About this topic
Summary Mathematical platonism is the view on which mathematical objects exist and are abstract (aspatial, atemporal and acausal) and independent of human minds and linguistic practices. According to mathematical platonism, mathematical theories are true in virtue of those objects possessing (or not) certain properties. One important challenge to platonism is explaining how biological organisms such as human beings could have knowledge of such objects. Another is to explain why mathematical theories about such objects should turn out to be applicable in sciences concerned with the physical world. 
Key works One of the most famous platonists was Frege (see e.g. Frege & Beaney 1997) and his line of thought is currently continued by neologicists (Wright 1983Wright & Hale 2001). Other famous platonists were Quine 2004 and Gödel 1947. Another group of platonists are structuralists, see the category summary for mathematical structuralism.
Introductions It's good to start with Linnebo 2009 and references therein. 
Related categories

400 found
Order:
1 — 50 / 400
  1. added 2020-03-30
    How Can Mathematical Objects Be Real but Mind-Dependent?Hazhir Roshangar - manuscript
    Taking mathematics as a language based on empirical experience, I argue for an account of mathematics in which its objects are abstracta that describe and communicate the structure of reality based on some of our ancestral interactions with their environment. I argue that mathematics as a language is mostly invented, and it is mind-dependent in a specific sense. However, the bases of mathematics will characterize it as a real, non-fictional science of structures.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  2. added 2020-02-21
    The Ontology of Number.Jeremy Horne - manuscript
    What is a number? Answering this will answer questions about its philosophical foundations - rational numbers, the complex numbers, imaginary numbers. If we are to write or talk about something, it is helpful to know whether it exists, how it exists, and why it exists, just from a common-sense point of view [Quine, 1948, p. 6]. Generally, there does not seem to be any disagreement among mathematicians, scientists, and logicians about numbers existing in some way, but currently, in the mainstream (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  3. added 2020-02-12
    Platonism and Anti-Platonism in Mathematics.Matthew McGrath - 2001 - Philosophy and Phenomenological Research 63 (1):239-242.
    Mark Balaguer has written a provocative and original book. The book is as ambitious as a work of philosophy of mathematics could be. It defends both of the dominant views concerning the ontology of mathematics, Platonism and Anti-Platonism, and then closes with an argument that there is no fact of the matter which is right.
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   84 citations  
  4. added 2020-02-07
    How to Make Reflectance a Surface Property.Nicholas Danne - forthcoming - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics.
    Reflectance physicalists define reflectance as the intrinsic disposition of a surface to reflect light at a given efficiency per wavelength. I criticize a leading account of dispositional reflectance for failing to account for what I call 'harmonic dispersion', the inverse relationship of a light pulse's duration to its bandwidth. I argue that harmonic dispersion renders reflectance defined in terms of light pulses an extrinsic disposition. Reflectance defined as the per-wavelength efficiency to reflect the superimposed, infinite-duration, Fourier harmonics of pulses can (...)
    Remove from this list   Direct download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  5. added 2020-02-04
    A Dilemma for Mathematical Constructivism.Samuel Kahn - 2020 - Axiomathes:01-10.
    In this paper I argue that constructivism in mathematics faces a dilemma. In particular, I maintain that constructivism is unable to explain (i) the application of mathematics to nature and (ii) the intersubjectivity of mathematics unless (iii) it is conjoined with two theses that reduce it to a form of mathematical Platonism. The paper is divided into five sections. In the first section of the paper, I explain the difference between mathematical constructivism and mathematical Platonism and I outline my argument. (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  6. added 2020-01-28
    Ptolemy’s Philosophy: Mathematics as a Way of Life. By Jacqueline Feke. Princeton: Princeton University Press, 2018. Pp. Xi + 234. [REVIEW]Nicholas Danne - 2020 - Metaphilosophy 51 (1):151-155.
  7. added 2020-01-28
    Visa to Heaven: Orpheus, Pythagoras, and Immortality.Alex V. Halapsis - 2016 - ScienceRise 25 (8):60-65.
    The article deals with the doctrines of Orpheus and Pythagoras about the immortality of the soul in the context of the birth of philosophy in ancient Greece. Orpheus demonstrated the closeness of heavenly (divine) and earthly (human) worlds, and Pythagoras mathematically proved their fundamental identity. Greek philosophy was “an investment in the afterlife future”, being the product of the mystical (Orpheus) and rationalist (Pythagoras) theology.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  8. added 2020-01-28
    Number and Reality: Sources of Scientific Knowledge.Alex V. Halapsis - 2016 - ScienceRise 23 (6):59-64.
