Aristotle’s theory that mathematics is the “science of quantity” is a good account of at least elementarymathematics: the ratio of two heights, for example, is a (...)
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  26. added 2017-03-03
    Discourse on Method, Optics, Geometry, Meteorology, Translated by Paul J. Olscamp.Descartes René (ed.) - 1965 - New York: Bobbs-Merrill.
    René Descartes, Discourse on Method, Optics, Geometry, and Meteorology. Trans., with an Introduction, by Paul J. Olscamp. Indianapolis: The Bobbs-Merrill Co., 1965. Pp. xxxvi + 361. = The Library of Liberal Arts, 211. Paper, $2.25. -/- From the notice in Journal of the History of Philosophy 5 (1967), 311: "In the introduction, Professor Olscamp calls attention to the fact that Descartes intended the other three pieces in this volume to serve as examples of the method set forth in the Discourse. (...)
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  27. added 2017-03-02
    The Argument From Agreement and Mathematical Realism.Pieranna Garavaso - 1992 - Journal of Philosophical Research 17:173-187.
    Traditionally, in the philosophy of mathematics realists claim that mathematical objects exist independently of the human mind, whereas idealists regard them as mental constructions dependent upon human thought.It is tempting for realists to support their view by appeal to our widespread agreement on mathematical results. Roughly speaking, our agreement is explained by the fact that these results are about the same mathematical objects. It is alleged that the idealist’s appeal to mental constructions precludes any such explanation. I argue that realism (...)
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  28. added 2017-02-25
    C. S. Peirce and the Square Root of Minus One: Quaternions and a Complex Approach to Classes of Signs and Categorical Degeneration.Rafael Duarte Oliveira Venancio - 2017 - SSRN Electronic Journal 2017 (1):1-17.
    The beginning for C. S. Peirce was the reduction of the traditional categories in a list composed of a fundamental triad: quality, respect and representation. Thus, these three would be named as Firstness, Secondness and Thirdness, as well given the ability to degeneration. Here we show how this degeneration categorical is related to mathematical revolution which Peirce family, especially his father Benjamin Peirce, took part: the advent of quaternions by William Rowan Hamilton, a number system that extends the complex numbers, (...)
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  29. added 2017-02-24
    Knowledge of Abstract Objects in Physics and Mathematics.J. Shaffer Michael - forthcoming - Acta Analytica:1-13.
  30. added 2017-02-23
    Introduction.Salvatore Florio - 2017 - Philosophia Mathematica 25 (1):1-2.
    Introduction to a special issue on abstraction principles.
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  31. added 2017-02-23
    Structuralism and Isomorphism.C. McCarty - 2015 - Philosophia Mathematica 23 (1):1-10.
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  32. added 2017-02-23
    Shlomo Sternberg. Curvature in Mathematics and Physics. Mineola, N.Y.: Dover Publications, 2012. ISBN 978-0-486-47855-5. Pp. Ii + 405. [REVIEW]D. Kutach - 2014 - Philosophia Mathematica 22 (1):129-130.
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  33. added 2017-02-23
    Marco Panza and Andrea Sereni. Plato's Problem: An Introduction to Mathematical Platonism. London and New York: Palgrave Macmillan, 2013. Isbn 978-0-230-36548-3 ; 978-0-230-36549-0 ; 978-1-13726147-2 ; 978-1-13729813-3 . Pp. XI + 306. [REVIEW]J. R. Brown - 2014 - Philosophia Mathematica 22 (1):135-138.
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  34. added 2017-02-23
    David Papineau. Philosophical Devices: Proofs, Probabilities, Possibilities, and Sets. Oxford: Oxford University Press, 2012. Isbn 978-0-19965173-3. Pp. XIX + 224. [REVIEW]A. C. Paseau - 2014 - Philosophia Mathematica 22 (1):121-123.
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  35. added 2017-02-23
    PATRICIA A. BLANCHETTE. Frege's Conception of Logic. Oxford University Press, 2012. ISBN 978-0-19-926925-9 . Pp. Xv + 256. [REVIEW]R. T. Cook - 2014 - Philosophia Mathematica 22 (1):108-120.
