Search results for 'mathematical Platonism' (try it on Scholar)

1000+ found
Sort by:
  1. Gilbert B. Côté (2013). Mathematical Platonism and the Nature of Infinity. Open Journal of Philosophy 3 (3):372-375.score: 240.0
    An analysis of the counter-intuitive properties of infinity as understood differently in mathematics, classical physics and quantum physics allows the consideration of various paradoxes under a new light (e.g. Zeno’s dichotomy, Torricelli’s trumpet, and the weirdness of quantum physics). It provides strong support for the reality of abstractness and mathematical Platonism, and a plausible reason why there is something rather than nothing in the concrete universe. The conclusions are far reaching for science and philosophy.
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  2. Charles Sayward (2002). Is an Unpictorial Mathematical Platonism Possible? Journal of Philosophical Research 27:199-212.score: 186.0
    In his book 'Wittgenstein on the foundations of Mathematics', Crispin Wright notes that remarkably little has been done to provide an unpictorial, substantial account of what mathematical platoninism comes to. Wright proposes to investigate whether there is not some more substantial doctrine than the familiar images underpinning the platonist view. He begins with the suggestion that the essential element in the platonist claim is that mathematical truth is objective. Although he does not demarcate them as such, Wright proposes (...)
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  3. Massimo Pigliucci (2011). Mathematical Platonism. Philosophy Now 84:47-47.score: 180.0
    Are numbers and other mathematical objects "out there" in some philosophically meaningful sense?
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  4. Øystein Linnebo (2006). Epistemological Challenges to Mathematical Platonism. Philosophical Studies 129 (3):545-574.score: 180.0
    Since Benacerraf’s “Mathematical Truth” a number of epistemological challenges have been launched against mathematical platonism. I first argue that these challenges fail because they unduely assimilate mathematics to empirical science. Then I develop an improved challenge which is immune to this criticism. Very roughly, what I demand is an account of how people’s mathematical beliefs are responsive to the truth of these beliefs. Finally I argue that if we employ a semantic truth-predicate rather than just a (...)
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  5. Jacques Bouveresse (2004). On the Meaning of the Word 'Platonism' in the Expression 'Mathematical Platonism'. Proceedings of the Aristotelian Society 105 (1):55–79.score: 180.0
    The expression 'platonism in mathematics' or 'mathematical platonism' is familiar in the philosophy of mathematics at least since the use Paul Bernays made of it in his paper of 1934, 'Sur le Platonisme dans les Mathématiques'. But he was not the first to point out the similarities between the conception of the defenders of mathematical realism and the ideas of Plato. Poincaré had already stressed the 'platonistic' orientation of the mathematicians he called'Cantorian', as opposed to those (...)
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  6. William J. Melanson (2011). Reassessing the Epistemological Challenge to Mathematical Platonism. Croatian Journal of Philosophy 11 (3):295-304.score: 180.0
    In his Realism, Mathematics, and Modality, Hartry Field attempted to revitalize the epistemological case against mathematical platontism by challenging mathematical platonists to explain how we could be epistemically reliable with regard to the abstract objects of mathematics. Field suggested that the seeming impossibility of providing such an explanation tends to undermine belief in the existence of abstract mathematical objects regardless of whatever reason we have for believing in their existence. After more than two decades, Field’s explanatory challenge (...)
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  7. Jacques Bouveresse (2005). III *-on the Meaning of the Word 'Platonism' in the Expression 'Mathematical Platonism'. Proceedings of the Aristotelian Society 105 (1):55-79.score: 180.0
    The expression 'platonism in mathematics' or 'mathematical platonism' is familiar in the philosophy of mathematics at least since the use Paul Bernays made of it in his paper of 1934, 'Sur le Platonisme dans les Math?matiques'. But he was not the first to point out the similarities between the conception of the defenders of mathematical realism and the ideas of Plato. Poincar? had already stressed the 'platonistic' orientation of the mathematicians he called 'Cantorian', as opposed to (...)
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  8. Colin McLarty (2005). `Mathematical Platonism' Versus Gathering the Dead: What Socrates Teaches Glaucon. Philosophia Mathematica 13 (2):115-134.score: 180.0
    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 (...)
    Direct download (12 more)  
     
    My bibliography  
     
    Export citation  
  9. James Robert Brown (2012/2011). Platonism, Naturalism, and Mathematical Knowledge. Routledge.score: 160.0
    Mathematical explanation -- What is naturalism? -- Perception, practice, and ideal agents: Kitcher's naturalism -- Just metaphor?: Lakoff's language -- Seeing with the mind's eye: the Platonist alternative -- Semi-naturalists and reluctant realists -- A life of its own?: Maddy and mathematical autonomy.
     
