The Philosophy of Mathematical Practice

The Philosophy of Mathematical Practice
Author: Paolo Mancosu
Publisher: Oxford University Press on Demand
Total Pages: 460
Release: 2008-06-19
Genre: Philosophy
ISBN: 0199296456

There is an urgent need in philosophy of mathematics for new approaches which pay closer attention to mathematical practice. This book will blaze the trail: it offers philosophical analyses of important characteristics of contemporary mathematics and of many aspects of mathematical activity which escape purely formal logical treatment.

A Mathematical Prelude to the Philosophy of Mathematics

A Mathematical Prelude to the Philosophy of Mathematics
Author: Stephen Pollard
Publisher: Springer
Total Pages: 206
Release: 2014-05-12
Genre: Science
ISBN: 3319058169

This book is based on two premises: one cannot understand philosophy of mathematics without understanding mathematics and one cannot understand mathematics without doing mathematics. It draws readers into philosophy of mathematics by having them do mathematics. It offers 298 exercises, covering philosophically important material, presented in a philosophically informed way. The exercises give readers opportunities to recreate some mathematics that will illuminate important readings in philosophy of mathematics. Topics include primitive recursive arithmetic, Peano arithmetic, Gödel's theorems, interpretability, the hierarchy of sets, Frege arithmetic and intuitionist sentential logic. The book is intended for readers who understand basic properties of the natural and real numbers and have some background in formal logic.

More Precisely: The Math You Need to Do Philosophy - Second Edition

More Precisely: The Math You Need to Do Philosophy - Second Edition
Author: Eric Steinhart
Publisher: Broadview Press
Total Pages: 250
Release: 2017-11-21
Genre: Philosophy
ISBN: 155481345X

More Precisely is a rigorous and engaging introduction to the mathematics necessary to do philosophy. Eric Steinhart provides lucid explanations of many basic mathematical concepts and sets out the most commonly used notational conventions. He also demonstrates how mathematics applies to fundamental issues in various branches of philosophy, including metaphysics, philosophy of language, epistemology, and ethics. This second edition adds a substantial section on decision and game theory, as well as a chapter on information theory and the efficient coding of information.

Towards Mathematical Philosophy

Towards Mathematical Philosophy
Author: David Makinson
Publisher: Springer Science & Business Media
Total Pages: 344
Release: 2008-11-09
Genre: Mathematics
ISBN: 1402090846

area and in applications to linguistics, formal epistemology, and the study of norms. The second contains papers on non-classical and many-valued logics, with an eye on applications in computer science and through it to engineering. The third concerns the logic of belief management,whichis likewise closely connected with recent work in computer science but also links directly with epistemology, the philosophy of science, the study of legal and other normative systems, and cognitive science. The grouping is of course rough, for there are contributions to the volume that lie astride a boundary; at least one of them is relevant, from a very abstract perspective, to all three areas. We say a few words about each of the individual chapters, to relate them to each other and the general outlook of the volume. Modal Logics The ?rst bundle of papers in this volume contains contribution to modal logic. Three of them examine general problems that arise for all kinds of modal logics. The ?rst paper is essentially semantical in its approach, the second proof-theoretic, the third semantical again: • Commutativity of quanti?ers in varying-domain Kripke models,by R. Goldblatt and I. Hodkinson, investigates the possibility of com- tation (i.e. reversing the order) for quanti?ers in ?rst-order modal logics interpreted over relational models with varying domains. The authors study a possible-worlds style structural model theory that does not v- idate commutation, but satis?es all the axioms originally presented by Kripke for his familiar semantics for ?rst-order modal logic.

Towards a Philosophy of Critical Mathematics Education

Towards a Philosophy of Critical Mathematics Education
Author: Ole Skovsmose
Publisher: Springer Science & Business Media
Total Pages: 312
Release: 2013-03-09
Genre: Education
ISBN: 9401735565

In Nineteen Eighty-Four George Orwell gives a description of different forms of suppression. We learn about the telescreens placed everywhere, through which it is possible for Big-Brother to watch the inhabitants of Oceania. However, it is not only important to control the activities of the inhabitants, it is important as well to control their thoughts, and the Thought Police are on guard. This is a very direct form of monitoring and control, but Orwell also outlines a more imperceptible and calculated line of thought control. In the Appendix to Nineteen Eighty-Four Orwell explains some struc tures of 'Newspeak', which is going to become the official language of Oceania. Newspeak is being developed by the Ministry of Truth, and this language has to substitute 'Oldspeak' (similar to standard English). Newspeak should fit with the official politics of Oceania ruled by the Ingsoc party: "The purpose of Newspeak was not only to provide a medium of expression for the world-view and mental habits proper to the devotees of Ingsoc, but to make all other modes of thought impos sible. It was intended that when Newspeak had been adopted once and for all and Oldspeak forgotten, a heretical thought - that is, a thought diverging from the principles of Ingsoc - should be literally unthink able, at least as far as thought is dependent on words.

