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Plato on Why Mathematics is Good for the Soul

In T. Smiley (ed.), Mathematics and Necessity: Essays in the History of Philosophy. pp. 1-81 (2000)

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  1. What Are the Objects of Dianoia?Lloyd P. Gerson - 2018 - Plato Journal 18:45-53.
    In this paper, I examine the problem of the so-called Mathematical Objects within the context of the Divided Line. I argue that Plato believes that there are such objects but their distinctness and the mode of cognition relative to them can only be understood in relation to the superordinate, unhypothetical first principle of all, the Idea of the Good. The objects of mathematics or διάνοια are, unlike the objects of intellection or νόησις, cognized independently of the Good.
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  • I—Plato’s Philebus and Some ‘Value of Knowledge’ Problems.Verity Harte - 2018 - Aristotelian Society Supplementary Volume 92 (1):27-48.
    In modern epistemology, one ‘value of knowledge’ problem concerns the question why knowledge should be valued more highly than mere true belief. Though this problem has a background in Plato, the present paper, focused on Philebus 55–9, is concerned with a different question: what questions might one ask about the value of knowledge, and what question does Plato ask here? The paper aims to articulate the kind of value Plato here attributes to ‘useless’ knowledge, knowledge pursued without practical object; and (...)
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  • Plato on Self-Motion in Laws X.Rareș Ilie Marinescu - 2021 - Rhizomata 9 (1):96-122.
    In this paper, I argue that Plato conceives self-motion as non-spatial in Laws X. I demonstrate this by focusing on the textual evidence and by refuting interpretations according to which self-motion either is a specific type of spatial motion or is said to require space as a necessary condition for its occurrence. Moreover, I show that this non-spatial understanding differs from the identification of the soul’s motion with locomotion in the Timaeus. Consequently, I provide an explanation for this difference between (...)
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  • 'Appearing Equal' at Phaedo 74 B 4-C 6: An Epistemic Interpretation.Thomas M. Tuozzo - 2018 - Oxford Studies in Ancient Philosophy 54.
    The argument at Phaedo 74 B 4‐C 6 that the equal itself is ‘something different from’ sets of physical equals depends on Leibniz's Law: there is a property that perceptible equals have that the equal itself does not have. What I call the ‘epistemic interpretation’ holds that the property is an epistemic one: having appeared unequal. The ‘ontological interpretation’ holds that the property is not epistemic, but simply the property of being unequal. The most natural reading of the text favours (...)
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  • ‘Let No-One Ignorant of Geometry…’: Mathematical Parallels for Understanding the Objectivity of Ethics.James Franklin - 2021 - Journal of Value Inquiry 55:1-20.
    It may be a myth that Plato wrote over the entrance to the Academy “Let no-one ignorant of geometry enter here.” But it is a well-chosen motto for his view in the Republic that mathematical training is especially productive of understanding in abstract realms, notably ethics. That view is sound and we should return to it. Ethical theory has been bedevilled by the idea that ethics is fundamentally about actions (right and wrong, rights, duties, virtues, dilemmas and so on). That (...)
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  • Minding the Gap in Plato's Republic.Eric Brown - 2004 - Philosophical Studies 117 (1-2):275-302.
    At least since Sachs' well-known essay, readers of Plato's Republic have worried that there is a gap between the challenge posed to Socrates--to show that it is always in one's interest to act justly--and his response--to show that it is always in one's interest to have a just soul. The most popular response has been that Socrates fills this gap in Books Five through Seven by supposing that knowledge of the Forms motivates those with just souls to act justly. I (...)
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  • Proclus on Nature: Philosophy of Nature and its Methods in Proclus’ Commentary on Plato’s Timaeus.Marije Martijn - 2010 - Brill.
    One of the hardest questions to answer for a (Neo)platonist is to what extent and how the changing and unreliable world of sense perception can itself be an object of scientific knowledge. My dissertation is a study of the answer given to that question by the Neoplatonist Proclus (Athens, 411-485) in his Commentary on Plato’s Timaeus. I present a new explanation of Proclus’ concept of nature and show that philosophy of nature consists of several related subdisciplines matching the ontological stratification (...)
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  • When and Why Understanding Needs Phantasmata: A Moderate Interpretation of Aristotle’s De Memoria and De Anima on the Role of Images in Intellectual Activities.Caleb Cohoe - 2016 - Phronesis: A Journal for Ancient Philosophy 61 (3):337-372.
    I examine the passages where Aristotle maintains that intellectual activity employs φαντάσματα (images) and argue that he requires awareness of the relevant images. This, together with Aristotle’s claims about the universality of understanding, gives us reason to reject the interpretation of Michael Wedin and Victor Caston, on which φαντάσματα serve as the material basis for thinking. I develop a new interpretation by unpacking the comparison Aristotle makes to the role of diagrams in doing geometry. In theoretical understanding of mathematical and (...)