    My bibliography  
     
    Export citation  
  10. Colin Cheyne (1997). Getting in Touch with Numbers: Intuition and Mathematical Platonism. Philosophy and Phenomenological Research 57 (1):111-125.score: 156.0
    Mathematics is about numbers, sets, functions, etc. and, according to one prominent view, these are abstract entities lacking causal powers and spatio-temporal location. If this is so, then it is a puzzle how we come to have knowledge of such remote entities. One suggestion is intuition. But `intuition' covers a range of notions. This paper identifies and examines those varieties of intuition which are most likely to play a role in the acquisition of our mathematical knowledge, and argues that (...)
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  11. Vladimir Drekalović (forthcoming). Some Aspects of Understanding Mathematical Reality: Existence, Platonism, Discovery. Axiomathes:1-21.score: 156.0
    The sum of all objects of a science, the objects’ features and their mutual relations compose the reality described by that sense. The reality described by mathematics consists of objects such as sets, functions, algebraic structures, etc. Generally speaking, the use of terms reality and existence, in relation to describing various objects’ characteristics, usually implies an employment of physical and perceptible attributes. This is not the case in mathematics. Its reality and the existence of its objects, leaving aside its application, (...)
    No categories
    Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  12. Marco Panza (2013). Plato's Problem: An Introduction to Mathematical Platonism. Palgrave Macmillan.score: 154.0
  13. Mark Balaguer (2008). Mathematical Platonism. In Bonnie Gold & Roger Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy. Mathematical Association of America. 179--204.score: 152.0
     
    My bibliography  
     
    Export citation  
  14. Julian C. Cole, Mathematical Platonism. Internet Encyclopedia of Philosophy.score: 150.0
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  15. James Robert Brown (2013). 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 (Hbk); 978-0-230-36549-0 (Pbk); 978-1-13726147-2 (E-Book); 978-1-13729813-3 (Pdf). Pp. Xi + 306. [REVIEW] Philosophia Mathematica (1):nkt031.score: 150.0
  16. Berislav Žarnić (1999). Mathematical Platonism: From Objects to Patterns. Synthesis Philosophica 14 (1/2):53-64.score: 150.0
    Direct download  
     
    My bibliography  
     
    Export citation  
  17. John McDowell (1989). Mathematical Platonism and Dummettian Anti‐Realism. Dialectica 43 (1‐2):173-192.score: 150.0
    Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  18. Ulrich Blau (2009). The Self in Logical-Mathematical Platonism. Mind and Matter 7 (1):37-57.score: 150.0
    Direct download  
     
    My bibliography  
     
    Export citation  
  19. Anna Lemanska (2012). Remarks on Mathematical Platonism. Filozofia Nauki 20 (2).score: 150.0
     
    My bibliography  
     
    Export citation  
  20. Nicolas Pain (2011). Mathematical Platonism. In Michael Bruce & Steven Barbone (eds.), Just the Arguments: 100 of the Most Important Arguments in Western Philosophy. Wiley-Blackwell.score: 150.0
    Direct download  
     
    My bibliography  
     
    Export citation  
  21. Clevis Headley (1997). Platonism and Metaphor in the Texts of Mathematics: GöDel and Frege on Mathematical Knowledge. [REVIEW] Man and World 30 (4):453-481.score: 144.0
    In this paper, I challenge those interpretations of Frege that reinforce the view that his talk of grasping thoughts about abstract objects is consistent with Russell's notion of acquaintance with universals and with Gödel's contention that we possess a faculty of mathematical perception capable of perceiving the objects of set theory. Here I argue the case that Frege is not an epistemological Platonist in the sense in which Gödel is one. The contention advanced is that Gödel bases his (...) on a literal comparison between mathematical intuition and physical perception. He concludes that since we accept sense perception as a source of empirical knowledge, then we similarly should posit a faculty of mathematical intuition to serve as the source of mathematical knowledge. Unlike Gödel, Frege does not posit a faculty of mathematical intuition. Frege talks instead about grasping thoughts about abstract objects. However, despite his hostility to metaphor, he uses the notion of ‘grasping’ as a strategic metaphor to model his notion of thinking, i.e., to underscore that it is only by logically manipulating the cognitive content of mathematical propositions that we can obtain mathematical knowledge. Thus, he construes ‘grasping’ more as theoretical activity than as a kind of inner mental ‘seeing’. (shrink)
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  22. Øystein Linnebo (2009). Platonism in the Philosophy of Mathematics. In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy.score: 138.0
    Platonism about mathematics (or mathematical platonism) is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thought, and practices. In this survey article, the view is clarified and distinguished from some related views, and arguments for and against the view are discussed.
    Direct download  
     
