Results for 'Platonism'

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  1. Platonism and Anti-Platonism in Mathematics.Mark Balaguer - 1998 - New York, NY, USA: Oxford University Press.
    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 we do (...)
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  2. 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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  3.  4
    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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  4. A Platonist Epistemology.Mark Balaguer - 1995 - 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 attain knowledge about (...)
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  5. 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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  6. Platonism in the Philosophy of Mathematics.Øystein Linnebo - forthcoming - Stanford Encyclopedia of Philosophy.
    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. There are mathematical (...)
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  7. Platonism and Anti-Platonism in Mathematics.Mark Balaguer - 1998 - Bulletin of Symbolic Logic 8 (4):516-518.
    This book does three main things. First, it defends mathematical platonism against the main objections to that view (most notably, the epistemological objection and the multiple-reductions objection). Second, it defends anti-platonism (in particular, fictionalism) against the main objections to that view (most notably, the Quine-Putnam indispensability objection and the objection from objectivity). Third, it argues that there is no fact of the matter whether abstract mathematical objects exist and, hence, no fact of the matter whether platonism or (...)
     
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  8.  29
    Autonomy Platonism and the Indispensability Argument.Russell Marcus - 2015 - Lexington Books.
    This book includes detailed critical analysis of a wide variety of versions of the indispensability argument, as well as a novel approach to traditional views about mathematics.
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  9. Deep Platonism.Chad Carmichael - 2016 - Philosophy and Phenomenological Research 92 (2):307-328.
    According to the traditional bundle theory, particulars are bundles of compresent universals. I think we should reject the bundle theory for a variety of reasons. But I will argue for the thesis at the core of the bundle theory: that all the facts about particulars are grounded in facts about universals. I begin by showing how to meet the main objection to this thesis (which is also the main objection to the bundle theory): that it is inconsistent with the possibility (...)
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  10. Naturalized Platonism Versus Platonized Naturalism.Bernard Linsky & Edward N. Zalta - 1995 - Journal of Philosophy 92 (10):525-555.
    In this paper, we develop an alternative strategy, Platonized Naturalism, for reconciling naturalism and Platonism and to account for our knowledge of mathematical objects and properties. A systematic (Principled) Platonism based on a comprehension principle that asserts the existence of a plenitude of abstract objects is not just consistent with, but required (on transcendental grounds) for naturalism. Such a comprehension principle is synthetic, and it is known a priori. Its synthetic a priori character is grounded in the fact (...)
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  11.  21
    Thrasyllan Platonism.Harold Tarrant - 1993 - Cornell University Press.
    Thrasyllus, best known as the Roman emperor Tiberius' astrologist, figured prominently in the development of ancient Platonism. How prominently and to what effect are questions that have puzzled philosophers down to our day; Harold Tarrant's important new book attempts to answer them.
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  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.
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  13. Nominalist Platonism.George Boolos - 1985 - Philosophical Review 94 (3):327-344.
  14.  5
    Thrasyllan Platonism.Harold Tarrant - 2020 - Cornell University Press.
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  15.  41
    Platonism Vs. Nominalism in Contemporary Musical Ontology.Andrew Kania - 2013 - In Christy Mag Uidhir (ed.), Art and Abstract Objects. Oxford University Press. pp. 197.
    In this essay I first outline contemporary Platonism about musical works – the theory that musical works are abstract objects. I then consider reasons to be suspicious of such a view, motivating a consideration of nominalist theories of musical works. I argue for two conclusions: first, that there are no compelling reasons to be a nominalist about musical works in particular, i.e. that nominalism about musical works rests on arguments for thoroughgoing nominalism, and, second, that if Platonism fails, (...)
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  16. Platonism in Music: A Kind of Defense.Peter Kivy - 1983 - Grazer Philosophische Studien 19 (1):109-129.
    Various criticisms have been brought against a Platonistic construal of the musical work: that is, against the view that the musical work is a universal or kind or type, of which the performances are instances or tokens. Some of these criticisms are: (1) that musical works possess perceptual properties and universals do not; (2) that musical works are created and universals cannot be; (3) that universals cannot be destroyed and musical works can; (4) that parts of tokens of the same (...)