    Pythagoras’s number doctrine had a great effect on the development of science. Number – the key to the highest reality, and such approach allowed Pythagoras to transform mathematics from craft into science, which continues implementation of its project of “digitization of being”. Pythagoras's project underwent considerable transformation, but it only means that the plan in knowledge is often far from result.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  9. added 2020-01-22
    Gonit Dorshon.Avijit Lahiri - manuscript
    This article briefly reviews a few of the major points of view toward mathematics and the world of mathematical entities, and interprets the philosophy of mathematics as an interaction between these. The existence of these different points of view is indicative that mathematics, in spite of being of universal validity, can nevertheless accommodate alternatives. In particular, I review the alternative viewpoints of Platonism and Intuitionism and present the case that in spite of their great differences, they are not mutually exclusive (...)
    Remove from this list   Direct download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  10. added 2019-12-19
    Einführung in die Philosophie der Mathematik.Jörg Neunhäuserer - 2019 - Wiesbaden, Deutschland: Springer Spektrum.
    Welche Art von Gegenständen untersucht die Mathematik und in welchem Sinne existieren diese Gegenstände? Warum dürfen wir die Aussagen der Mathematik zu unserem Wissen zählen und wie lassen sich diese Aussagen rechtfertigen? Eine Philosophie der Mathematik versucht solche Fragen zu beantworten. In dieser Einführung stellen wir maßgeblichen Positionen in der Philosophie der Mathematik vor und formulieren die Essenz dieser Positionen in möglichst einfachen Thesen. Der Leser erfährt, auf welche Philosophen eine Position zurückgeht und in welchem historischen Kontext diese entstand. Ausgehend (...)
    Remove from this list   Direct download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  11. added 2019-12-11
    A Geneticist's Roadmap to Sanity.Gilbert B. Côté - manuscript
    World news can be discouraging these days. In order to counteract the effects of fake news and corruption, scientists have a duty to present the truth and propose ethical solutions acceptable to the world at large. -/- By starting from scratch, we can lay down the scientific principles underlying our very existence, and reach reasonable conclusions on all major topics including quantum physics, infinity, timelessness, free will, mathematical Platonism, happiness, ethics and religion, all the way to creation and a special (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  12. added 2019-11-29
    Reseña de 'The Outer Limits of Reason' por Noson Yanofsky 403p (2013).Michael Richard Starks - 2019 - In Observaciones Sobre Imposibilidad, Incompleta, Paracoherencia,Indecisión,Aleatoriedad, Computabilidad, Paradoja E Incertidumbre En Chaitin, Wittgenstein, Hofstadter, Wolpert, Doria, Dacosta, Godel, Searle, Rodych, Berto,Floyd, Moyal-Sharrock Y Yanofsky. Las Vegas, NV USA: Reality Press. pp. 71-90.
    Doy una revisión detallada de ' los límites externos de la razón ' por Noson Yanofsky desde una perspectiva unificada de Wittgenstein y la psicología evolutiva. Yo indiqué que la dificultad con cuestiones como la paradoja en el lenguaje y las matemáticas, la incompletitud, la indeterminación, la computabilidad, el cerebro y el universo como ordenadores, etc., surgen de la falta de mirada cuidadosa a nuestro uso del lenguaje en el adecuado contexto y, por tanto, el Error al separar los problemas (...)
    Remove from this list   Direct download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  13. added 2019-11-22
    Why Do Certain States of Affairs Call Out for Explanation? A Critique of Two Horwichian Accounts.Dan Baras - 2018 - Philosophia 47 (5):1405-1419.
    Motivated by examples, many philosophers believe that there is a significant distinction between states of affairs that are striking and therefore call for explanation and states of affairs that are not striking. This idea underlies several influential debates in metaphysics, philosophy of mathematics, normative theory, philosophy of modality, and philosophy of science but is not fully elaborated or explored. This paper aims to address this lack of clear explanation first by clarifying the epistemological issue at hand. Then it introduces an (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  14. added 2019-11-16
    The Problem of Fregean Equivalents.Joongol Kim - 2019 - Dialectica 73 (3):367-394.
