Aristotle and Mathematics

Aristotle and Mathematics

Author: John J. Cleary

Publisher: BRILL

Published: 2016-06-21

Total Pages: 597

ISBN-13: 9004320903

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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.


Mathematics in Aristotle

Mathematics in Aristotle

Author: Thomas Heath

Publisher: St. Augustine's Press

Published: 1998

Total Pages: 0

ISBN-13: 9781855065642

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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.


Explorations in Ancient and Modern Philosophy

Explorations in Ancient and Modern Philosophy

Author: M. F. Burnyeat

Publisher: Cambridge University Press

Published: 2012-06-14

Total Pages: 393

ISBN-13: 0521750725

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The first of two volumes collecting the published work of one of the greatest living ancient philosophers, M.F. Burnyeat.


An Aristotelian Realist Philosophy of Mathematics

An Aristotelian Realist Philosophy of Mathematics

Author: J. Franklin

Publisher: Springer

Published: 2014-04-09

Total Pages: 316

ISBN-13: 1137400730

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Mathematics is as much a science of the real world as biology is. It is the science of the world's quantitative aspects (such as ratio) and structural or patterned aspects (such as symmetry). The book develops a complete philosophy of mathematics that contrasts with the usual Platonist and nominalist options.


Aristotle's Theory of Bodies

Aristotle's Theory of Bodies

Author: Christian Pfeiffer

Publisher: Oxford University Press

Published: 2018-07-12

Total Pages: 240

ISBN-13: 0191085308

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Christian Pfeiffer explores an important, but neglected topic in Aristotle's theoretical philosophy: the theory of bodies. A body is a three-dimensionally extended and continuous magnitude bounded by surfaces. This notion is distinct from the notion of a perceptible or physical substance. Substances have bodies, that is to say, they are extended, their parts are continuous with each other and they have boundaries, which demarcate them from their surroundings. Pfeiffer argues that body, thus understood, has a pivotal role in Aristotle's natural philosophy. A theory of body is a presupposed in, e.g., Aristotle's account of the infinite, place, or action and passion, because their being bodies explains why things have a location or how they can act upon each other. The notion of body can be ranked among the central concepts for natural science which are discussed in Physics III-IV. The book is the first comprehensive and rigorous account of the features substances have in virtue of being bodies. It provides an analysis of the concept of three-dimensional magnitude and related notions like boundary, extension, contact, continuity, often comparing it to modern conceptions of it. Both the structural features and the ontological status of body is discussed. This makes it significant for scholars working on contemporary metaphysics and mereology because the concept of a material object is intimately tied to its spatial or topological properties.


The Metaphysics

The Metaphysics

Author: Aristotle

Publisher: Penguin UK

Published: 2004-05-27

Total Pages: 546

ISBN-13: 0141912014

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The Metaphysics presents Aristotle's mature rejection of both the Platonic theory that what we perceive is just a pale reflection of reality and the hardheaded view that all processes are ultimately material. He argued instead that the reality or substance of things lies in their concrete forms, and in so doing he probed some of the deepest questions of philosophy: What is existence? How is change possible? And are there certain things that must exist for anything else to exist at all? The seminal notions discussed in The Metaphysics - of 'substance' and associated concepts of matter and form, essence and accident, potentiality and actuality - have had a profound and enduring influence, and laid the foundations for one of the central branches of Western philosophy.


Contemporary Aristotelian Metaphysics

Contemporary Aristotelian Metaphysics

Author: Tuomas E. Tahko

Publisher: Cambridge University Press

Published: 2011-12-08

Total Pages: 277

ISBN-13: 1139502697

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Aristotelian (or neo-Aristotelian) metaphysics is currently undergoing something of a renaissance. This volume brings together fourteen essays from leading philosophers who are sympathetic to this conception of metaphysics, which takes its cue from the idea that metaphysics is the first philosophy. The primary input from Aristotle is methodological, but many themes familiar from his metaphysics will be discussed, including ontological categories, the role and interpretation of the existential quantifier, essence, substance, natural kinds, powers, potential, and the development of life. The volume mounts a strong challenge to the type of ontological deflationism which has recently gained a strong foothold in analytic metaphysics. It will be a useful resource for scholars and advanced students who are interested in the foundations and development of philosophy.


One and Many in Aristotle's Metaphysics

One and Many in Aristotle's Metaphysics

Author: Edward C. Halper

Publisher: Parmenides Publishing

Published: 2005-01-12

Total Pages: 401

ISBN-13: 1930972474

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The problem of the one and the many is central to ancient Greek philosophy, but surprisingly little attention has been paid to Aristotle's treatment of it in the Metaphysics. This omission is all the more surprising because the Metaphysics is one of our principal sources for thinking that the problem is central and for the views of other ancient philosophers on it.The Central Books of the Metaphysics are widely recognized as the most difficult portion of a most difficult work. Halper uses the problem of the one and the many as a lens through which to examine the Central Books. What he sees is an extraordinary degree of doctrinal cogency and argumentative coherence in a work that almost everyone else supposes to be some sort of patchwork. Rather than trying to elucidate Aristotle's doctrines-most of which have little explicitly to do with the problem, Halper holds that the problem of the one and the many, in various formulations, is the key problematic from which Aristotle begins and with which he constructs his arguments. Thus, exploring the problem of the one and the many turns out to be a way to reconstruct Aristotle's arguments in the Metaphysics. Armed with the arguments, Halper is able to see Aristotle's characteristic doctrines as conclusions. These latter are, for the most part, supported by showing that they resolve otherwise insoluble problems. Moreover, having Aristotle's arguments enables Halper to delimit those doctrines and to resolve the apparent contradiction in Aristotle's account of primary ousia, the classic problem of the Central Books. Although there is no way to make the Metaphysics easy, this very thorough treatment of the text succeeds in making it surprisingly intelligible.


Philosophy of Mathematics

Philosophy of Mathematics

Author: Øystein Linnebo

Publisher: Princeton University Press

Published: 2020-03-24

Total Pages: 214

ISBN-13: 069120229X

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A sophisticated, original introduction to the philosophy of mathematics from one of its leading thinkers Mathematics is a model of precision and objectivity, but it appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic, accessible introduction to the field that is trying to answer that question: the philosophy of mathematics. Øystein Linnebo, one of the world's leading scholars on the subject, introduces all of the classical approaches to the field as well as more specialized issues, including mathematical intuition, potential infinity, and the search for new mathematical axioms. Sophisticated but clear and approachable, this is an essential book for all students and teachers of philosophy and of mathematics.