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  • The Good, the Bad, and the Ugly: Does Plato Make Room for Negative Forms in His Ontology?Necip Fikri Alican - 2017 - Cosmos and History 13 (3):154–191.
    Plato seems to countenance both positive and negative Forms, that is to say, both good and bad ones. He may not say so outright, but he invokes both and rejects neither. The apparent finality of this impression creates a lack of direct interest in the subject: Plato scholars do not give negative Forms much thought except as the prospect relates to something else they happen to be doing. Yet when they do give the matter any thought, typically for the sake (...)
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  • « The Role Of Stereometry In Plato’s Republic ».Chiye Izumi - 2011 - Plato Journal 11.
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  • Aristotle on Kind‐Crossing.Philipp Steinkrüger - 2018 - Oxford Studies in Ancient Philosophy 54:107-158.
    This paper concerns Aristotle's kind‐crossing prohibition. My aim is twofold. I argue that the traditional accounts of the prohibition are subject to serious internal difficulties and should be questioned. According to these accounts, Aristotle's prohibition is based on the individuation of scientific disciplines and the general kind that a discipline is about, and it says that scientific demonstrations must not cross from one discipline, and corresponding kind, to another. I propose a very different account of the prohibition. The prohibition is (...)
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  • The One Over Many Principle of Republic 596a.José Edgar González-Varela - 2020 - Apeiron 53 (4):339-361.
    Republic 596a introduces a One over Many principle that has traditionally been considered as an argument for the existence of Forms, according to which, one Form should be posited for each like-named plurality. This interpretation was challenged by (Smith, J. A. 1917. “General Relative Clauses in Greek.” Classical Review 31: 69–71.), who interpreted it rather as a statement that each Form is unique and correlated to a plurality of things that have the same name as it. (Sedley, D. 2013. “Plato (...)
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  • The Ethics–Mathematics Analogy.Justin Clarke-Doane - 2020 - Philosophy Compass 15 (1).
    Ethics and mathematics have long invited comparisons. On the one hand, both ethical and mathematical propositions can appear to be knowable a priori, if knowable at all. On the other hand, mathematical propositions seem to admit of proof, and to enter into empirical scientific theories, in a way that ethical propositions do not. In this article, I discuss apparent similarities and differences between ethical (i.e., moral) and mathematical knowledge, realistically construed -- i.e., construed as independent of human mind and languages. (...)
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  • Plato’s Forms as Functions and Structures.Dorothea Frede - 2020 - History of Philosophy & Logical Analysis 23 (2):291-316.
    Despite the fact that the theory of Forms is regarded as the hallmark of Plato’s philosophy, it has remained remarkably elusive, because it is more hinted at than explained in his dialogues. Given the uncertainty concerning the nature and extension of the Forms, this article makes no pretense to coming up with solutions to all problems that have occupied scholars since antiquity. It aims to elucidate only two aspects of that theory: the indication in certain dialogues that the Forms are (...)
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  • One, Two, Three… A Discussion on the Generation of Numbers in Plato’s Parmenides.Florin George Calian - 2015 - New Europe College:49-78.
    One of the questions regarding the Parmenides is whether Plato was committed to any of the arguments developed in the second part of the dialogue. This paper argues for considering at least one of the arguments from the second part of the Parmenides, namely the argument of the generation of numbers, as being platonically genuine. I argue that the argument at 142b-144b, which discusses the generation of numbers, is not deployed for the sake of dialectical argumentation alone, but it rather (...)
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  • Moral Geometries.Adir H. Petel - 2020 - Common Knowledge 26 (3):453-551.
    The literary and critical discourse about characters and characterization in Anglophone drama and fiction since the Renaissance shows a persistent but underrecognized presence of three idioms and vocabularies, two highly developed and one nascent, that either derive from the rhetoric of mathematics in classical antiquity or participate in its modern afterlife. Those discourses—which this article studies in detail—are, first, an explicitly Theophrastan one, in which taxonomies of character are constructed; second, an explicitly Euclidean one, in which characterization is discussed and (...)
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  • An Unexplained Overlap Between Sophist 232b1-236d4 and Republic X.Nicholas Zucchetti - 2020 - Archai: Revista de Estudos Sobre as Origens Do Pensamento Ocidental 30:e03014.
    Although most scholars agree that the lexicon of Sophist 232b1-236d4 is similar to that of Republic X, they leave undetermined whether they are theoretically compatible. Notably, both dialogues elucidate the art of imitation through the metaphor of the painter who deceives his pupils through φαντάσματα. I argue that Plato’s conception of imitation of the Republic is not only consistent with that presented in the Sophist, but also importantly integrates it.
