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  1. The Platonist Absurd Accumulation of Geometrical Objects: Metaphysics Μ.2.José Edgar González-Varela - 2020 - Phronesis 65 (1):76-115.
    In the first argument of Metaphysics Μ.2 against the Platonist introduction of separate mathematical objects, Aristotle purports to show that positing separate geometrical objects to explain geometrical facts generates an ‘absurd accumulation’ of geometrical objects. Interpretations of the argument have varied widely. I distinguish between two types of interpretation, corrective and non-corrective interpretations. Here I defend a new, and more systematic, non-corrective interpretation that takes the argument as a serious and very interesting challenge to the Platonist.
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  2. An Absurd Accumulation: Metaphysics M.2, 1076b11-36.Emily Katz - 2014 - Phronesis 59 (4):343-368.
    The opening argument in the Metaphysics M.2 series targeting separate mathematical objects has been dismissed as flawed and half-hearted. Yet it makes a strong case for a point that is central to Aristotle’s broader critique of Platonist views: if we posit distinct substances to explain the properties of sensible objects, we become committed to an embarrassingly prodigious ontology. There is also something to be learned from the argument about Aristotle’s own criteria for a theory of mathematical objects. I hope to (...)
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  3. Aristotle on Mathematical Truth.Phil Corkum - 2012 - British Journal for the History of Philosophy 20 (6):1057-1076.
    Both literalism, the view that mathematical objects simply exist in the empirical world, and fictionalism, the view that mathematical objects do not exist but are rather harmless fictions, have been both ascribed to Aristotle. The ascription of literalism to Aristotle, however, commits Aristotle to the unattractive view that mathematics studies but a small fragment of the physical world; and there is evidence that Aristotle would deny the literalist position that mathematical objects are perceivable. The ascription of fictionalism also faces a (...)
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  4. Rationes ex machina. La micrologie à l’âge de l’industrie de l’argument.Leone Gazziero - 2008 - Paris: Vrin.
    Do Ideas exist and can we prove it ? Do proofs of their existence have all the same value or not ? Aristotle addresses these issues in two famous documents of the controversy that pitted supporters of the theory of Forms against its opponents within Plato’s Academy : his lost work, quoted by Alexander of Aphrodisias by the title of Peri Ideon, and the lengthy thrust against Ideas that can be read, with some minor variations, in books A, chapter 9, (...)
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