By John J. Cleary

John Cleary the following explores the function which the mathematical sciences play in Aristotle's philosophical idea, specifically in his cosmology, metaphysics, and epistemology. He additionally thematizes the aporetic process via which he bargains with philosophical questions about the principles of arithmetic. the 1st chapters ponder Plato's mathematical cosmology within the mild of Aristotle's severe contrast among physics and arithmetic. next chapters research 3 easy aporiae approximately mathematical items which Aristotle himself develops in his technological know-how of first philosophy. What emerges from this dialectical inquiry is a distinct belief of substance and of order within the universe, which provides precedence to physics over arithmetic because the cosmological technological know-how. inside of this various world-view, we will larger comprehend what we now name Aristotle's philosophy of arithmetic.

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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.

Thus, he rejects the One Itself along with Being Itself as general ontological principles. Furthermore, the putative failure of the Platonists to establish any causal role for Forms in relation to the sensible world is a decisive factor in Aristotle's rejection of these entities along with mathematical objects as supersensible substances. By contrast, he attributes such a mode of being to the Prime Mover precisely because it functions within his own cosmological system as the final cause of motion in the sensible universe.

But yet his discussions of quantity in the Categories and Metaphysics V seem to treat mathematical entities as if they were independent subjects of attributes. While this conforms with the practice of mathematicians, it will not do for Aristode because he regards quantity as being a different category from that of substance. As he points out in Metaphysics VI, however, this whole question about foundations is not the business of mathematicians but is rather a task for (first) philosophers. Thus the fourth chapter of my book is pivotal, since it explores Aristode's dialectical method of inquiry in metaphysical treatises where questions about first principles are being considered.