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  36. added 2017-02-23
    LISA A. SHABEL. Mathematics in Kant's Critical Philosophy: Reflections on Mathematical Practice. Studies in Philosophy Outstanding Dissertations, Robert Nozick, Ed. New York & London: Routledge, 2003. ISBN 0-415-93955-0. Pp. 178. [REVIEW]R. Jagnow - 2007 - Philosophia Mathematica 15 (3):366-386.
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  37. added 2017-02-23
    Mending the Master: JOHN P. BURGESS, Fixing Frege. Princeton, N. J.: Princeton University Press, 2005. ISBN 0-691-12231-8. Pp. Xii + 257. [REVIEW]O. Linnebo - 2006 - Philosophia Mathematica 14 (3):338-400.
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  38. added 2017-02-23
    From Bayesianism to the Epistemic View of Mathematics: Richard Jeffrey. Subjective Probability: The Real Thing. Cambridge: Cambridge University Press, 2004. Isbn 0-521-82971-2 , 0-521-53668-5 . Pp. XVI + 124. [REVIEW]J. Williamson - 2006 - Philosophia Mathematica 14 (3):365-369.
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  39. added 2017-02-23
    Burgess on Plural Logic and Set Theory.O. Linnebo - 2006 - Philosophia Mathematica 15 (1):79-93.
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  40. added 2017-02-23
    Joan Weiner. Frege Explained: From Arithmetic to Analytic Philosophy. Chicago: Open Court, 2004. Pp. Xvi + 179. ISBN 0-8126-9460-0. [REVIEW]B. Michael - 2006 - Philosophia Mathematica 15 (1):126-128.
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  41. added 2017-02-23
    Critical Studies / Book Reviews.B. V. Kerkhove - 2004 - Philosophia Mathematica 12 (1):69-74.
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  42. added 2017-02-23
    Critical Studies/Book Reviews.O. Linnebo - 2003 - Philosophia Mathematica 11 (1):92-104.
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  43. added 2017-02-23
    John W. Dawson, Jr. Logical Dilemmas: The Life and Work of Kurt Gödel. Wellesley, Massachusetts: A. K. Peters, 1997. Pp. Xiv + 361. ISBN 1-56881-025-3. [REVIEW] Davis - 1998 - Philosophia Mathematica 6 (1):116-128.
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  44. added 2017-02-23
    The Non-Boolean Logic of Natural Language Negation.Reyes Marie la Palme, Macnamara John, E. Reyes Gonzalo & Zolfaghari Houman - 1994 - Philosophia Mathematica 2 (1):45-68.
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  45. added 2017-02-23
    Idola Foil Et Theatri.I. Fang - 1991 - Philosophia Mathematica 2:200-218.
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  46. added 2017-02-23
    Kant and Modern Mathematics.J. Fang - 1965 - Philosophia Mathematica 2:52-57.
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  47. added 2017-02-21
    Mark Colyvan. An Introduction to the Philosophy of Mathematics. Cambridge: Cambridge University Press, 2012. ISBN 978-0-521-82602-0 ; 978-0-521-53341-6 . Pp. Ix &Plus; 188: Critical Studies/Book Reviews. [REVIEW]Andrew David Irvine - 2014 - Philosophia Mathematica 22 (1):124-125.
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  48. added 2017-02-21
    Gregory H. Moore. Zermelo’s Axiom of Choice: Its Origins, Development, and Influence. Mineola, N.Y.: Dover Publications, 2013. ISBN 978-0-48648841-7 . Pp. 448: Critical Studies/Book Reviews. [REVIEW]John L. Bell - 2014 - Philosophia Mathematica 22 (1):131-134.
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  49. added 2017-02-21
    Gregory Landini. Zermelo and Russell’s Paradox: Is There a Universal Set?: Correction Notice.Gregory Landini - 2014 - Philosophia Mathematica 22 (1):142-142.
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  50. added 2017-02-21
    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 &Plus; 222†: Critical Studies/Book Reviews. [REVIEW]Stefania Centrone - 2014 - Philosophia Mathematica 22 (1):126-129.
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