Search results for 'platonism' (try it on Scholar)

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  1. John Russell Roberts, Innate Ideas Without Abstract Ideas: An Essay on Berkeley's Platonism.score: 24.0
    Draft. Berkeley denied the existence of abstract ideas and any faculty of abstraction. At the same time, however, he embraced innate ideas and a faculty of pure intellect. This paper attempts to reconcile the tension between these commitments by offering an interpretation of Berkeley's Platonism.
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  2. Joel I. Friedman (2005). Modal Platonism: An Easy Way to Avoid Ontological Commitment to Abstract Entities. [REVIEW] Journal of Philosophical Logic 34 (3):227 - 273.score: 24.0
    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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  3. Øystein Linnebo (2009). Platonism in the Philosophy of Mathematics. In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy.score: 24.0
    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.
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  4. Mark Balaguer (1995). A Platonist Epistemology. Synthese 103 (3):303 - 325.score: 24.0
    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 knowledge about (...)
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  5. Chris Daly & Simon Langford (2011). Two Anti-Platonist Strategies. Mind 119 (476):1107-1116.score: 24.0
    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 for (...)
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  6. Srećko Kovač (1999). Quine's Platonism and Antiplatonism. Synthesis Philosophica 14 (1999):45-52.score: 24.0
    Quine rejects intensional Platonism and, with it, also rejects attributes (properties) as designations of predicates. He pragmatically accepts extensional Platonism, but conceives of classes as merely auxiliary entities needed to express some laws of set theory. At the elementary logical level, Quine develops an “ontologically innocent” logic of predicates. What in standard quantification theory is the work of variables is in the logic of predicates the work of a few functors that operate on predicates themselves: variables are eliminated. (...)
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  7. Colin Cheyne & Charles R. Pigden (1996). Pythagorean Powers or a Challenge to Platonism. Australasian Journal of Philosophy 74 (4):639 – 645.score: 24.0
    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 their (...)
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  8. Gilbert B. Côté (2013). Mathematical Platonism and the Nature of Infinity. Open Journal of Philosophy 3 (3):372-375.score: 24.0
    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.
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  9. Bill Wringe (2008). Making the Lightness of Being Bearable: Arithmetical Platonism, Fictional Realism and Cognitive Command. Canadian Journal of Philosophy 38 (3):pp. 453-487.score: 24.0
    In this paper I argue against Divers and Miller's 'Lightness of Being' objection to Hale and Wright's neo-Fregean Platonism. According to the 'Lightness of Being' objection, the neo-Fregean Platonist makes existence too cheap: the same principles which allow her to argue that numbers exist also allow her to claim that fictional objects exist. I claim that this is no objection at all" the neo-Fregean Platonist should think that fictional characters exist. However, the pluralist approach to truth developed by WQright (...)
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  10. Robert Arp (2005). Frege, as-If Platonism, and Pragmatism. Journal of Critical Realism 4 (1):1-27.score: 24.0
    This paper is divided into two main sections. In the first, I attempt to show that the characterization of Frege as a redundancy theorist is not accurate. Using one of Wolfgang Carl's recent works as a foil, I argue that Frege countenances a realm of abstract objects including truth, and that Frege's Platonist commitments inform his epistemology and embolden his antipsychologistic project. In the second section, contrasting Frege's Platonism with pragmatism, I show that even though Frege's metaphysical position concerning (...)
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  11. Charles Sayward (2002). Is an Unpictorial Mathematical Platonism Possible? Journal of Philosophical Research 27:199-212.score: 24.0
    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 several different (...)
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  12. Bernard Wills (2012). Pascal and the Persistence of Platonism in Early Modern Thought. International Journal of the Platonic Tradition 6 (2):186-200.score: 24.0
    The following paper argues that Blaise Pascal, in spite of his famous opposition between the God of the Philosophers and the God of “Abraham, Isaac and Jacob” has significant affinities with the tradition of Renaissance Platonism and is in fact a Platonist in his overall outlook. This is shown in three ways. Firstly, it is argued that Pascal’s skeptical fideism has roots in the notion of faith developed in post-Plotinian neo-Platonism. Secondly, it is argued that Pascal makes considerable (...)