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  17.  80
    Platonism in Music: A Kind of Defense.Peter Kivy - 1983 - Grazer Philosophische Studien 19 (1):109-129.
    Various criticisms have been brought against a Platonistic construal of the musical work: that is, against the view that the musical work is a universal or kind or type, of which the performances are instances or tokens. Some of these criticisms are: that musical works possess perceptual properties and universals do not; that musical works are created and universals cannot be; that universals cannot be destroyed and musical works can; that parts of tokens of the same type can be interchanged (...)
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  18. Platonist Philosophy 80 Bc to Ad 250: An Introduction and Collection of Sources in Translation.George Boys-Stones - 2017 - Cambridge University Press.
    'Middle' Platonism has some claim to be the single most influential philosophical movement of the last two thousand years, as the common background to 'Neoplatonism' and the early development of Christian theology. This book breaks with the tradition of considering it primarily in terms of its sources, instead putting its contemporary philosophical engagements front and centre to reconstruct its philosophical motivations and activity across the full range of its interests. The volume explores the ideas at the heart of Platonist (...)
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  19. Modal Platonism: An Easy Way to Avoid Ontological Commitment to Abstract Entities.Joel I. Friedman - 2005 - Journal of Philosophical Logic 34 (3):227-273.
    Modal Platonism utilizes "weak" logical possibility, such that it is logically possible there are abstract entities, and logically possible there are none. Modal Platonism also utilizes a non-indexical actuality operator. Modal Platonism is the EASY WAY, neither reductionist nor eliminativist, but embracing the Platonistic language of abstract entities while eliminating ontological commitment to them. Statement of Modal Platonism. Any consistent statement B ontologically committed to abstract entities may be replaced by an empirically equivalent modalization, MOD(B), not (...)
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  20.  27
    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.
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  21. Prioritizing Platonism.Kelly Trogdon & Sam Cowling - 2019 - Philosophical Studies 176 (8):2029-2042.
    Discussion of atomistic and monistic theses about abstract reality.
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  22.  13
    From Platonism to Neoplatonism.Philip Merlan - 1953 - Martinus Nijhoff.
  23.  32
    Aristotle and Other Platonists.Lloyd P. Gerson - 2005 - Cornell University Press.
    Aristotle and Other Platonists concludes with an assessment of some of the philosophical results of acknowledging harmony."--BOOK JACKET.
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  24. Platonism in Metaphysics.Mark Balaguer - 2008 - Stanford Encyclopedia of Philosophy.
    Platonism is the view that there exist such things as abstract objects — where an abstract object is an object that does not exist in space or time and which is therefore entirely non-physical and nonmental. Platonism in this sense is a contemporary view. It is obviously related to the views of Plato in important ways, but it is not entirely clear that Plato endorsed this view, as it is defined here. In order to remain neutral on this (...)
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  25.  2
    Christian Platonism: A History.Alexander J. B. Hampton & John Peter Kenney (eds.) - 2020 - Cambridge University Press.
    Platonism has played a central role in Christianity and is essential to a deep understanding of the Christian theological tradition. At times, Platonism has constituted an essential philosophical and theological resource, furnishing Christianity with an intellectual framework that has played a key role in its early development, and in subsequent periods of renewal. Alternatively, it has been considered a compromising influence, conflicting with the faith's revelatory foundations and distorting its inherent message. In both cases the fundamental importance of (...)
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  26.  19
    Mathematical Platonism Meets Ontological Pluralism?Matteo Plebani - 2020 - Inquiry: An Interdisciplinary Journal of Philosophy 63 (6):655-673.
    Mathematical platonism is the view that abstract mathematical objects exist. Ontological pluralism is the view that there are many modes of existence. This paper examines the prospects for plural platonism, the view that results from combining mathematical platonism and ontological pluralism. I will argue that some forms of platonism are in harmony with ontological pluralism, while other forms of platonism are in tension with it. This shows that there are some interesting connections between the (...)–antiplatonism dispute and recent debates over ontological pluralism. (shrink)
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  27. Platonism and the Origins of Modernity: The Platonic Tradition and the Rise of Modern Philosophy.Douglas Hedley & Sarah Hutton (eds.) - 2008 - Springer.
