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David Liggins - One of the best experts on this subject based on the ideXlab platform.
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the reality of field s epistemological challenge to Platonism
Erkenntnis, 2018Co-Authors: David LigginsAbstract:In the introduction to his Realism, mathematics and modality (1989), and in earlier papers included in that collection, Hartry Field offered an epistemological challenge to Platonism in the philosophy of mathematics. Justin Clarke-Doane (in: Fabrice Pataut (ed.) Truth, objects, infinity: New perspectives on the philosophy of Paul Benacerraf, 2016) argues that Field’s challenge is an illusion: it does not pose a genuine problem for Platonism. My aim is to show that Clarke-Doane’s argument relies on a misunderstanding of Field’s challenge.
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The Reality of Field’s Epistemological Challenge to Platonism
Erkenntnis, 2017Co-Authors: David LigginsAbstract:In the introduction to his Realism, mathematics and modality (1989), and in earlier papers included in that collection, Hartry Field offered an epistemological challenge to Platonism in the philosophy of mathematics. Justin Clarke-Doane (in: Fabrice Pataut (ed.) Truth, objects, infinity: New perspectives on the philosophy of Paul Benacerraf, 2016) argues that Field’s challenge is an illusion: it does not pose a genuine problem for Platonism. My aim is to show that Clarke-Doane’s argument relies on a misunderstanding of Field’s challenge.
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Nominalism, Trivialist Platonism and Benacerraf's dilemma
Analysis, 2014Co-Authors: Chris Daly, David LigginsAbstract:In his stimulating new book The Construction of Logical Space, Agustin Rayo offers a new account of mathematics, which he calls �Trivialist Platonism�. In this article, we take issue with Rayo�s case for Trivialist Platonism and his claim that the view overcomes Benacerraf�s dilemma. Our conclusion is that Rayo has not shown that Trivialist Platonism has any advantage over nominalism.
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Is there a good epistemological argument against Platonism
Analysis, 2006Co-Authors: David LigginsAbstract:One important disagreement within the philosophy of mathematics is over the existence of mathematical objects such as numbers. Platonists assert that mathematical objects exist, whereas nominalists deny their existence. According to platonists, mathematical objects are abstract: in other words, platonists think of mathematical objects as neither causally active nor spatially located. Nominalists tend to agree that if there were mathematical objects, then they would be abstract. But they claim that there are no mathematical objects. Nominalists have various ways of arguing against Platonism. For instance, they can try to provide nominalist accounts of mathematics which provide better explanations of the phenomena than the platonist competition. Nominalists also argue against Platonism more directly. Of recent direct attacks on Platonism, Hartry Field?s (1988, 1989) is perhaps the strongest, and has certainly been the most-discussed. 1 As we shall see, it is ? broadly speaking ? epistemological in character. In their recent article ?Nominalism reconsidered? (2005: 520?23), John Burgess and Gideon Rosen contend that there is no good epistemological argument against Platonism. They propose a dilemma, claiming that epistemological arguments against Platonism either (i) rely on a dubious epistemology, or (ii) resemble a dubious sceptical argument concerning perceptual knowledge. I take it that impalement on either horn of the dilemma would seriously weaken Field?s argument. In what follows, I will defend Field?s argument by showing that it escapes both horns. I begin by reviewing Field?s argument; then I take on (i) and (ii) in turn.
Joel I. Friedman - One of the best experts on this subject based on the ideXlab platform.
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Modal Platonism: an Easy Way to Avoid Ontological Commitment to Abstract Entities
Journal of Philosophical Logic, 2005Co-Authors: Joel I. FriedmanAbstract: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 so ontologically committed. This equivalence is provable using Modal/Actuality Logic S5@. Let MAX be a strong set theory with individuals. Then the following Schematic Bombshell Result (SBR) can be shown: MAX logically yields [T is true if and only if MOD(T) is true], for scientific theories T. The proof utilizes Stephen Neale’s clever model-theoretic interpretation of Quantified Lewis S5, which I extend to S5@.
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Modal Platonism : An easy way to avoid ontological commitment to abstract entities
Journal of Philosophical Logic, 2005Co-Authors: Joel I. FriedmanAbstract: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.
Adam Lee - One of the best experts on this subject based on the ideXlab platform.
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The Platonism of Walter Pater - The Revelation of Plato and Platonism and the Authority of Affinity
The Platonism of Walter Pater, 2020Co-Authors: Adam LeeAbstract:This chapter traces the momentum of Platonic themes in essays leading up to Plato and Platonism (1893) and explores the book as a revelation of Pater’s lifelong philosophy informing his work. The structure of the book is explained as representative of Oxonian Platonism without losing sight of what makes it so characteristic of Pater. The central themes of Pater’s writing are elucidated through his understanding of Platonism, particularly through The Republic. Concerned with Plato as an author, Pater explains how he seeks organization in things, States as well as persons as well as artwork, for the sake of sanity, a conservative commitment that fights against decadence. The maintenance of sanity, the reason in beauty, is sought for the sake of one’s soul in Platonic education. It is Platonic love, explained as the affinity for persons like-to-like, that enables one to attain knowledge and express oneself with authority.
