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

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  1. Gilbert B. Côté (2013). Mathematical Platonism and the Nature of Infinity. Open Journal of Philosophy 3 (3):372-375.
    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.
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  2. Øystein Linnebo (2006). Epistemological Challenges to Mathematical Platonism. Philosophical Studies 129 (3):545-574.
    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 (...)
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  3.  23
    Mark Mcevoy (2005). Mathematical Apriorism and Warrant: A Reliabilist-Platonist Account. Philosophical Forum 36 (4):399–417.
    Mathematical apriorism holds that mathematical truths must be established using a priori processes. Against this, it has been argued that apparently a priori mathematical processes can, under certain circumstances, fail to warrant the beliefs they produce; this shows that these warrants depend on contingent features of the contexts in which they are used. They thus cannot be a priori. -/- In this paper I develop a position that combines a reliabilist version of mathematical apriorism with a (...)
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  4.  13
    Charles Sayward (2002). Is an Unpictorial Mathematical Platonism Possible? Journal of Philosophical Research 27:199-212.
    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 (...)
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  5. Massimo Pigliucci (2011). Mathematical Platonism. Philosophy Now 84:47-47.
    Are numbers and other mathematical objects "out there" in some philosophically meaningful sense?
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  6.  23
    Colin McLarty (2005). `Mathematical Platonism' Versus Gathering the Dead: What Socrates Teaches Glaucon. 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 (...)
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  7.  32
    William J. Melanson (2011). Reassessing the Epistemological Challenge to Mathematical Platonism. Croatian Journal of Philosophy 11 (3):295-304.
    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 (...)
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  8.  11
    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.
    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 (...)
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  9.  36
    Jacques Bouveresse (2004). On the Meaning of the Word 'Platonism' in the Expression 'Mathematical Platonism'. Proceedings of the Aristotelian Society 105 (1):55–79.
    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 (...)
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  10.  4
    Ulrich Blau (2009). The Self in Logical-Mathematical Platonism. Mind and Matter 7 (1):37-57.
    A non-classical logic is proposed that extends classical logic and set theory as conservatively as possible with respect to three domains: the logic of natural language, the logcal foundations of mathematics, and the logical-philosophical paradoxes. A universal mechanics of consciousness connects these domains, and its best witness is the liar paradox. Its solution rests formally on a subject-object partition, mentally arising and disappearing perpetually. All deep paradoxes are paradoxes of consciousness. There are two kinds, solvable ones and unsolvable ones. The (...)
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  11. Seth Crook (1994). Contingency, Coincidence, Bruteness and the Correlation Challenge: Some Issues in the Area of Mathematical Platonism. Dissertation, University of Southern California
    My thesis is devoted to an attempt to offer, on behalf of mathematical Platonism, a reply to what may seem to be a powerful objection to it. The objection is this: If there is, as the Platonist supposes, mathematical knowledge of abstract objects, then there is a correlation between our beliefs and the mathematical facts. However, how is such a correlation to be explained given that mathematical objects are a-causal? The worry is that no explanation (...)
     
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  12.  15
    John McDowell (1989). Mathematical Platonism and Dummettian Anti‐Realism. Dialectica 43 (1‐2):173-192.
    SummaryThe platonist, in affirming the principle of bivalence for sentences for which there is no decision procedure, disconnects their truth‐conditions from conditions that would enable us to prove them ‐ as if Goldbach's conjecture, say, might just happen to be true. According to Dummett, what has gone wrong here is that the meaning of the relevant sentences has been conceived so as to go beyond what could be learned in learning to use them, or displayed in using them competently. Dummett (...)
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  13. Stuart Cornwell (1991). Mathematical Platonism. Dissertation, University of Southern California
    The present dissertation includes three chapters: chapter one 'Challenges to platonism'; chapter two 'counterparts of non-mathematical statements'; chapter three 'Nominalizing platonistic accounts of the predictive success of mathematics'. The purpose of the dissertation is to articulate a fundamental problem in the philosophy of mathematics and explore certain solutions to this problem. The central problematic is that platonistic mathematics is involved in the explanation and prediction of physical phenomena and hence its role in such explanations gives us good reason (...)
     
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  14. Marco Panza & Andrea Sereni (2013). Plato's Problem: An Introduction to Mathematical Platonism. Palgrave Macmillan.
  15.  79
    Colin Cheyne (1997). Getting in Touch with Numbers: Intuition and Mathematical Platonism. Philosophy and Phenomenological Research 57 (1):111-125.
    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, (...)
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  16.  12
    Vladimir Drekalović (2015). Some Aspects of Understanding Mathematical Reality: Existence, Platonism, Discovery. Axiomathes 25 (3):313-333.
    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, (...)
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  17.  14
    Øystein Linnebo (2006). Epistemological Challenges to Mathematical Platonism. Philosophical Studies 129 (3):545-574.
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  18.  21
    Julian C. Cole, Mathematical Platonism. Internet Encyclopedia of Philosophy.
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  19.  21
    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.
  20.  11
    Berislav Žarnić (1999). Mathematical Platonism: From Objects to Patterns. Synthesis Philosophica 14 (1/2):53-64.
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  21. Mark Balaguer (2008). Mathematical Platonism. In Bonnie Gold & Roger Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy. Mathematical Association of America 179--204.
     
