Mathematics And Metaphysics In Aristotle

John Cleary here explores the role which the mathematical sciences play in Aristotle's philosophical thought, especially in his cosmology, metaphysics, and epistemology. He also thematizes the aporetic method by means of which he deals with philosophical questions about the foundations of mathematics. The first two chapters consider Plato's mathematical cosmology in the light of Aristotle's critical distinction between physics and mathematics. Subsequent chapters examine three basic aporiae about mathematical objects which Aristotle himself develops in his science of first philosophy. What emerges from this dialectical inquiry is a different conception of substance and of order in the universe, which gives priority to physics over mathematics as the cosmological science. Within this different world-view, we can better understand what we now call Aristotle's philosophy of mathematics.

This is a detailed exposition of Aristotelian mathematics and mathematical terminology. It contains clear translations of all the most important passages on mathematics in the writings of Aristotle, together with explanatory notes and commentary by Heath. Particularly interesting are the discussions of hypothesis and related terms, of Zeno's paradox, and of the relation of mathematics to other sciences. The book includes a comprehensive index of the passages translated.

Originally published in 1949. This meticulously researched book presents a comprehensive outline and discussion of Aristotle’s mathematics with the author's translations of the greek. To Aristotle, mathematics was one of the three theoretical sciences, the others being theology and the philosophy of nature (physics). Arranged thematically, this book considers his thinking in relation to the other sciences and looks into such specifics as squaring of the circle, syllogism, parallels, incommensurability of the diagonal, angles, universal proof, gnomons, infinity, agelessness of the universe, surface of water, meteorology, metaphysics and mechanics such as levers, rudders, wedges, wheels and inertia. The last few short chapters address ‘problems’ that Aristotle posed but couldn’t answer, related ethics issues and a summary of some short treatises that only briefly touch on mathematics.

Metaphysics is Aristotle's version of philosophy examining the nature of reality, including the relationship between mind and matter, substance and attribute, fact and value. Aristotle argues that there are a handful of universal truths. Aristotle's works have influenced science, religion, and philosophy for nearly two thousand years. He could be thought of as the father of logical thought. Aristotle wrote: "There is nothing in the intellect that was not first in the senses." He wrote that everything that is learned in life is learned through sensory perception. Aristotle was the first to establish the founding principle of logic. The great writer Dante called Aristotle "The Master of those who know."

The ancient Greek thinker refutes skepticism, demonstrates God's existence, compares metaphysics to the other sciences, elucidates the nature of the infinite, and explores other major philosophical issues.