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  • Plato’s Use of the Term Stoicheion.Pia De Simone - 2020 - Archai: Revista de Estudos Sobre as Origens Do Pensamento Ocidental 30:e03005.
    The aim of this paper is to examine the implications of Plato’s use of the term stoicheion, since his awareness of stoicheion’s polysemy reveals his view of the origin, the complexity and, at the same time, the order of reality. Moreover, his use of stoicheion allowed him both to inherit and to detach himself from his predecessors. I begin by presenting the history of the notion of stoicheion; then, since one of the meanings of stoicheion is ‘letter of the alphabet’, (...)
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  • Dianoia Left and Right.S. Pollard - 2013 - Philosophia Mathematica 21 (3):309-322.
    In Plato's Phaedrus, Socrates offers two speeches, the first portraying madness as mere disease, the second celebrating madness as divine inspiration. Each speech is correct, says Socrates, though neither is complete. The two kinds of madness are like the left and right sides of a living body: no account that focuses on just one half can be adequate. In a recent paper, Hugh Benson gives a left-handed speech about a psychic condition endemic among mathematicians: dianoia. Benson acknowledges that his account (...)
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  • The Problem is Not Mathematics, but Mathematicians: Plato and the Mathematicians Again.H. H. Benson - 2012 - Philosophia Mathematica 20 (2):170-199.
    I argue against a formidable interpretation of Plato’s Divided Line image according to which dianoetic correctly applies the same method as dialectic. The difference between the dianoetic and dialectic sections of the Line is not methodological, but ontological. I maintain that while this interpretation correctly identifies the mathematical method with dialectic, ( i.e. , the method of philosophy), it incorrectly identifies the mathematical method with dianoetic. Rather, Plato takes dianoetic to be a misapplication of the mathematical method by a subset (...)
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  • Mathematics, Mental Imagery, and Ontology: A New Interpretation of the Divided Line.Miriam Byrd - 2018 - International Journal of the Platonic Tradition 12 (2):111-131.
    This paper presents a new interpretation of the objects of dianoia in Plato’s divided line, contending that they are mental images of the Forms hypothesized by the dianoetic reasoner. The paper is divided into two parts. A survey of the contemporary debate over the identity of the objects of dianoia yields three criteria a successful interpretation should meet. Then, it is argued that the mental images interpretation, in addition to proving consistent with key passages in the middle books of the (...)
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  • Plato Was NOT A Mathematical Platonist.Elaine Landry - unknown
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  • Beginning the 'Longer Way'.Mitchell Miller - 2007 - In G. R. F. Ferrari (ed.), The Cambridge Companion to Plato's Republic. Cambridge University Press. pp. 310--344.
    At 435c-d and 504b ff., Socrates indicates that there is a "longer and fuller way" that one must take in order to get "the best possible view" of the soul and its virtues. But Plato does not have him take this "longer way." Instead Socrates restricts himself to an indirect indication of its goals by his images of sun, line, and cave and to a programmatic outline of its first phase, the five mathematical studies. Doesn't this pointed restraint function as (...)
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  • Plato on Education and Art.Rachana Kamtekar - 2008 - In Gail Fine (ed.), The Oxford Handbook of Plato. Oxford University Press. pp. 336--359.
    The article resonates Plato's ideas on education and art. In the Apology, Socrates describes his life's mission of practicing philosophy as aimed at getting the Athenians to care for virtue; in the Gorgias, Plato claims that happiness depends entirely on education and justice; in the Protagoras and the Meno, he puzzles about whether virtue is teachable or how else it might be acquired; in the Phaedrus, he explains that teaching and persuading require knowledge of the soul and its powers, which (...)
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  • Aristotle's Ethics and the Crafts: A Critique.Thomas Peter Stephen Angier - unknown
    This dissertation is a study of the relation between Aristotle’s ethics and the crafts (or technai). My thesis is that Aristotle’s argument is at key points shaped by models proper to the crafts, this shaping being deeper than is generally acknowledged, and philosophically more problematic. Despite this, I conclude that the arguments I examine can, if revised, be upheld. The plan of the dissertation is as follows – Preface: The relation of my study to the extant secondary literature; Introduction: The (...)
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  • Early Education in Plato's Republic.Michelle Jenkins - 2015 - British Journal for the History of Philosophy 23 (5):843-863.
    In this paper, I reconsider the commonly held position that the early moral education of the Republic is arational since the youths of the Kallipolis do not yet have the capacity for reason. I argue that, because they receive an extensive mathematical education alongside their moral education, the youths not only have a capacity for reason but that capacity is being developed in their early education. If this is so, though, then we must rethink why the early moral education is (...)
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