    My bibliography  
     
    Export citation  
  23. Simon B. Duffy (2012). Badiou’s Platonism: The Mathematical Ideas of Post-Cantorian Set-Theory. In Sean Bowden & Simon B. Duffy (eds.), Badiou and Philosophy. Edinburgh University Press.score: 124.0
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  24. Charles Parsons (1995). Platonism and Mathematical Intuition in Kurt Gödel's Thought. Bulletin of Symbolic Logic 1 (1):44-74.score: 120.0
  25. Mark Mcevoy (2005). Mathematical Apriorism and Warrant: A Reliabilist-Platonist Account. Philosophical Forum 36 (4):399–417.score: 120.0
    Direct download (9 more)  
     
    My bibliography  
     
    Export citation  
  26. Emily Katz (2013). Aristotle's Critique of Platonist Mathematical Objects: Two Test Cases From Metaphysics M 2. Apeiron 46 (1):26-47.score: 120.0
  27. A. C. Paseau (2012). James Robert Brown. Platonism, Naturalism, and Mathematical Knowledge. New York and London: Routledge, 2012. Isbn 978-0-415-87266-9. Pp. X + 182. [REVIEW] Philosophia Mathematica 20 (3):359-364.score: 120.0
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  28. Michael D. Resnik (1989). A Naturalized Epistemology for a Platonist Mathematical Ontology. Philosophica 43.score: 120.0
    Direct download  
     
    My bibliography  
     
    Export citation  
  29. W. D. Hart (1987). Review: Paul Benacerraf, Mathematical Truth; Michael Jubien, Ontology and Mathematical Truth; Philip Kitcher, The Plight of the Platonist. [REVIEW] Journal of Symbolic Logic 52 (2):552-554.score: 120.0
    Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  30. B. Borstner (2002). Mathematical Structuralism is a Kind of Platonism. Filozofski Vestnik 23 (1):7-24.score: 120.0
  31. Bob Hale (2005). Mathematical Knowledge. A Defence of Modest and Sober Platonism. In Rene van Woudenberg, Sabine Roeser & Ron Rood (eds.), Basic Belief and Basic Knowledge. Ontos-Verlag. 4--107.score: 120.0
    No categories
     
    My bibliography  
     
    Export citation  
  32. M. Trobok (2000). Ante Rem Structuralism (Non-Traditional Platonism, Shapiro's Theory on Mathematical Objects). Filozofski Vestnik 21 (1):81-89.score: 120.0
     
    My bibliography  
     
    Export citation  
  33. Mark Balaguer (1998). Platonism and Anti-Platonism in Mathematics. Oxford University Press.score: 106.0
    In this book, Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He does this by establishing that both platonism and anti-platonism are defensible views. Introducing a form of platonism ("full-blooded platonism") that solves all problems traditionally associated with the view, he proceeds to defend anti-platonism (in particular, mathematical fictionalism) against various attacks, most notably the Quine-Putnam indispensability attack. He concludes by arguing that it is not simply that (...)
    Direct download  
     
    My bibliography  
     
    Export citation  
  34. Steven M. Duncan, Platonism by the Numbers.score: 96.0
    In this paper, I defend traditional Platonic mathematical realism from its contemporary detractors, arguing that numbers, understood as abstract, non-physical objects of rational intuition, are indispensable for the act of counting.
    Direct download  
     