    It would seem that some statements like ‘There are exactly four moons of Jupiter’ and ‘The number of moons of Jupiter is four’ have the same truth-conditions and yet differ in ontological commitment. One strategy to resolve this paradoxical phenomenon is to insist that the statements have not only the same truth-conditions but also the same ontological commitments; the other strategy is to reject the presumption that they have the same truth-conditions. This paper critically examines some popular versions of these (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  15. added 2019-11-15
    Counterfactual Scheming.Sam Baron - 2020 - Mind 129 (514):535-562.
    Mathematics appears to play a genuine explanatory role in science. But how do mathematical explanations work? Recently, a counterfactual approach to mathematical explanation has been suggested. I argue that such a view fails to differentiate the explanatory uses of mathematics within science from the non-explanatory uses. I go on to offer a solution to this problem by combining elements of the counterfactual theory of explanation with elements of a unification theory of explanation. The result is a theory according to which (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  16. added 2019-11-15
    Mathematical Explanation by Law.Sam Baron - 2019 - British Journal for the Philosophy of Science 70 (3):683-717.
    Call an explanation in which a non-mathematical fact is explained—in part or in whole—by mathematical facts: an extra-mathematical explanation. Such explanations have attracted a great deal of interest recently in arguments over mathematical realism. In this article, a theory of extra-mathematical explanation is developed. The theory is modelled on a deductive-nomological theory of scientific explanation. A basic DN account of extra-mathematical explanation is proposed and then redeveloped in the light of two difficulties that the basic theory faces. The final view (...)
    Remove from this list   Direct download (7 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  17. added 2019-11-15
    How Mathematics Can Make a Difference.Sam Baron, Mark Colyvan & David Ripley - 2017 - Philosophers' Imprint 17.
    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.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   16 citations  
  18. added 2019-09-22
    Mathematical Creation in Frege's Grundgesetze.Philip A. Ebert & Marcus Rossberg - 2019 - In Philip A. Ebert & Marcus Rossberg (eds.), Essays on Frege's Basic Laws of Arithmetic. Oxford: Oxford University Press. pp. 325-342.
  19. added 2019-09-20
    Platonistic Physicalism Without Tears.D. G. Witmer - 2017 - Journal of Consciousness Studies 24 (9-10):72-90.
    Susan Schneider argues that the entities to be identified as part of the 'physical base' for physicalism must be in part abstract and that this fact either falsifies physicalism or renders it so problematic as to be 'no physicalism worth having'. I accept the abstractness of the entities but argue both that physicalism is consistent with such and that none of the alleged problems for Platonistic physicalism are serious.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  20. added 2019-09-16
    Hitting a Moving Target: Gödel, Carnap, and Mathematics as Logical Syntax.Gregory Lavers - 2019 - Philosophia Mathematica 27 (2):219-243.
    From 1953 to 1959 Gödel worked on a response to Carnap’s philosophy of mathematics. The drafts display Gödel’s familiarity with Carnap’s position from The Logical Syntax of Language, but they received a dismissive reaction on their eventual, posthumous, publication. Gödel’s two principal points, however, will here be defended. Gödel, though, had wished simply to append a few paragraphs to show that the same arguments apply to Carnap’s later views. Carnap’s position, however, had changed significantly in the intervening years, and to (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  21. added 2019-09-09
    Alain Badiou : un philosophe face au concept de modèle.Franck Varenne - 2008 - Natures Sciences Sociétés 16 (3):252-257.
    In 1969, the influent French philosopher Alain Badiou published a book called "The concept of Model: An Introduction to the Materialist Epistemology of Mathematics". A recent reprint gives the opportunity to trace back and analyze its main arguments. This paper essentially aims to present and explain Badiou's arguments against the representationalist vision of models in empirical sciences and for a materialist interpretation of formal systems coupled with semantic models in mathematics. Now that the practices of scientific modeling and simulation have (...)
    Remove from this list   Direct download (3 more)  
    Translate
     
     
    Export citation  
     
    Bookmark  
  22. added 2019-09-05
    Mathematicians and Their Gods: Interactions Between Mathematics and Religious Beliefs.Snezana Lawrence & Mark McCartney (eds.) - 2015 - Oxford: Oxford University Press UK.
    To open a newspaper or turn on the television it would appear that science and religion are polar opposites - mutually exclusive bedfellows competing for hearts and minds. There is little indication of the rich interaction between religion and science throughout history, much of which continues today. From ancient to modern times, mathematicians have played a key role in this interaction. This is a book on the relationship between mathematics and religious beliefs. It aims to show that, throughout scientific history, (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  23. added 2019-08-14
    Mathematical and Moral Disagreement.Silvia Jonas - 2020 - Philosophical Quarterly 70 (279):302-327.
