Results for 'mathematical Platonism'

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  1. Mathematical Platonism and the Nature of Infinity.Gilbert B. Côté - 2013 - 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. Epistemological Challenges to Mathematical Platonism.Øystein Linnebo - 2006 - 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 a (...)
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    Mathematical Apriorism and Warrant: A Reliabilist-Platonist Account.Mark Mcevoy - 2005 - 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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    Is an Unpictorial Mathematical Platonism Possible?Charles Sayward - 2002 - 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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    `Mathematical Platonism' Versus Gathering the Dead: What Socrates Teaches Glaucon.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 (...)
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    Reassessing the Epistemological Challenge to Mathematical Platonism.William J. Melanson - 2011 - 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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    III *-on the Meaning of the Word 'Platonism' in the Expression 'Mathematical Platonism'.Jacques Bouveresse - 2005 - 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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  8. Science with Numbers: A Naturalistic Defense of Mathematical Platonism.Oystein Linnebo - 2002 - Dissertation, Harvard University
    My thesis discusses the unique challenge that platonistic mathematics poses to philosophical naturalism. It has two main parts. ;The first part discusses the three most important approaches to my problem found in the literature: First, W. V. Quine's holistic empiricist defense of mathematical platonism; then, the nominalists' argument that mathematical platonism is naturalistically unacceptable; and finally, a radical form of naturalism, due to John Burgess and Penelope Maddy, which dismisses any philosophical criticism of a successful science (...)
     
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  9.  38
    On the Meaning of the Word 'Platonism' in the Expression 'Mathematical Platonism'.Jacques Bouveresse - 2004 - 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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    The Self in Logical-Mathematical Platonism.Ulrich Blau - 2009 - 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. Contingency, Coincidence, Bruteness and the Correlation Challenge: Some Issues in the Area of Mathematical Platonism.Seth Crook - 1994 - 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. Is an Unpictorial Mathematical Platonism Possible?Charles W. Sayward Jr - 2002 - Journal of Philosophical Research 27:201-214.
    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 platonism 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 platonist claim is that mathematical truth is objective. Although he does not demarcate them as such, Wright proposes several different (...)
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  13. Mathematical Platonism.Massimo Pigliucci - 2011 - Philosophy Now 84:47-47.
    Are numbers and other mathematical objects "out there" in some philosophically meaningful sense?
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    Mathematical Platonism and Dummettian Anti‐Realism.John McDowell - 1989 - 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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  15. Mathematical Platonism.Stuart Cornwell - 1991 - 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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  16.  11
    ¿ES LA MATEMÁTICA LA NOMOGONÍA DE LA CONCIENCIA? REFLEXIONES ACERCA DEL ORIGEN DE LA CONCIENCIA Y EL PLATONISMO MATEMÁTICO DE ROGER PENROSE / Is Mathematics the “nomogony” of Consciousness? Reflections on the origin of consciousness and mathematical Platonism of Roger Penrose.Miguel Acosta - 2016 - Naturaleza y Libertad. Revista de Estudios Interdisciplinares 7:15-39.
    Al final de su libro “La conciencia inexplicada”, Juan Arana señala que la nomología, explicación según las leyes de la naturaleza, requiere de una nomogonía, una consideración del origen de las leyes. Es decir, que el orden que observamos en el mundo natural requiere una instancia previa que ponga ese orden específico. Sabemos que desde la revolución científica la mejor manera de explicar dicha nomología ha sido mediante las matemáticas. Sin embargo, en las últimas décadas se han presentado algunas propuestas (...)
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  17. Plato's Problem: An Introduction to Mathematical Platonism.Marco Panza & Andrea Sereni - 2013 - Palgrave-Macmillan.
  18.  94
    Getting in Touch with Numbers: Intuition and Mathematical Platonism.Colin Cheyne - 1997 - 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, and argues that (...)
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    Some Aspects of Understanding Mathematical Reality: Existence, Platonism, Discovery.Vladimir Drekalović - 2015 - 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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  20. Getting in Touch with Numbers: Intuition and Mathematical Platonism.Colin Cheyne - 1997 - 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 playa role in the acquisition of our mathematical knowledge, and argues that none (...)
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  21. Getting in Touch with Numbers: Intuition and Mathematical Platonism.Colin Cheyne - 1997 - Philosophy and Phenomenological Research: A Quarterly Journal 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, and argues that (...)
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    Mathematical Platonism.Julian C. Cole - 2010 - Internet Encyclopedia of Philosophy.
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    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]James Robert Brown - 2013 - Philosophia Mathematica (1):nkt031.
  24. Mathematical Platonism.Mark Balaguer - 2008 - In Bonnie Gold & Roger Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy. Mathematical Association of America. pp. 179--204.
     