    International Archives of the History of Ideas Archives internationales d'histoire des idées, Vol. 196. -/- Introduction, S. Hutton; Nicholas of Cusa : Platonism at the Dawn of Modernity, D. Moran; At Variance: Marsilio Ficino Platonism And Heresy, M.J.B. Allen; Going Naked into the Shrine:Herbert, Plotinus and the Consructive Metaphor, S.R.L.Clark; Commenius, Light Metaphysics and Educational Reform, J. Rohls ; Robert Fludd’s Kabbalistic Cosmos, W. Schmidt-Biggeman; Reconciling Theory and Fact:The Problem of ‘Other Faiths’ in Lord Herbert and the Cambridge (...)
     
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  28. Platonism and Mathematical Intuition in Kurt Gödel's Thought.Charles Parsons - 1995 - Bulletin of Symbolic Logic 1 (1):44-74.
  29.  51
    Platonism and Anti-Platonism in Mathematics.John P. Burgess - 2001 - Philosophical Review 110 (1):79.
    Mathematics tells us there exist infinitely many prime numbers. Nominalist philosophy, introduced by Goodman and Quine, tells us there exist no numbers at all, and so no prime numbers. Nominalists are aware that the assertion of the existence of prime numbers is warranted by the standards of mathematical science; they simply reject scientific standards of warrant.
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  30.  22
    Between Platonism and Phenomenalism: Reply to Cao.Steven French & James Ladyman - 2003 - Synthese 136 (1):73-78.
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  31.  72
    Mathematical Platonism Meets Ontological Pluralism?Matteo Plebani - 2017 - Inquiry: An Interdisciplinary Journal of Philosophy:1-19.
    Mathematical platonism is the view that abstract mathematical objects exist. Ontological pluralism is the view that there are many modes of existence. This paper examines the prospects for...
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  32. Heavy Duty Platonism.Robert Knowles - 2015 - Erkenntnis 80 (6):1255-1270.
    Heavy duty platonism is of great dialectical importance in the philosophy of mathematics. It is the view that physical magnitudes, such as mass and temperature, are cases of physical objects being related to numbers. Many theorists have assumed HDP’s falsity in order to reach their own conclusions, but they are only justified in doing so if there are good arguments against HDP. In this paper, I present all five arguments against HDP alluded to in the literature and show that (...)
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  33.  16
    Platonism and Naturalism: The Possibility of Philosophy.Lloyd P. Gerson - 2020 - Cornell University Press.
    "An account of the central tradition in the history of philosophy, Platonism, along with the class of philosophical positions collectively known as Naturalism and the 'anti-Platonism' of Naturalism both in antiquity and in contemporary philosophy"--.
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  34. The Platonism of Aristotle.G. E. L. Owen - 1967
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  35.  76
    ‘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 (...)
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  36. Platonism in Metaphysics.Markn D. Balaguer - 2016 - Stanford Encyclopedia of Philosophy 1 (1):1.
     
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  37.  8
    Abolishing Platonism in Multiverse Theories.Stathis Livadas - 2020 - Axiomathes 32 (2):321-343.
    A debated issue in the mathematical foundations in at least the last two decades is whether one can plausibly argue for the merits of treating undecidable questions of mathematics, e.g., the Continuum Hypothesis, by relying on the existence of a plurality of set-theoretical universes except for a single one, i.e., the well-known set-theoretical universe V associated with the cumulative hierarchy of sets. The multiverse approach has some varying versions of the general concept of multiverse yet my intention is to primarily (...)
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  38.  2
    Rationalism, Platonism and God: A Symposium on Early Modern Philosophy.Michael Ayers (ed.) - 2007 - Published for the British Academy by Oxford University Press.
    Rationalism, Platonism and God comprises three main papers on Descartes, Spinoza and Leibniz, with extensive responses. It provides a significant contribution to the exploration of the common ground of the great early-modern Rationalist theories, and an examination of the ways in which the mainstream Platonic tradition permeates these theories. -/- John Cottingham identifies characteristically Platonic themes in Descartes's cosmology and metaphysics, finding them associated with two distinct, even opposed attitudes to nature and the human condition, one ancient and 'contemplative', (...)
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  39. Platonism in Music: Another Kind of Defense.Peter Kivy - 1987 - American Philosophical Quarterly 24 (3):245 - 252.