    The existence of fundamental moral disagreements is a central problem for moral realism and has often been contrasted with an alleged absence of disagreement in mathematics. However, mathematicians do in fact disagree on fundamental questions, for example on which set-theoretic axioms are true, and some philosophers have argued that this increases the plausibility of moral vis-à-vis mathematical realism. I argue that the analogy between mathematical and moral disagreement is not as straightforward as those arguments present it. In particular, I argue (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  24. added 2019-06-24
    The Uncanny Accuracy of God's Mathematical Beliefs.Robert Knowles - forthcoming - Religious Studies.
    I show how mathematical platonism combined with belief in the God of classical theism can respond to Field's epistemological objection. I defend an account of divine mathematical knowledge by showing that it falls out of an independently motivated general account of divine knowledge. I use this to explain the accuracy of God's mathematical beliefs, which in turn explains the accuracy of our own. My arguments provide good news for theistic platonists, while also shedding new light on Field's influential objection.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  25. added 2019-06-12
    Mathematical Explanations and the Piecemeal Approach to Thinking About Explanation.Gabriel Târziu - 2018 - Logique Et Analyse 61 (244):457-487.
    A new trend in the philosophical literature on scientific explanation is that of starting from a case that has been somehow identified as an explanation and then proceed to bringing to light its characteristic features and to constructing an account for the type of explanation it exemplifies. A type of this approach to thinking about explanation – the piecemeal approach, as I will call it – is used, among others, by Lange (2013) and Pincock (2015) in the context of their (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  26. added 2019-06-12
    Can We Have Mathematical Understanding of Physical Phenomena?Gabriel Târziu - 2018 - Theoria : An International Journal for Theory, History and Fundations of Science 33 (1):91-109.
    Can mathematics contribute to our understanding of physical phenomena? One way to try to answer this question is by getting involved in the recent philosophical dispute about the existence of mathematical explanations of physical phenomena. If there is such a thing, given the relation between explanation and understanding, we can say that there is an affirmative answer to our question. But what if we do not agree that mathematics can play an explanatory role in science? Can we still consider that (...)
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  27. added 2019-06-12
    Importance and Explanatory Relevance: The Case of Mathematical Explanations.Gabriel Târziu - 2018 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 49 (3):393-412.
    A way to argue that something plays an explanatory role in science is by linking explanatory relevance with importance in the context of an explanation. The idea is deceptively simple: a part of an explanation is an explanatorily relevant part of that explanation if removing it affects the explanation either by destroying it or by diminishing its explanatory power, i.e. an important part is an explanatorily relevant part. This can be very useful in many ontological debates. My aim in this (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  28. added 2019-06-06
    Xavier Sabatier. Les Formes du Réalisme Mathématique. Paris: Vrin, 2009. ISBN 978-2-7116-2193-4. Pp. 304: Critical Studies/Book Reviews. [REVIEW]André Lebel - 2011 - Philosophia Mathematica 19 (1):95-103.
    The book under review discusses the most standard forms of mathematical realism, a.k.a. ‘Platonism’, elaborated in the mainstream of twentieth-century philosophy of mathematics. Its purpose is therefore to introduce franco phone readers to an important set of ideas that have been, for the most part, cultivated by analytic philosophers. It originates from a doctoral dissertation at Université Paris 1. It comprises 287 pages of text divided into four main parts, completed by an eight-page bibliography. Beginning with Frege, Russell, and Gödel, (...)
    Remove from this list   Direct download (7 more)  
     
    Export citation  
     
    Bookmark  
  29. added 2019-06-06
    Review of C. S. Jenkins, Grounding Concepts: An Empirical Basis for Arithmetical Knowledge[REVIEW]Neil Tennant - 2010 - Philosophia Mathematica 18 (3):360-367.
    This book is written so as to be ‘accessible to philosophers without a mathematical background’. The reviewer can assure the reader that this aim is achieved, even if only by focusing throughout on just one example of an arithmetical truth, namely ‘7+5=12’. This example’s familiarity will be reassuring; but its loneliness in this regard will not. Quantified propositions — even propositions of Goldbach type — are below the author’s radar.The author offers ‘a new kind of arithmetical epistemology’, one which ‘respects (...)