Towards Mathematical Philosophy

Towards Mathematical Philosophy
Author: David Makinson
Publisher: Springer
Total Pages: 0
Release: 2010-10-28
Genre: Mathematics
ISBN: 9789048180653

area and in applications to linguistics, formal epistemology, and the study of norms. The second contains papers on non-classical and many-valued logics, with an eye on applications in computer science and through it to engineering. The third concerns the logic of belief management,whichis likewise closely connected with recent work in computer science but also links directly with epistemology, the philosophy of science, the study of legal and other normative systems, and cognitive science. The grouping is of course rough, for there are contributions to the volume that lie astride a boundary; at least one of them is relevant, from a very abstract perspective, to all three areas. We say a few words about each of the individual chapters, to relate them to each other and the general outlook of the volume. Modal Logics The ?rst bundle of papers in this volume contains contribution to modal logic. Three of them examine general problems that arise for all kinds of modal logics. The ?rst paper is essentially semantical in its approach, the second proof-theoretic, the third semantical again: • Commutativity of quanti?ers in varying-domain Kripke models,by R. Goldblatt and I. Hodkinson, investigates the possibility of com- tation (i.e. reversing the order) for quanti?ers in ?rst-order modal logics interpreted over relational models with varying domains. The authors study a possible-worlds style structural model theory that does not v- idate commutation, but satis?es all the axioms originally presented by Kripke for his familiar semantics for ?rst-order modal logic.

An Introduction to the Philosophy of Mathematics

An Introduction to the Philosophy of Mathematics
Author: Mark Colyvan
Publisher: Cambridge University Press
Total Pages: 199
Release: 2012-06-14
Genre: Mathematics
ISBN: 0521826020

A fascinating journey through intriguing mathematical and philosophical territory - a lively introduction to this contemporary topic.

Lectures on the Philosophy of Mathematics

Lectures on the Philosophy of Mathematics
Author: Joel David Hamkins
Publisher: MIT Press
Total Pages: 350
Release: 2021-03-09
Genre: Mathematics
ISBN: 0262542234

An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.

Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century
Author: Paolo Mancosu
Publisher: Oxford University Press, USA
Total Pages: 290
Release: 1999
Genre: Matematik
ISBN: 0195132440

1. Philosophy of Mathematics and Mathematical Practice in the Early Seventeenth Century p. 8 1.1 The Quaestio de Certitudine Mathematicarum p. 10 1.2 The Quaestio in the Seventeenth Century p. 15 1.3 The Quaestio and Mathematical Practice p. 24 2. Cavalieri's Geometry of Indivisibles and Guldin's Centers of Gravity p. 34 2.1 Magnitudes, Ratios, and the Method of Exhaustion p. 35 2.2 Cavalieri's Two Methods of Indivisibles p. 38 2.3 Guldin's Objections to Cavalieri's Geometry of Indivisibles p. 50 2.4 Guldin's Centrobaryca and Cavalieri's Objections p. 56 3. Descartes' Geometrie p. 65 3.1 Descartes' Geometrie p. 65 3.2 The Algebraization of Mathematics p. 84 4. The Problem of Continuity p. 92 4.1 Motion and Genetic Definitions p. 94 4.2 The "Causal" Theories in Arnauld and Bolzano p. 100 4.3 Proofs by Contradiction from Kant to the Present p. 105 5. Paradoxes of the Infinite p. 118 5.1 Indivisibles and Infinitely Small Quantities p. 119 5.2 The Infinitely Large p. 129 6. Leibniz's Differential Calculus and Its Opponents p. 150 6.1 Leibniz's Nova Methodus and L'Hopital's Analyse des Infiniment Petits p. 151 6.2 Early Debates with Cluver and Nieuwentijt p. 156 6.3 The Foundational Debate in the Paris Academy of Sciences p. 165 Appendix Giuseppe Biancani's De Mathematicarum Natura p. 178 Notes p. 213 References p. 249 Index p. 267.