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  13. Massimo Pigliucci (2011). Mathematical Platonism. Philosophy Now 84:47-47.score: 21.0
    Are numbers and other mathematical objects "out there" in some philosophically meaningful sense?
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  14. Anne Newstead & James Franklin (2012). Indispensability Without Platonism. In Alexander Bird, Brian Ellis & Howard Sankey (eds.), Properties, Powers and Structures. Routledge.score: 21.0
    According to Quine’s indispensability argument, we ought to believe in just those mathematical entities that we quantify over in our best scientific theories. Quine’s criterion of ontological commitment is part of the standard indispensability argument. However, we suggest that a new indispensability argument can be run using Armstrong’s criterion of ontological commitment rather than Quine’s. According to Armstrong’s criterion, ‘to be is to be a truthmaker (or part of one)’. We supplement this criterion with our own brand of metaphysics, 'Aristotelian (...)
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  15. Michael S. Gazzaniga & Shaun Gallagher (1998). The Neuronal Platonist. Journal of Consciousness Studies 5 (5-6):706-717.score: 21.0
    Psychology is dead. The self is a fiction invented by the brain. Brain plasticity isn?t all it?s cracked up to be. Our conscious learning is an observation post factum, a recollection of something already accomplished by the brain. We don?t learn to speak; speech is generated when the brain is ready to say something. False memories are more prevalent than one might think, and they aren?t all that bad. We think we?re in charge of our lives, but actually we are (...)
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  16. Bob Hale (1984). Frege's Platonism. Philosophical Quarterly 34 (136):225-241.score: 21.0
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  17. Edward Moore, Middle Platonism. Internet Encyclopedia of Philosophy.score: 21.0
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  18. Stephen L. Brock (2006). On Whether Aquinas's Ipsum Esse is “Platonism”. Review of Metaphysics 60 (2):269-303.score: 21.0
    Enrico Berti and others hold that Aquinas’s notion of God as ipsum esse subsistens conflicts with Aristotle’s view that positing an Idea of being treats being as a genus and nullifies all differences. The paper first shows how one of Aquinas’s ways of distinguishing esse from essence supposes an intimate tie between a thing’s esse and its differentia. Then it argues that for Aquinas the (one) divine essence differs from the (manifold) “essence of esse.” God is his very esse. This (...)
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  19. Steven M. Duncan, Platonism by the Numbers.score: 21.0
    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.
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  20. Mark Balaguer (1998). Platonism and Anti-Platonism in Mathematics. Oxford University Press.score: 20.0
    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 we do (...)
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  21. Mark Ralkowski (2009). Heidegger's Platonism. Continuum.score: 20.0
    Introduction -- What is platonism? -- Schleiermacher's pedagogical interpretation of Plato -- What's wrong with the current debate -- The romantic rediscovery of Plato's ineffable ontology -- Conclusions: Ineffability and dialogue form -- Untying Schleiermacher's gordian knot -- Metaphysical ineffability : the argument from language and human finitude -- Spiritual ineffability: the argument from self-transformation -- Existential ineffability : the argument from life choice -- Platonism reconsidered -- The context of Heidegger's interpretation of Plato -- What it all (...)
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  22. Michael Ayers (ed.) (2007). Rationalism, Platonism, and God. Published for the British Academy by Oxford University Press.score: 20.0
    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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  23. James Robert Brown (2012/2011). Platonism, Naturalism, and Mathematical Knowledge. Routledge.score: 20.0
    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.
     
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  24. Øystein Linnebo (2006). Epistemological Challenges to Mathematical Platonism. Philosophical Studies 129 (3):545-574.score: 18.0
    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 deflationary one, there (...)
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  25. David Liggins (2006). Is There a Good Epistemological Argument Against Platonism? Analysis 66 (290):135–141.score: 18.0
    Platonism in the philosophy of mathematics is the doctrine that there are mathematical objects such as numbers. John Burgess and Gideon Rosen have argued that that there is no good epistemological argument against platonism. They propose a dilemma, claiming that epistemological arguments against platonism either rely on a dubious epistemology, or resemble a dubious sceptical argument concerning perceptual knowledge. Against Burgess and Rosen, I show that an epistemological anti-platonist argument proposed by Hartry Field avoids both horns of (...)