    Remove from this list   Direct download (7 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  30. added 2019-06-06
    Platonism: An Atrium to Christianity.Alice von Hilderbrand - 2007 - Logos: A Journal of Catholic Thought and Culture 10 (2):29-37.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  31. added 2019-06-06
    ‘Mathematical Platonism’ Versus Gathering the Dead: What Socrates Teaches Glaucon &Dagger.Colin McLarty - 2005 - Philosophia Mathematica 13 (2):115-134.
    Glaucon in Plato's _Republic_ fails to grasp intermediates. He confuses pursuing a goal with achieving it, and so he adopts ‘mathematical platonism’. He says mathematical objects are eternal. Socrates urges a seriously debatable, and seriously defensible, alternative centered on the destruction of hypotheses. He offers his version of geometry and astronomy as refuting the charge that he impiously ‘ponders things up in the sky and investigates things under the earth and makes the weaker argument the stronger’. We relate his account (...)
    Remove from this list   Direct download (9 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  32. added 2019-06-06
    Questioning Platonism: Continental Interpretations of Plato. [REVIEW]Christopher Roberts - 2005 - Graduate Faculty Philosophy Journal 26 (1):219-223.
    Given the history between us, it appears that any serious interpretation of Plato’s philosophy must now be prepared to answer questions such as: Which characters speak for Plato? When are their words really his? Did Plato’s philosophy develop as he grew older in years? And, of course, Why did Plato write dialogues? If one perseveres long enough, a question that has caused many lengthy and passionate responses cannot be avoided: Was Plato a Platonist? It seems as if all interpretations of (...)
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  33. added 2019-06-06
    Platonism, Metaphor, and Mathematics.Glenn G. Parsons And James Robert Brown - 2004 - Dialogue 43 (1):47-66.
    Contemporary analytic philosophy recognizes few principled constraints on its subject matter. When other disciplines also lay claim to a particular topic, however, important questions arise concerning the relation between these other disciplines and philosophy. A case in point is mathematics: traditional philosophy of mathematics defines a set of problems and certain general answers to those problems. However, mathematics is a subject matter that can be studied in many other ways: historically, sociologically, or even aesthetically, for example. Given this, we may (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  34. added 2019-06-06
    Patterns in the Philosophy of Mathematics.Rieger Adam - 2002 - Philosophical Quarterly 52 (207):247-255.
    Mathematics as a Science of Patterns . By Michael D. Resnik. (Oxford: Clarendon Press, 1997. Pp. xiii + 285. Price £35.00.) Naturalism in Mathematics . By Penelope Maddy. (Oxford: Clarendon Press, 1998. Pp. viii + 254. Price £32.50.) Realistic Rationalism . By Jerrold J. Katz. ( MIT Press, 1998. Pp. xxxiv + 226. Price £22.50.) The Principles of Mathematics Revisited . By Jaakko Hintikka. ( Cambridge UP, 1996. Pp. xii + 288. Price £40.00.).
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  35. added 2019-06-06
    Practical Reason and Mathematical Argument.John O'Neill - 1998 - Studies in History and Philosophy of Science Part A 29 (2):195-205.
  36. added 2019-06-06
    Benacerraf's Dilemma.W. D. Hart - 1991 - Critica 23 (68):87-103.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  37. added 2019-06-06
    Scientific Platonism.Brian Ellis - 1991 - Studies in History and Philosophy of Science Part A 23 (4):665-679.
  38. added 2019-06-06
    Platonism and Anti-Platonism in Nicholas of Cusa’s Philosophy of Mathematics.Vittorio Hösle - 1990 - Graduate Faculty Philosophy Journal 13 (2):79-112.
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  39. added 2019-06-06
    The Roots of Contemporary Platonism.Penelope Maddy - 1989 - Journal of Symbolic Logic 54 (4):1121-1144.
    Though many working mathematicians embrace a rough and ready form of Platonism, that venerable position has suffered a checkered philosophical career. Indeed the three schools of thought with which most of us began our official philosophizing about mathematics—Intuitionism, Formalism, and Logicism—all stand in fundamental disagreement with Platonism. Nevertheless, various versions of Platonistic thinking survive in contemporary philosophical circles. The aim of this paper is to describe these views, and, as my title suggests, to trace their roots.I'll begin with some preliminary (...)
    Remove from this list   Direct download (8 more)  
     
    Export citation  
     
    Bookmark   11 citations  
  40. added 2019-06-06
    Mathematical Naturalism: An Anthropological Perspective.Stephen Pollard & Robert Bates Graber - 1989 - Southern Journal of Philosophy 27 (3):427-441.