    My bibliography  
     
    Export citation  
  35. Jonathan Tallant (2013). Optimus Prime: Paraphrasing Prime Number Talk. Synthese 190 (12):2065-2083.score: 90.0
    Baker (Mind 114:223–238, 2005; Brit J Philos Sci 60:611–633, 2009) has recently defended what he calls the “enhanced” version of the indispensability argument for mathematical Platonism. In this paper I demonstrate that the nominalist can respond to Baker’s argument. First, I outline Baker’s argument in more detail before providing a nominalistically acceptable paraphrase of prime-number talk. Second, I argue that, for the nominalist, mathematical language is used to express physical facts about the world. In endorsing this line (...)
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  36. Øystein Linnebo (forthcoming). Platonism in the Philosophy of Mathematics. Stanford Encyclopedia of Philosophy.score: 90.0
    Platonism about mathematics (or mathematical platonism) isthe metaphysical view that there are abstract mathematical objectswhose existence is independent of us and our language, thought, andpractices. Just as electrons and planets exist independently of us, sodo numbers and sets. And just as statements about electrons and planetsare made true or false by the objects with which they are concerned andthese objects' perfectly objective properties, so are statements aboutnumbers and sets. Mathematical truths are therefore discovered, notinvented., Existence. (...)
    Direct download  
     
    My bibliography  
     
    Export citation  
  37. Charles Sayward (2010). Dialogues Concerning Natural Numbers. Peter Lang.score: 90.0
    Two philosophical theories, mathematical Platonism and nominalism, are the background of six dialogues in this book. There are five characters in these dialogues: three are nominalists; the fourth is a Platonist; the main character is somewhat skeptical on most issues in the philosophy of mathematics, and is particularly skeptical regarding the two background theories.
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  38. Burt C. Hopkins (2012). De regreso a la fuente del platonismo en la filosofía de las matemáticas: la crítica de Aristóteles a los números eidéticos. Areté. Revista de Filosofía 22 (1):27-50.score: 90.0
    De acuerdo con la así llamada concepción platonista de la naturaleza de las entidades matemáticas, las afirmaciones matemáticas son análogas a las afirmaciones acerca de objetos físicos reales y sus relaciones, con la diferencia decisiva de que las entidades matemáticas no son ni físicas ni espacio temporalmente individuales, y, por tanto, no son percibidas sensorialmente. El platonismo matemático es, por lo tanto, de la misma índole que el platonismo en general, el cual postula la tesis de un mundo ideal de (...)
    No categories
    Translate to English
    | Direct download (10 more)  
     
    My bibliography  
     
    Export citation  
  39. Mark Balaguer (1995). A Platonist Epistemology. Synthese 103 (3):303 - 325.score: 84.0
    A response is given here to Benacerraf's 1973 argument that mathematical platonism is incompatible with a naturalistic epistemology. Unlike almost all previous platonist responses to Benacerraf, the response given here is positive rather than negative; that is, rather than trying to find a problem with Benacerraf's argument, I accept his challenge and meet it head on by constructing an epistemology of abstract (i.e., aspatial and atemporal) mathematical objects. Thus, I show that spatio-temporal creatures like ourselves can attain (...)
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  40. Chris Daly & Simon Langford (2011). Two Anti-Platonist Strategies. Mind 119 (476):1107-1116.score: 84.0
    This paper considers two strategies for undermining indispensability arguments for mathematical Platonism. We defend one strategy (the Trivial Strategy) against a criticism by Joseph Melia. In particular, we argue that the key example Melia uses against the Trivial Strategy fails. We then criticize Melia’s chosen strategy (the Weaseling Strategy.) The Weaseling Strategy attempts to show that it is not always inconsistent or irrational knowingly to assert p and deny an implication of p . We argue that Melia’s case (...)
    Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  41. Richard Tieszen (2010). Mathematical Problem-Solving and Ontology: An Exercise. [REVIEW] Axiomathes 20 (2-3):295-312.score: 84.0
    In this paper the reader is asked to engage in some simple problem-solving in classical pure number theory and to then describe, on the basis of a series of questions, what it is like to solve the problems. In the recent philosophy of mind this “what is it like” question is one way of signaling a turn to phenomenological description. The description of what it is like to solve the problems in this paper, it is argued, leads to several morals (...)
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  42. David Sherry (2009). The Role of Diagrams in Mathematical Arguments. Foundations of Science 14 (1-2):59-74.score: 84.0
    Recent accounts of the role of diagrams in mathematical reasoning take a Platonic line, according to which the proof depends on the similarity between the perceived shape of the diagram and the shape of the abstract object. This approach is unable to explain proofs which share the same diagram in spite of drawing conclusions about different figures. Saccheri’s use of the bi-rectangular isosceles quadrilateral in Euclides Vindicatus provides three such proofs. By forsaking abstract objects it is possible to give (...)
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  43. Elijah Chudnoff (2014). Intuition in Mathematics. In Barbara Held & Lisa Osbeck (eds.), Rational Intuition. Cambridge University Press.score: 82.0
    The literature on mathematics suggests that intuition plays a role in it as a ground of belief. This article explores the nature of intuition as it occurs in mathematical thinking. Section 1 suggests that intuitions should be understood by analogy with perceptions. Section 2 explains what fleshing out such an analogy requires. Section 3 discusses Kantian ways of fleshing it out. Section 4 discusses Platonist ways of fleshing it out. Section 5 sketches a proposal for resolving the main problem (...)
    Direct download  
     