  40.  39
    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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  41. Platonism and Aristotelianism in Mathematics.Richard Pettigrew - 2008 - Philosophia Mathematica 16 (3):310-332.
    Philosophers of mathematics agree that the only interpretation of arithmetic that takes that discourse at 'face value' is one on which the expressions 'N', '0', '1', '+', and 'x' are treated as proper names. I argue that the interpretation on which these expressions are treated as akin to free variables has an equal claim to be the default interpretation of arithmetic. I show that no purely syntactic test can distinguish proper names from free variables, and I observe that any semantic (...)
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  42.  4
    From Plato to Platonism.Lloyd P. Gerson - 2017 - Cornell University Press.
    Was Plato a Platonist? While ancient disciples of Plato would have answered this question in the affirmative, modern scholars have generally denied that Plato's own philosophy was in substantial agreement with that of the Platonists of succeeding centuries. In From Plato to Platonism, Lloyd P. Gerson argues that the ancients are correct in their assessment. He arrives at this conclusion in an especially ingenious manner, challenging fundamental assumptions about how Plato's teachings have come to be understood. Through deft readings (...)
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  43.  20
    Contextualizing Platonism and Decontextualizing Aristotelianism in the Ontology of Music.Nemesio García-Carril Puy - 2020 - Journal of Aesthetics and Art Criticism 78 (2):183-196.
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  44. Should Scientific Realists Be Platonists?Jacob Busch & Joe Morrison - 2016 - Synthese 193 (2):435-449.
    Enhanced indispensability arguments claim that Scientific Realists are committed to the existence of mathematical entities due to their reliance on Inference to the best explanation. Our central question concerns this purported parity of reasoning: do people who defend the EIA make an appropriate use of the resources of Scientific Realism to achieve platonism? We argue that just because a variety of different inferential strategies can be employed by Scientific Realists does not mean that ontological conclusions concerning which things we (...)
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  45.  57
    The Platonism Vs. Nominalism Debate From a Meta-Metaphysical Perspective.Guido Imaguire - 2015 - Revista Portuguesa de Filosofia 71 (2-3):375-398.
    Resumo Neste artigo o autor apresenta cinco abordagens diferentes ao debate entre o platonismo e o nominalismo: a quantificacional, a reducionista, a dependência da mente / linguagem, a extensional versus intensional, a hierárquica. Cada uma apresenta suas vantagens e desvantagens que devem ser discutidas em detalhe. Palavras-chave : existência, meta-metafísica, nominalismo, platonismoIn this paper I present five different approaches to the debate between Platonism and Nominalism: the quantifier approach, the reductionist approach, the mind / language dependence approach, the extension (...)
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  46.  75
    The Midwife of Platonism: Text and Subtext in Plato's Theaetetus.David Sedley - 2004 - Oxford University Press.
    Plato's Theaetetus is an acknowledged masterpiece, and among the most influential texts in the history of epistemology. Since antiquity it has been debated whether this dialogue was written by Plato to support his familiar metaphysical doctrines, or represents a self-distancing from these. David Sedley's book offers a via media, founded on a radical separation of the author, Plato, from his main speaker, Socrates. The dialogue, it is argued, is addressed to readers familiar with Plato's mature doctrines, and sets out to (...)
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  47. Platonism and the Causal Theory of Knowledge.Mark Steiner - 1973 - Journal of Philosophy 70 (3):57-66.
  48. Platonism for Cheap? Crispin Wright on Frege's Context Principle.Hartry Field - 1984 - Canadian Journal of Philosophy 14:637--62.
  49. Platonism and the 'Epistemic Role Puzzle'.Mark McEvoy - 2012 - Philosophia Mathematica 20 (3):289-304.
    Jody Azzouni has offered the following argument against the existence of mathematical entities: if, as it seems, mathematical entities play no role in mathematical practice, we therefore have no reason to believe in them. I consider this argument as it applies to mathematical platonism, and argue that it does not present a legitimate novel challenge to platonism. I also assess Azzouni's use of the ‘epistemic role puzzle’ (ERP) to undermine the platonist's alleged parallel between skepticism about mathematical entities (...)
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  50. 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 deflationary one, there (...)
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