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Aristotle's philosophy of mathematics

In Christopher Shields (ed.), The Oxford Handbook of Aristotle. Oup Usa. pp. 465 (2012)

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  1. Quantity and number.James Franklin - 2013 - In Daniel Novotný & Lukáš Novák (eds.), Neo-Aristotelian Perspectives in Metaphysics. London: Routledge. pp. 221-244.
    Quantity is the first category that Aristotle lists after substance. It has extraordinary epistemological clarity: "2+2=4" is the model of a self-evident and universally known truth. Continuous quantities such as the ratio of circumference to diameter of a circle are as clearly known as discrete ones. The theory that mathematics was "the science of quantity" was once the leading philosophy of mathematics. The article looks at puzzles in the classification and epistemology of quantity.
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  • Avicenna on the Nature of Mathematical Objects.Mohammad Saleh Zarepour - 2016 - Dialogue 55 (3):511-536.
    Some authors have proposed that Avicenna considers mathematical objects, i.e., geometric shapes and numbers, to be mental existents completely separated from matter. In this paper, I will show that this description, though not completely wrong, is misleading. Avicenna endorses, I will argue, some sort of literalism, potentialism, and finitism.
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