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  41. added 2019-06-06
    Husserl and Realism in Logic and Mathematics.Dermot Moran - 1986 - Philosophical Studies 31:361-365.
  42. added 2019-06-06
    Frege and the Philosophy of Mathematics. [REVIEW]B. J. - 1981 - Review of Metaphysics 35 (1):160-161.
    Are the truths of arithmetic analytic, as Frege insisted in opposition to Kant? Although bits and pieces of an adequate answer to the question are doubtless to be found scattered throughout the literature, one continues to be disappointed by the absence of any extended treatment of the issue that would undertake to digest the rich body of diverse material that has accumulated since the publication of Frege's Begriffsschrift in 1879.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  43. added 2019-06-06
    Platonism, Neo-Platonism and Thomism: Convergencies and Divergencies.Cornelio Fabro - 1970 - New Scholasticism 44 (1):69-100.
  44. added 2019-06-05
    Realism in Mathematics. Penelope Maddy.Jill Dieterle & Stewart Shapiro - 1993 - Philosophy of Science 60 (4):659-660.
  45. added 2019-05-28
    The Enhanced Indispensability Argument, the Circularity Problem, and the Interpretability Strategy.Jan Heylen & Lars Arthur Tump - forthcoming - Synthese:1-13.
    Within the context of the Quine–Putnam indispensability argument, one discussion about the status of mathematics is concerned with the ‘Enhanced Indispensability Argument’, which makes explicit in what way mathematics is supposed to be indispensable in science, namely explanatory. If there are genuine mathematical explanations of empirical phenomena, an argument for mathematical platonism could be extracted by using inference to the best explanation. The best explanation of the primeness of the life cycles of Periodical Cicadas is genuinely mathematical, according to Baker (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  46. added 2019-05-14
    How Does God Know That 2 + 2 = 4?Andrew Brenner - forthcoming - Religious Studies:1-16.
    Sometimes theists wonder how God's beliefs track particular portions of reality, e.g. contingent states of affairs, or facts regarding future free actions. In this article I sketch a general model for how God's beliefs track reality. God's beliefs track reality in much the same way that propositions track reality, namely via grounding. Just as the truth values of true propositions are generally or always grounded in their truthmakers, so too God's true beliefs are grounded in the subject matters of those (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  47. added 2019-04-06
    Animal Cognition, Species Invariantism, and Mathematical Realism.Helen De Cruz - 2019 - In Andrew Aberdein & Matthew Inglis (eds.), Advances in Experimental Philosophy of Logic and Mathematics. London: Bloomsbury Academic. pp. 39-61.
    What can we infer from numerical cognition about mathematical realism? In this paper, I will consider one aspect of numerical cognition that has received little attention in the literature: the remarkable similarities of numerical cognitive capacities across many animal species. This Invariantism in Numerical Cognition (INC) indicates that mathematics and morality are disanalogous in an important respect: proto-moral beliefs differ substantially between animal species, whereas proto-mathematical beliefs (at least in the animals studied) seem to show more similarities. This makes moral (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  48. added 2019-03-26
    Thin Objects.Øystein Linnebo - 2018 - Oxford: Oxford University Press.
    Are there objects that are “thin” in the sense that their existence does not make a substantial demand on the world? Frege famously thought so. He claimed that the equinumerosity of the knives and the forks suffices for there to be objects such as the number of knives and the number of forks, and for these objects to be identical. The idea of thin objects holds great philosophical promise but has proved hard to explicate. This book attempts to develop the (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   5 citations  
  49. added 2019-03-07
    Another Fine Footnote to Plato: Sam Cowling: Abstract Entities. Milton Park, UK and New York: Routledge, X+281pp, £31.99 PB.James Brown - 2018 - Metascience 27 (3):477-480.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  50. added 2019-02-22
    Platonism in Lotze and Frege Between Psyschologism and Hypostasis.Nicholas Stang - 2019 - In Sandra Lapointe (ed.), Logic from Kant to Russell. Routledge. pp. 138–159.
    In the section “Validity and Existence in Logik, Book III,” I explain Lotze’s famous distinction between existence and validity in Book III of Logik. In the following section, “Lotze’s Platonism,” I put this famous distinction in the context of Lotze’s attempt to distinguish his own position from hypostatic Platonism and consider one way of drawing the distinction: the hypostatic Platonist accepts that there are propositions, whereas Lotze rejects this. In the section “Two Perspectives on Frege’s Platonism,” I argue that this (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
1 — 50 / 400