Aristotle and Mathematics: Aporetic Method in Cosmology and by John J. Cleary

By John J. Cleary

John Cleary the following explores the function which the mathematical sciences play in Aristotle's philosophical suggestion, specifically in his cosmology, metaphysics, and epistemology. He additionally thematizes the aporetic procedure via which he offers with philosophical questions on the rules of arithmetic. the 1st chapters contemplate Plato's mathematical cosmology within the gentle of Aristotle's severe contrast among physics and arithmetic. next chapters study 3 easy aporiae approximately mathematical items which Aristotle himself develops in his technology of first philosophy. What emerges from this dialectical inquiry is a special belief of substance and of order within the universe, which provides precedence to physics over arithmetic because the cosmological technological know-how. inside this diversified world-view, we will be able to greater comprehend what we now name Aristotle's philosophy of arithmetic.

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In fact, I argue that the terms for an adequate solution are set by this dialectical procedure because his goal of 'saving the phenomena' requires that the difficulties be resolved, while the grain of truth in previous opinions be preserved. Within Aristode's own dialectical method, I distinguish between this first aporetic stage of reviewing the common opinions and a second elenctic stage, which involves the refutation of some (or all) of the conflicting views so that the initial impasse is broken.

The proposed reforms of astronomy are introduced (529C) so that the discipline will function better in orienting the soul towards intelligible reality. e. invisible) objects. In this case Socrates does not mention any sensible opposites that would force their souls to seek help from the intellect, as in the case of arithmetic and geometry. 30 Even though he concedes that the heavenly bodies are the most beautiful and most exact of sensible things, he insists (529C-D) that they fall short of the real beings which can be grasped only by reason.

INTRODUCTION XXVll It seems clear that the Kantian presuppositions which underpin the intuitionist view render it anachronistic for the purposes of discussing Greek philosophy of mathematics. Although it is not obvious that the logicist view is similarly anachronistic, it may be argued that neither Plato nor Aristode ever tried to reduce mathematics to logic. That seems to leave platonism as the only viable modern parallel to ancient views on the foundations of mathematics. However, the term 'platonism' should not lull us into a false sense of security about the dangers of anachronism, as the terms of the modern debate are likely to be shaped by modern philosophical presuppositions.

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