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  22. Anna Lemanska (2012). Remarks on Mathematical Platonism. Filozofia Nauki 20 (2).
     
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  23. 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
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  24.  30
    Emily Katz (2013). Aristotle's Critique of Platonist Mathematical Objects: Two Test Cases From Metaphysics M 2. Apeiron 46 (1):26-47.
    Books M and N of Aristotle's Metaphysics receive relatively little careful attention. Even scholars who give detailed analyses of the arguments in M-N dismiss many of them as hopelessly flawed and biased, and find Aristotle's critique to be riddled with mistakes and question-begging. This assessment of the quality of Aristotle's critique of his predecessors (and of the Platonists in particular), is widespread. The series of arguments in M 2 (1077a14-b11) that targets separate mathematical objects is the subject of particularly (...)
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  25. James Robert Brown (2012/2011). Platonism, Naturalism, and Mathematical Knowledge. Routledge.
    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.
     
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  26. James Robert Brown (2014). Platonism, Naturalism, and Mathematical Knowledge. Routledge.
    This study addresses a central theme in current philosophy: Platonism vs Naturalism and provides accounts of both approaches to mathematics, crucially discussing Quine, Maddy, Kitcher, Lakoff, Colyvan, and many others. Beginning with accounts of both approaches, Brown defends Platonism by arguing that only a Platonistic approach can account for concept acquisition in a number of special cases in the sciences. He also argues for a particular view of applied mathematics, a view that supports Platonism against Naturalist alternatives. (...)
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  27. James Robert Brown (2013). Platonism, Naturalism, and Mathematical Knowledge. Routledge.
    This study addresses a central theme in current philosophy: Platonism vs Naturalism and provides accounts of both approaches to mathematics, crucially discussing Quine, Maddy, Kitcher, Lakoff, Colyvan, and many others. Beginning with accounts of both approaches, Brown defends Platonism by arguing that only a Platonistic approach can account for concept acquisition in a number of special cases in the sciences. He also argues for a particular view of applied mathematics, a view that supports Platonism against Naturalist alternatives. (...)
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  28. Charles Parsons (1995). Platonism and Mathematical Intuition in Kurt Gödel's Thought. Bulletin of Symbolic Logic 1 (1):44-74.
  29.  13
    Christopher Pincock (2014). Platonism, Naturalism, and Mathematical Knowledge, by James Robert Brown. Mind 123 (492):1174-1177.
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  30.  24
    Michael D. Resnik (1989). A Naturalized Epistemology for a Platonist Mathematical Ontology. Philosophica 43.
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  31.  2
    Emily Katz (2013). Aristotle’s Critique of Platonist Mathematical Objects: Two Test Cases From Metaphysics M 2. Apeiron 46 (1).
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  32.  17
    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
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  33. Mary Leng (2002). Mathematical Practice as a Guide to Ontology: Evaluating Quinean Platonism by its Consequences for Theory Choice. Logique Et Analyse 45.
     
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  34.  22
    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.
  35.  13
    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.
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  36.  4
    Bernd Buldt, Mathematical Practice and Platonism: A Phenomenological Perspective.
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  37.  6
    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.
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  38. B. Borstner (2002). Mathematical Structuralism is a Kind of Platonism. Filozofski Vestnik 23 (1):7-24.
  39. 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.
     
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  40. M. Trobok (2000). Ante Rem Structuralism (Non-Traditional Platonism, Shapiro's Theory on Mathematical Objects). Filozofski Vestnik 21 (1):81-89.
     
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  41.  34
    Alan Baker (forthcoming). Parsimony and Inference to the Best Mathematical Explanation. Synthese:1-18.
    Indispensability-based arguments for mathematical platonism are typically motivated by drawing an analogy between abstract mathematical objects and concrete scientific posits. In this paper, I argue that mathematics can sometimes help to reduce our concrete ontological, ideological, and structural commitments. My focus is on optimization explanations, and in particular the case study involving periodical cicadas. I argue that in this case, stronger mathematical apparatus yields explanations that have fewer concrete commitments. The nominalist cannot accept these more parsimonious (...)
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  42. Øystein Linnebo (2009). Platonism in the Philosophy of Mathematics. In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy.
    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.
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  43.  38
    Steven M. Duncan, Platonism by the Numbers.
    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.
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  44.  76
    Jonathan Tallant (2013). Optimus Prime: Paraphrasing Prime Number Talk. Synthese 190 (12):2065-2083.
    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 (...)
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  45.  4
    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.
    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 (...)
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  46.  22
    Charles Sayward (2010). Dialogues Concerning Natural Numbers. Peter Lang.
    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.
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  47.  62
    David Sherry (2009). The Role of Diagrams in Mathematical Arguments. Foundations of Science 14 (1-2):59-74.
    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 (...)
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  48.  50
    Richard Tieszen (2010). Mathematical Problem-Solving and Ontology: An Exercise. [REVIEW] Axiomathes 20 (2-3):295-312.
    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 (...)
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  49. Elijah Chudnoff (2014). Intuition in Mathematics. In Barbara Held & Lisa Osbeck (eds.), Rational Intuition. Cambridge University Press
    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 (...)
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  50. Mark Balaguer (1995). A Platonist Epistemology. Synthese 103 (3):303 - 325.
    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 (...)
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