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  1. Measuring Humans Against Gods: On the Digression of Plato’s Theaetetus.Jens Kristian Larsen - 2019 - Archiv für Geschichte der Philosophie 101 (1):1-29.
    The digression of Plato’s Theaetetus (172c2–177c2) is as celebrated as it is controversial. A particularly knotty question has been what status we should ascribe to the ideal of philosophy it presents, an ideal centered on the conception that true virtue consists in assimilating oneself as much as possible to god. For the ideal may seem difficult to reconcile with a Socratic conception of philosophy, and several scholars have accordingly suggested that it should be read as ironic and directed only at (...)
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  2. Univocity, Duality, and Ideal Genesis: Deleuze and Plato.John Bova & Paul M. Livingston - 2017 - In Contemporary Encounters with Ancient Metaphysics. Edinburgh University Press.
    In this essay, we consider the formal and ontological implications of one specific and intensely contested dialectical context from which Deleuze’s thinking about structural ideal genesis visibly arises. This is the formal/ontological dualism between the principles, ἀρχαί, of the One (ἕν) and the Indefinite/Unlimited Dyad (ἀόριστος δυάς), which is arguably the culminating achievement of the later Plato’s development of a mathematical dialectic.3 Following commentators including Lautman, Oskar Becker, and Kenneth M. Sayre, we argue that the duality of the One and (...)
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  3. 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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  4. Kallikles i geometria. Przyczynek do Platońskiej koncepcji sprawiedliwości [Callicles and Geometry: On Plato’s Conception of Justice].Marek Piechowiak - 2013 - In Zbigniew Władek (ed.), Księga życia i twórczości. Księga pamiątkowa dedykowana Profesorowi Romanowi A. Tokarczykowi. Wydawnictwo Polihymnia. pp. vol. 5, 281-291.
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  5. A Likely Account of Necessity: Plato's Receptacle as a Physical and Metaphysical Foundation for Space.Barbara Sattler - 2012 - Journal of the History of Philosophy 50 (2):159-195.
    This paper aims to show that—and how—Plato’s notion of the receptacle in the Timaeus provides the conditions for developing a mathematical as well as a physical space without itself being space. In response to the debate whether Plato’s receptacle is a conception of space or of matter, I suggest employing criteria from topology and the theory of metric spaces as the most basic ones available. I show that the receptacle fulfils its main task–allowing the elements qua images of the Forms (...)
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  6. 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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  7. Plato on Why Mathematics is Good for the Soul.Myles Burnyeat - 2000 - In T. Smiley (ed.), Mathematics and Necessity: Essays in the History of Philosophy. pp. 1-81.
    Anyone who has read Plato’s Republic knows it has a lot to say about mathematics. But why? I shall not be satisfied with the answer that the future rulers of the ideal city are to be educated in mathematics, so Plato is bound to give some space to the subject. I want to know why the rulers are to be educated in mathematics. More pointedly, why are they required to study so much mathematics, for so long?
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  8. Figure, Ratio, Form: Plato's Five Mathematical Studies.Mitchell Miller - 1999 - Apeiron 32 (4):73-88.
    A close reading of the five mathematical studies Socrates proposes for the philosopher-to-be in Republic VII, arguing that (1) each study proposes an object the thought of which turns the soul towards pure intelligibility and that (2) the sequence of studies involves both a departure from the sensible and a return to it in its intelligible structure.
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  9. Plato as "Architect of Science".Leonid Zhmud - 1998 - Phronesis 43 (3):211-244.
    The figure of the cordial host of the Academy, who invited the most gifted mathematicians and cultivated pure research, whose keen intellect was able if not to solve the particular problem then at least to show the method for its solution: this figure is quite familiar to students of Greek science. But was the Academy as such a center of scientific research, and did Plato really set for mathematicians and astronomers the problems they should study and methods they should use? (...)
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