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  26. Michael Bergmann & Jeffrey E. Brower (2006). A Theistic Argument Against Platonism (and in Support of Truthmakers and Divine Simplicity). Oxford Studies in Metaphysics 2:357-386.score: 18.0
    Predication is an indisputable part of our linguistic behavior. By contrast, the metaphysics of predication has been a matter of dispute ever since antiquity. According to Plato—or at least Platonism, the view that goes by Plato’s name in contemporary philosophy—the truths expressed by predications such as “Socrates is wise” are true because there is a subject of predication (e.g., Socrates), there is an abstract property or universal (e.g., wisdom), and the subject exemplifies the property.1 This view is supposed to (...)
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  27. Christia Mercer (2008). The Platonism at the Core of Leibniz's Metaphysics: God and Knowledge. In S. Hutton (ed.), Platonism and the Origins of Modernity: The Platonic Tradition and the Rise of Modern Philosophy. Ashgate Press.score: 18.0
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  28. Otavio Bueno, Interpreting Music: Beyond Platonism.score: 18.0
    Central to the philosophical understanding of music is the status of musical works. According to the Platonist, musical works are abstract objects; that is, they are not located in space or time, and we have no causal access to them. Moreover, only a particular physical occurrence of these musical works is instantiated when a performance ofthe latter takes place. But even if no performance ever took place, the Platonist insists, the musical work would still exist, since its existence is not (...)
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  29. Ivan Kasa (2010). On Field's Epistemological Argument Against Platonism. Studia Logica 96 (2):141-147.score: 18.0
    Hartry Field's formulation of an epistemological argument against platonism is only valid if knowledge is constrained by a causal clause. Contrary to recent claims (e.g. in Liggins (2006), Liggins (2010)), Field's argument therefore fails the very same criterion usually taken to discredit Benacerraf's earlier version.
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  30. Mary Leng (2005). Platonism and Anti-Platonism: Why Worry? International Studies in the Philosophy of Science 19 (1):65 – 84.score: 18.0
    This paper argues that it is scientific realists who should be most concerned about the issue of Platonism and anti-Platonism in mathematics. If one is merely interested in accounting for the practice of pure mathematics, it is unlikely that a story about the ontology of mathematical theories will be essential to such an account. The question of mathematical ontology comes to the fore, however, once one considers our scientific theories. Given that those theories include amongst their laws assertions (...)
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  31. Mark Balaguer, Platonism in Metaphysics. Stanford Encyclopedia of Philosophy.score: 18.0
    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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  32. Daniel W. Smith (2005). The Concept of the Simulacrum: Deleuze and the Overturning of Platonism. [REVIEW] Continental Philosophy Review 38 (1-2):89-123.score: 18.0
    This article examines Gilles Deleuze’s concept of the simulacrum, which Deleuze formulated in the context of his reading of Nietzsche’s project of “overturning Platonism.” The essential Platonic distinction, Deleuze argues, is more profound than the speculative distinction between model and copy, original and image. The deeper, practical distinction moves between two kinds of images or eidolon, for which the Platonic Idea is meant to provide a concrete criterion of selection “Copies” or icons (eikones) are well-grounded claimants to the transcendent (...)
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  33. Benjamin Callard (2007). The Conceivability of Platonism. Philosophia Mathematica 15 (3):347-356.score: 18.0
    It is widely believed that platonists face a formidable problem: that of providing an intelligible account of mathematical knowledge. The problem is that we seem unable, if the platonist is right, to have the causal relationships with the objects of mathematics without which knowledge of these objects seems unintelligible. The standard platonist response to this challenge is either to deny that knowledge without causation is unintelligible, or to make room for causal interactions by softening the platonism at issue. In (...)
