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    It is a mistake to assume that any mention of mathematics... — Carmelics
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    It is a mistake to assume that any mention of mathematics in Plato indicates Pythagorean influence.

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    2 reasons for
    1 reason against

    Reasons For

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    • 1.Plato's mathematical philosophy in the Republic and Meno draws on the Socratic method of recollection and dialectic, not Pythagorean numerology.
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    • 2.The Forms as mathematical objects in Plato derive from his own theory of participation, which differs structurally from Pythagorean number-as-substance doctrines.
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    • 3.Walter Burkert's landmark 1972 study demonstrated that many supposed Pythagorean mathematical doctrines were actually later Platonist retrojections onto the tradition.
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    Reason for 2 of 2
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    • 1.Independent mathematical traditions flourished in fifth-century Athens through figures like Hippocrates of Chios, providing non-Pythagorean sources for Plato's mathematical interests.
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    • 2.Plato's treatment of mathematical objects as intermediaries between Forms and particulars has no clear precedent in surviving Pythagorean texts, indicating original development.
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    Reasons Against

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    • 1.The role of Pythagoreanism in Greek mathematics has been overstated.
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    • 2.The most prominent mathematicians in Plato's dialogues, Theodorus and Theaetetus, are not Pythagoreans.
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    • 3.Although Plato had contact with Pythagorean mathematicians such as Archytas, this contact does not make mathematics in the dialogues broadly Pythagorean.
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    Although Plato had contact with Pythagorean mathematicians such as Archytas, thi...Independent mathematical traditions flourished in fifth-century Athens through f...Plato's mathematical philosophy in the Republic and Meno draws on the Socratic m...Plato's treatment of mathematical objects as intermediaries between Forms and pa...
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    The Forms as mathematical objects in Plato derive from his own theory of partici...The most prominent mathematicians in Plato's dialogues, Theodorus and Theaetetus...The role of Pythagoreanism in Greek mathematics has been overstated.Walter Burkert's landmark 1972 study demonstrated that many supposed Pythagorean...

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    In recent studies of the topic that lie somewhere between these extremes, one approach is to argue that there is clear Pythagorean influence on Plato but that its scope is much more limited than often assumed (Huffman 2013). Plato explicitly mentions Pythagoras and the Pythagoreans only one time each in the dialogues and this provides prima facie evidence that Pythagorean influence was not extensive. Moreover, at Metaphysics 987a29–31 the “these men” that Aristole says Plato follows in most resp
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    3 (2 for, 1 against)
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    1 edit