An Aristotelian Realist Philosophy Of Mathematics
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Author | : J. Franklin |
Publisher | : Springer |
Total Pages | : 316 |
Release | : 2014-04-09 |
Genre | : Mathematics |
ISBN | : 1137400730 |
Download An Aristotelian Realist Philosophy of Mathematics Book in PDF, Epub and Kindle
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.
Author | : Woosuk Park |
Publisher | : Springer |
Total Pages | : 233 |
Release | : 2018-07-12 |
Genre | : Philosophy |
ISBN | : 3319951475 |
Download Philosophy's Loss of Logic to Mathematics Book in PDF, Epub and Kindle
This book offers a historical explanation of important philosophical problems in logic and mathematics, which have been neglected by the official history of modern logic. It offers extensive information on Gottlob Frege’s logic, discussing which aspects of his logic can be considered truly innovative in its revolution against the Aristotelian logic. It presents the work of Hilbert and his associates and followers with the aim of understanding the revolutionary change in the axiomatic method. Moreover, it offers useful tools to understand Tarski’s and Gödel’s work, explaining why the problems they discussed are still unsolved. Finally, the book reports on some of the most influential positions in contemporary philosophy of mathematics, i.e., Maddy’s mathematical naturalism and Shapiro’s mathematical structuralism. Last but not least, the book introduces Biancani’s Aristotelian philosophy of mathematics as this is considered important to understand current philosophical issue in the applications of mathematics. One of the main purposes of the book is to stimulate readers to reconsider the Aristotelian position, which disappeared almost completely from the scene in logic and mathematics in the early twentieth century.
Author | : James Robert Brown |
Publisher | : Routledge |
Total Pages | : 181 |
Release | : 2005-08-09 |
Genre | : Philosophy |
ISBN | : 1134806434 |
Download Philosophy of Mathematics Book in PDF, Epub and Kindle
Philosophy of Mathematics is an excellent introductory text. This student friendly book discusses the great philosophers and the importance of mathematics to their thought. It includes the following topics: * the mathematical image * platonism * picture-proofs * applied mathematics * Hilbert and Godel * knots and nations * definitions * picture-proofs and Wittgenstein * computation, proof and conjecture. The book is ideal for courses on philosophy of mathematics and logic.
Author | : Penelope Rush |
Publisher | : Cambridge University Press |
Total Pages | : 279 |
Release | : 2014-10-16 |
Genre | : Mathematics |
ISBN | : 1107039649 |
Download The Metaphysics of Logic Book in PDF, Epub and Kindle
This wide-ranging collection of essays explores the nature of logic and the key issues and debates in the metaphysics of logic.
Author | : M. F. Burnyeat |
Publisher | : Cambridge University Press |
Total Pages | : 393 |
Release | : 2012-06-14 |
Genre | : History |
ISBN | : 0521750725 |
Download Explorations in Ancient and Modern Philosophy Book in PDF, Epub and Kindle
The first of two volumes collecting the published work of one of the greatest living ancient philosophers, M.F. Burnyeat.
Author | : David Corfield |
Publisher | : Cambridge University Press |
Total Pages | : 300 |
Release | : 2003-04-24 |
Genre | : Philosophy |
ISBN | : 1139436392 |
Download Towards a Philosophy of Real Mathematics Book in PDF, Epub and Kindle
In this ambitious study, David Corfield attacks the widely held view that it is the nature of mathematical knowledge which has shaped the way in which mathematics is treated philosophically and claims that contingent factors have brought us to the present thematically limited discipline. Illustrating his discussion with a wealth of examples, he sets out a variety of approaches to new thinking about the philosophy of mathematics, ranging from an exploration of whether computers producing mathematical proofs or conjectures are doing real mathematics, to the use of analogy, the prospects for a Bayesian confirmation theory, the notion of a mathematical research programme and the ways in which new concepts are justified. His inspiring book challenges both philosophers and mathematicians to develop the broadest and richest philosophical resources for work in their disciplines and points clearly to the ways in which this can be done.
Author | : James Franklin |
Publisher | : JHU Press |
Total Pages | : 767 |
Release | : 2015-08-01 |
Genre | : Science |
ISBN | : 1421418819 |
Download The Science of Conjecture Book in PDF, Epub and Kindle
How did we make reliable predictions before Pascal and Fermat's discovery of the mathematics of probability in 1654? What methods in law, science, commerce, philosophy, and logic helped us to get at the truth in cases where certainty was not attainable? In The Science of Conjecture, James Franklin examines how judges, witch inquisitors, and juries evaluated evidence; how scientists weighed reasons for and against scientific theories; and how merchants counted shipwrecks to determine insurance rates. The Science of Conjecture provides a history of rational methods of dealing with uncertainty and explores the coming to consciousness of the human understanding of risk.
Author | : Geoffrey Hellman |
Publisher | : Cambridge University Press |
Total Pages | : 167 |
Release | : 2018-11-29 |
Genre | : Science |
ISBN | : 110863074X |
Download Mathematical Structuralism Book in PDF, Epub and Kindle
The present work is a systematic study of five frameworks or perspectives articulating mathematical structuralism, whose core idea is that mathematics is concerned primarily with interrelations in abstraction from the nature of objects. The first two, set-theoretic and category-theoretic, arose within mathematics itself. After exposing a number of problems, the Element considers three further perspectives formulated by logicians and philosophers of mathematics: sui generis, treating structures as abstract universals, modal, eliminating structures as objects in favor of freely entertained logical possibilities, and finally, modal-set-theoretic, a sort of synthesis of the set-theoretic and modal perspectives.
Author | : Michael D. Resnik |
Publisher | : Oxford University Press |
Total Pages | : 300 |
Release | : 1997 |
Genre | : Mathematics |
ISBN | : 9780198236085 |
Download Mathematics as a Science of Patterns Book in PDF, Epub and Kindle
Resnik expresses his commitment to a structuralist philosophy of mathematics and links this to a defence of realism about the metaphysics of mathematics - the view that mathematics is about things that really exist.
Author | : Emily Grosholz |
Publisher | : Springer Science & Business Media |
Total Pages | : 456 |
Release | : 2013-04-17 |
Genre | : Philosophy |
ISBN | : 9401595585 |
Download The Growth of Mathematical Knowledge Book in PDF, Epub and Kindle
Mathematics has stood as a bridge between the Humanities and the Sciences since the days of classical antiquity. For Plato, mathematics was evidence of Being in the midst of Becoming, garden variety evidence apparent even to small children and the unphilosophical, and therefore of the highest educational significance. In the great central similes of The Republic it is the touchstone ofintelligibility for discourse, and in the Timaeus it provides in an oddly literal sense the framework of nature, insuring the intelligibility ofthe material world. For Descartes, mathematical ideas had a clarity and distinctness akin to the idea of God, as the fifth of the Meditations makes especially clear. Cartesian mathematicals are constructions as well as objects envisioned by the soul; in the Principles, the work ofthe physicist who provides a quantified account ofthe machines of nature hovers between description and constitution. For Kant, mathematics reveals the possibility of universal and necessary knowledge that is neither the logical unpacking ofconcepts nor the record of perceptual experience. In the Critique ofPure Reason, mathematics is one of the transcendental instruments the human mind uses to apprehend nature, and by apprehending to construct it under the universal and necessary lawsofNewtonian mechanics.