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The Platonism of Walter Pater: Embodied Equity
2020Co-Authors: Adam LeeAbstract:This book examines Walter Pater’s deep engagement with Platonism throughout his career, as a teacher of Plato in Oxford’s Literae Humaniores, from his earliest known essay, ‘Diaphaneitè’ (1864), to his final book, Plato and Platonism (1893), treating both his criticism and fiction, including his studies on myth. Pater is influenced by several of Plato’s dialogues, including Phaedrus, Symposium, Theaetetus, Cratylus, and The Republic, which inform his philosophy of aesthetics, history, myth, epistemology, ethics, language, and style. As a philosopher, critic, and artist, Plato embodies what it means to be an author to Pater, who imitates his creative practice from vision to expression. Through the recognition of form in matter, Pater views education as a journey to refine one’s knowledge of beauty in order to transform oneself. Platonism is a point of contact with his contemporaries, including Matthew Arnold and Oscar Wilde, offering a means to take new measure of their literary relationships. The philosophy also provides boundaries for critical encounters with figures across history, including Wordsworth, Michelangelo and Pico della Mirandola in The Renaissance (1873), Marcus Aurelius and Apuleius in Marius the Epicurean (1885), and Montaigne and Giordano Bruno in Gaston de Latour (1896). In the manner Platonism holds that soul or mind is the essence of a person, Pater’s criticism seeks the mind of the author as an affinity, so that his writing enacts Platonic love.
Denis Robichaud - One of the best experts on this subject based on the ideXlab platform.
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tearing plato to pieces gianfrancesco pico della mirandola and marsilio ficino on the history of Platonism
Renaissance and Reformation, 2020Co-Authors: Denis RobichaudAbstract:This article considers Gianfrancesco Pico della Mirandola’s understanding of the history of Platonism in his Examen vanitatis. It analyzes his sources and methods for understanding the history of philosophy—genealogical source criticism, historiographical analysis, and comparative history—and argues that his approach is shaped by anti-Platonic Christian apologetics. It documents how Gianfrancesco Pico closely studies Marsilio Ficino’s and his uncle Giovanni Pico’s understandings of Platonism and its history, and how his contextualization of their work within the broader history of Platonism is part of a larger endeavour to turn the page and even close the book on this chapter of the Quattrocento. Although neither Ficino nor Gianfrancesco finds universal agreement among ancient Platonists, Ficino explains their history as one of inquiry and interpretation, in which Platonism and Christianity are inexorably united, whereas Gianfrancesco characterizes it as a history of lies and disagreements that threaten Christianity. In trying to protect sacred history, Gianfrancesco Pico helped develop the tools that would eventually critique it.
Robichaud, Denis J.-j. - One of the best experts on this subject based on the ideXlab platform.
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Tearing Plato to Pieces: Gianfrancesco Pico della Mirandola and Marsilio Ficino on the History of Platonism Denis J.-J. Robichaud
Iter Press, 2020Co-Authors: Robichaud, Denis J.-j.Abstract:This article considers Gianfrancesco Pico della Mirandola’s understanding of the history of Platonism in his Examen vanitatis. It analyzes his sources and methods for understanding the history of philosophy—genealogical source criticism, historiographical analysis, and comparative history—and argues that his approach is shaped by anti-Platonic Christian apologetics. It documents how Gianfrancesco Pico closely studies Marsilio Ficino’s and his uncle Giovanni Pico’s understandings of Platonism and its history, and how his contextualization of their work within the broader history of Platonism is part of a larger endeavour to turn the page and even close the book on this chapter of the Quattrocento. Although neither Ficino nor Gianfrancesco finds universal agreement among ancient Platonists, Ficino explains their history as one of inquiry and interpretation, in which Platonism and Christianity are inexorably united, whereas Gianfrancesco characterizes it as a history of lies and disagreements that threaten Christianity. In trying to protect sacred history, Gianfrancesco Pico helped develop the tools that would eventually critique it.Cet article examine la conception de l’histoire du Platonisme qui se détache de l’Examen vanitatis de Gianfrancesco Pico della Mirandola. Il analyse les sources et les méthodes utilisées par Gianfrancesco pour comprendre l’histoire de la philosophie — critique généalogique des sources, analyse historiographique et histoire comparée — et soutient que son Examen vanitatis est façonné par l’apologétique chrétienne anti-platonicienne. Il démontre qu’en s’intéressant de près aux interprétations que Marsilio Ficino et son oncle Giovanni Pico ont proposées de l’oeuvre de Platon et son histoire, et en replaçant ces dernières dans le contexte plus large de l’histoire du Platonisme, Gianfrancisco Pico a participé à une entreprise plus vaste qui visait à tourner la page, voire à refermer entièrement le livre de ce chapitre du Quattrocento. Bien que ni Ficino ni Gianfrancesco ne trouvent un accord universel parmi les anciens platoniciens, Ficino revisite cette période comme l’histoire d’une enquête herméneutique qui aurait inexorablement lié le Platonisme au christianisme, tandis que Gianfrancesco l’interprète comme une série de mensonges et de désaccords qui auraient à l’inverse menacé le christianisme. En essayant de protéger l’histoire sacrée, Gianfrancesco Pico a fini par contribuer à développer les outils qui serviront à la critiquer