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  34. Lloyd P. Gerson (2005). What is Platonism? Journal of the History of Philosophy 43 (3):253-276.score: 18.0
    The question posed in the title of this paper is an historical one. I am not, for example, primarily interested in the term 'Platonism' as used by modern philosophers to stand for a particular theory under discussion – a theory, which it is typically acknowledged, no one may have actually held.1 I am rather concerned to understand and articulate on an historical basis the core position of that 'school' of thought prominent in antiquity from the time of the 'founder' (...)
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  35. Bernard Linsky & Edward N. Zalta (1995). Naturalized Platonism Versus Platonized Naturalism. Journal of Philosophy 92 (10):525-555.score: 18.0
    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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  36. Greg Restall (2003). Just What is Full-Blooded Platonism? Philosophia Mathematica 11 (1):82--91.score: 18.0
    Mark Balaguer's Platonism and Anti-Platonism in Mathematics presents an intriguing new brand of platonism, which he calls plenitudinous platonism, or more colourfully, full-blooded platonism. In this paper, I argue that Balaguer's attempts to characterise full-blooded platonism fail. They are either too strong, with untoward consequences we all reject, or too weak, not providing a distinctive brand of platonism strong enough to do the work Balaguer requires of it.
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  37. Jc Beall (1999). Prom Full Blooded Platonism to Really Full Blooded Platonism. Philosophia Mathematica 7 (3):322-325.score: 18.0
    Mark Balaguer argues for full blooded platonism (FBP), and argues that FBP alone can solve Benacerraf's familiar epistemic challenge. I note that if FBP really can solve Benacerraf's epistemic challenge, then FBP is not alone in its capacity so to solve; RFBP—really full blooded platonism—can do the trick just as well, where RFBP differs from FBP by allowing entities from inconsistent mathematics. I also argue briefly that there is positive reason for endorsing RFBP.
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  38. Erich Reck, Frege on Numbers: Beyond the Platonist Picture.score: 18.0
    Gottlob Frege is often called a "platonist". In connection with his philosophy we can talk about platonism concerning three kinds of entities: numbers, or logical objects more generally; concepts, or functions more generally; thoughts, or senses more generally. I will only be concerned about the first of these three kinds here, in particular about the natural numbers. I will also focus mostly on Frege's corresponding remarks in The Foundations of Arithmetic (1884), supplemented by a few asides on Basic Laws (...)
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  39. S. Marc Cohen & David Keyt (1992). Analyzing Plato's Arguments: Plato and Platonism. In J. Klagge & N. Smith (eds.), Methods of Interpreting Plato and his Dialogues. Oxford University Press.score: 18.0
    The historian of philosophy often encounters arguments that are enthymematic: they have conclusions that follow from their explicit premises only by the addition of "tacit" or "suppressed" premises. It is a standard practice of interpretation to supply these missing premises, even where the enthymeme is "real," that is, where there is no other context in which the philosopher in question asserts the missing premises. To do so is to follow a principle of charity: other things being equal, one interpretation is (...)
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  40. Mark Balaguer (1994). Against (Maddian) Naturalized Platonism. Philosophia Mathematica 2 (2):97-108.score: 18.0
    It is argued here that mathematical objects cannot be simultaneously abstract and perceptible. Thus, naturalized versions of mathematical platonism, such as the one advocated by Penelope Maddy, are unintelligble. Thus, platonists cannot respond to Benacerrafian epistemological arguments against their view vias Maddy-style naturalization. Finally, it is also argued that naturalized platonists cannot respond to this situation by abandoning abstractness (that is, platonism); they must abandon perceptibility (that is, naturalism).
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  41. Jussi Haukioja (2005). A Middle Position Between Meaning Finitism and Meaning Platonism. International Journal of Philosophical Studies 13 (1):35 – 51.score: 18.0
    David Bloor and Crispin Wright have argued, independently, that the proper lesson to draw from Wittgenstein's so-called rule-following considerations is the rejection of meaning Platonism. According to Platonism, the meaningfulness of a general term is constituted by its connection with an abstract entity, the (possibly) infinite extension of which is determined independently of our classificatory practices. Having rejected Platonism, both Bloor and Wright are driven to meaning finitism, the view that the question of whether a meaningful term (...)