    My bibliography  
     
    Export citation  
  44. Juha Saatsi (2012). Mathematics and Program Explanations. Australasian Journal of Philosophy 90 (3):579-584.score: 76.0
    Aidan Lyon has recently argued that some mathematical explanations of empirical facts can be understood as program explanations. I present three objections to his argument.
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  45. Richard L. Tieszen (2011). After Gödel: Platonism and Rationalism in Mathematics and Logic. Oxford University Press.score: 72.0
    Gödel's relation to the work of Plato, Leibniz, Kant, and Husserl is examined, and a new type of platonic rationalism that requires rational intuition, called ...
    Direct download  
     
    My bibliography  
     
    Export citation  
  46. Donald Gillies (2010). Informational Realism and World 3. Knowledge, Technology and Policy 23 (1-2):7-24.score: 72.0
    This paper takes up a suggestion made by Floridi that the digital revolution is bringing about a profound change in our metaphysics. The paper aims to bring some older views from philosophy of mathematics to bear on this problem. The older views are concerned principally with mathematical realism—that is the claim that mathematical entities such as numbers exist. The new context for the discussion is informational realism, where the problem shifts to the question of the reality of information. (...)
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  47. Ricardo Da Silva (2013). Un acercamiento al platonismo absoluto de Cantor. Apuntes Filosóficos 22 (42).score: 72.0
    Hacia finales del siglo XIX se llevó a cabo una gran revolución conceptual y metodológica en la matemática. En tal revolución se empezaron a emplear conceptos, métodos y técnicas que dejaban de lado la antigua forma de hacer matemática, propia del siglo XVIII y principios del siglo XIX, y a su vez proponían un Hacer abstracto, es decir, una forma abstracta de ocuparse del ente matemático. Pero no sólo se trataba de un cambio metodológico, sino que la pregunta por los (...)
    No categories
    Translate to English
    | Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  48. Nicholas Maxwell (2010). Wisdom Mathematics. Friends of Wisdom Newsletter (6):1-6.score: 68.0
    For over thirty years I have argued that all branches of science and scholarship would have both their intellectual and humanitarian value enhanced if pursued in accordance with the edicts of wisdom-inquiry rather than knowledge-inquiry. I argue that this is true of mathematics. Viewed from the perspective of knowledge-inquiry, mathematics confronts us with two fundamental problems. (1) How can mathematics be held to be a branch of knowledge, in view of the difficulties that view engenders? What could mathematics be knowledge (...)
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  49. Colin Cheyne & Charles R. Pigden (1996). Pythagorean Powers or a Challenge to Platonism. Australasian Journal of Philosophy 74 (4):639 – 645.score: 66.0
    The Quine/Putnam indispensability argument is regarded by many as the chief argument for the existence of platonic objects. We argue that this argument cannot establish what its proponents intend. The form of our argument is simple. Suppose indispensability to science is the only good reason for believing in the existence of platonic objects. Either the dispensability of mathematical objects to science can be demonstrated and, hence, there is no good reason for believing in the existence of platonic objects, or (...)
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  50. Krzysztof Wójtowicz (1998). Unification of Mathematical Theories. Foundations of Science 3 (2):207-229.score: 66.0
    In this article the problem of unification of mathematical theories is discussed. We argue, that specific problems arise here, which are quite different than the problems in the case of empirical sciences. In particular, the notion of unification depends on the philosophical standpoint. We give an analysis of the notion of unification from the point of view of formalism, Gödel's platonism and Quine's realism. In particular we show, that the concept of “having the same object of study” should (...)
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
1 — 50 / 1000