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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. `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 relate his account (...)
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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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  • 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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  • 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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  • How to Know the Good: The Moral Epistemology of Plato's Republic.Jyl Gentzler - 2005 - Philosophical Review 114 (4):469-496.
    John Mackie famously dismissed the rational tenability of moral objectivism with two quick arguments. The second, the so-called “argument from queerness,” proceeds as follows. A commitment to moral objectivism brings with it a commitment to the existence of moral properties as “queer” as Platonic Forms that are apprehended only through occult faculties like so-called “moral intuition” (Mackie 1977, 38). Since we have no reason to believe that there is any faculty such as moral intuition that serves as a reliable Form (...)
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