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  42. Michael Liston (2004). Knowledge, Cause, and Abstract Objects: Causal Objections to Platonism. Australasian Journal of Philosophy 82 (2):356 – 359.score: 18.0
    Book Information Knowledge, Cause, and Abstract Objects: Causal Objections to Platonism. Knowledge, Cause, and Abstract Objects: Causal Objections to Platonism Colin Cheyne , Dordrecht: Kluwer Academic Publishers , 2001 , xvi + 236 , £55 ( cloth ) By Colin Cheyne. Dordrecht: Kluwer Academic Publishers. Pp. xvi + 236. £55.
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  43. Michael Potter (2001). Was Gödel a Gödelian Platonist? Philosophia Mathematica 9 (3):331-346.score: 18.0
    del's appeal to mathematical intuition to ground our grasp of the axioms of set theory, is notorious. I extract from his writings an account of this form of intuition which distinguishes it from the metaphorical platonism of which Gödel is sometimes accused and brings out the similarities between Gödel's views and Dummett's.
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  44. Alcinous (1995). The Handbook of Platonism. Oxford University Press.score: 18.0
    As well as acting as an introduction to the doctrines of Plato, the work provides a detailed survey of Platonist thought.
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  45. Jc Beall (2001). Existential Claims and Platonism. Philosophia Mathematica 9 (1):80-86.score: 18.0
    This paper responds to Colin Cheyne's new anti-platonist argument according to which knowledge of existential claims—claims of the form such-tmd-so exist—requires a caused connection with the given such-and-so. If his arguments succeed then nobody can know, or even justifiably believe, that acausal entities exist, in which case (standard) platonism is untenable. I argue that Cheyne's anti-platonist argument fails.
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  46. 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: 18.0
    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 who (like (...)
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  47. Colin Cheyne (1999). Problems with Profligate Platonism. Philosophia Mathematica 7 (2):164-177.score: 18.0
    According to standard mathematical platonism, mathematical entities (numbers, sets, etc.) are abstract entities. As such, they lack causal powers and spatio-temporal location. Platonists owe us an account of how we acquire knowledge of this inaccessible mathematical realm. Some recent versions of mathematical platonism postulate a plenitude of mathematical entities, and Mark Balaguer has argued that, given the existence of such a plenitude, the attainment of mathematical knowledge is rendered non-problematic. I assess his epistemology for such a profligate (...) and find it unsatisfactory because it lacks an adequate semantics, in particular, an adequate account of reference. (shrink)
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  48. Paul Redding, Mind of God, Point of View of Man, or Spirit of the World? Platonism and Organicism in the Thought of Kant and Hegel.score: 18.0
    In his account of Plato’s ideas in the first book of the “Transcendental Dialectic”, “On the concepts of pure reason”, Kant, in describing how for Plato ideas were “archetypes of things themselves”, adds that these ideas “flowed from the highest reason, through which human reason partakes in them”.1 Later, in the section of the Transcendental Dialectic treating the “ideals of pure reason”, he again attributes to Plato the notion of a “divine mind” within which the “ideas” exist. An “ideal”, Kant (...)
     
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  49. Michael D. Resnik (1985). Ontology and Logic: Remarks on Hartry Field's Anti-Platonist Philosophy of Mathematics. History and Philosophy of Logic 6 (1):191-209.score: 18.0
    In Science without numbers Hartry Field attempted to formulate a nominalist version of Newtonian physics?one free of ontic commitment to numbers, functions or sets?sufficiently strong to have the standard platonist version as a conservative extension. However, when uses for abstract entities kept popping up like hydra heads, Field enriched his logic to avoid them. This paper reviews some of Field's attempts to deflate his ontology by inflating his logic.
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  50. R. Urbaniak (2011). How Not To Use the Church-Turing Thesis Against Platonism. Philosophia Mathematica 19 (1):74-89.score: 18.0
    Olszewski claims that the Church-Turing thesis can be used in an argument against platonism in philosophy of mathematics. The key step of his argument employs an example of a supposedly effectively computable but not Turing-computable function. I argue that the process he describes is not an effective computation, and that the argument relies on the illegitimate conflation of effective computability with there being a way to find out . ‘Ah, but,’ you say, ‘what’s the use of its being right (...)
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