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    Mathematical Platonism: From Objects to Patterns.Berislav Žarnić - 1999 - Synthesis Philosophica 14 (1/2):53-64.
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  26.  1
    Mathematical Platonism.Nicolas Pain - 2011 - In Michael Bruce & Steven Barbone (eds.), Just the Arguments: 100 of the Most Important Arguments in Western Philosophy. Wiley-Blackwell.
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  27. 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 &Plus; 306: Critical Studies/Book Reviews. [REVIEW]James Robert Brown - 2013 - Philosophia Mathematica 22 (1):135-138.
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  28. 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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  29. Remarks on Mathematical Platonism.Anna Lemanska - 2012 - Filozofia Nauki 20 (2).
     
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  30.  35
    Aristotle's Critique of Platonist Mathematical Objects: Two Test Cases From Metaphysics M 2.Emily Katz - 2013 - 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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  31. Platonism, Naturalism, and Mathematical Knowledge.James Robert Brown - 2014 - 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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  32. Platonism, Naturalism, and Mathematical Knowledge.James Robert Brown - 2011 - 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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  33. Platonism and Mathematical Intuition in Kurt Gödel's Thought.Charles Parsons - 1995 - Bulletin of Symbolic Logic 1 (1):44-74.
  34.  30
    A Naturalized Epistemology for a Platonist Mathematical Ontology.Michael D. Resnik - 1989 - Philosophica 43.
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    Platonism, Naturalism, and Mathematical Knowledge, by James Robert Brown.Christopher Pincock - 2014 - Mind 123 (492):1174-1177.
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  36. Mathematical Practice as a Guide to Ontology: Evaluating Quinean Platonism by its Consequences for Theory Choice.Mary Leng - 2002 - Logique Et Analyse 45.
  37. Badiou’s Platonism: The Mathematical Ideas of Post-Cantorian Set-Theory.Simon B. Duffy - 2012 - In Sean Bowden & Simon B. Duffy (eds.), Badiou and Philosophy. Edinburgh University Press.
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  38.  24
    Platonism and Metaphor in the Texts of Mathematics: GöDel and Frege on Mathematical Knowledge. [REVIEW]Clevis Headley - 1997 - Man and World 30 (4):453-481.
  39.  14
    James Robert Brown. Platonism, Naturalism, and Mathematical Knowledge. New York and London: Routledge, 2012. Isbn 978-0-415-87266-9. Pp. X + 182. [REVIEW]A. C. Paseau - 2012 - Philosophia Mathematica 20 (3):359-364.
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    Mathematical Practice and Platonism: A Phenomenological Perspective.Bernd Buldt - unknown
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    Review: Paul Benacerraf, Mathematical Truth; Michael Jubien, Ontology and Mathematical Truth; Philip Kitcher, The Plight of the Platonist. [REVIEW]W. D. Hart - 1987 - Journal of Symbolic Logic 52 (2):552-554.
  42.  2
    Aristotle’s Critique of Platonist Mathematical Objects: Two Test Cases From Metaphysics M 2.Emily Katz - 2013 - Apeiron 46 (1).
  43. Mathematical Structuralism is a Kind of Platonism.B. Borstner - 2002 - Filozofski Vestnik 23 (1):7-24.
  44. Mathematical Knowledge. A Defence of Modest and Sober Platonism.Bob Hale - 2005 - In Rene van Woudenberg, Sabine Roeser & Ron Rood (eds.), Basic Belief and Basic Knowledge. Ontos-Verlag. pp. 4--107.
     
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  45. Benacerraf Paul. Mathematical Truth. The Journal of Philosophy, Vol. 70 , Pp. 661–679.Jubien Michael. Ontology and Mathematical Truth. Noûs, Vol. 11 , Pp. 133–150.Kitcher Philip. The Plight of the Platonist. Noûs, Vol. 12 , Pp. 119–136. [REVIEW]W. D. Hart - 1987 - Journal of Symbolic Logic 52 (2):552-554.
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  46. Ante Rem Structuralism (Non-Traditional Platonism, Shapiro's Theory on Mathematical Objects).M. Trobok - 2000 - Filozofski Vestnik 21 (1):81-89.
     
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  47. Platonism in the Philosophy of Mathematics.Øystein Linnebo - 2009 - 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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  48.  58
    Parsimony and Inference to the Best Mathematical Explanation.Alan Baker - forthcoming - 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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    Numerical Cognition and Mathematical Realism.Helen De Cruz - 2016 - Philosophers' Imprint 16 (16).
    Humans and other animals have an evolved ability to detect discrete magnitudes in their environment. Does this observation support evolutionary debunking arguments against mathematical realism, as has been recently argued by Clarke-Doane, or does it bolster mathematical realism, as authors such as Joyce and Sinnott-Armstrong have assumed? To find out, we need to pay closer attention to the features of evolved numerical cognition. I provide a detailed examination of the functional properties of evolved numerical cognition, and propose that (...)
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    Platonism by the Numbers.Steven M. Duncan - manuscript
    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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