Metamathematics and the Philosophical Tradition PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Metamathematics and the Philosophical Tradition PDF full book. Access full book title Metamathematics and the Philosophical Tradition by William Boos. Download full books in PDF and EPUB format.
Author: William Boos
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110572451
Category : Philosophy
Languages : en
Pages : 492
Get Book
Book Description
Metamathematics and the Philosophical Tradition is the first work to explore in such historical depth the relationship between fundamental philosophical quandaries regarding self-reference and meta-mathematical notions of consistency and incompleteness. Using the insights of twentieth-century logicians from Gödel through Hilbert and their successors, this volume revisits the writings of Aristotle, the ancient skeptics, Anselm, and enlightenment and seventeenth and eighteenth century philosophers Leibniz, Berkeley, Hume, Pascal, Descartes, and Kant to identify ways in which these both encode and evade problems of a priori definition and self-reference. The final chapters critique and extend more recent insights of late 20th-century logicians and quantum physicists, and offer new applications of the completeness theorem as a means of exploring "metatheoretical ascent" and the limitations of scientific certainty. Broadly syncretic in range, Metamathematics and the Philosophical Tradition addresses central and recurring problems within epistemology. The volume’s elegant, condensed writing style renders accessible its wealth of citations and allusions from varied traditions and in several languages. Its arguments will be of special interest to historians and philosophers of science and mathematics, particularly scholars of classical skepticism, the Enlightenment, Kant, ethics, and mathematical logic.
Author: William Boos
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110572451
Category : Philosophy
Languages : en
Pages : 492
Get Book
Book Description
Metamathematics and the Philosophical Tradition is the first work to explore in such historical depth the relationship between fundamental philosophical quandaries regarding self-reference and meta-mathematical notions of consistency and incompleteness. Using the insights of twentieth-century logicians from Gödel through Hilbert and their successors, this volume revisits the writings of Aristotle, the ancient skeptics, Anselm, and enlightenment and seventeenth and eighteenth century philosophers Leibniz, Berkeley, Hume, Pascal, Descartes, and Kant to identify ways in which these both encode and evade problems of a priori definition and self-reference. The final chapters critique and extend more recent insights of late 20th-century logicians and quantum physicists, and offer new applications of the completeness theorem as a means of exploring "metatheoretical ascent" and the limitations of scientific certainty. Broadly syncretic in range, Metamathematics and the Philosophical Tradition addresses central and recurring problems within epistemology. The volume’s elegant, condensed writing style renders accessible its wealth of citations and allusions from varied traditions and in several languages. Its arguments will be of special interest to historians and philosophers of science and mathematics, particularly scholars of classical skepticism, the Enlightenment, Kant, ethics, and mathematical logic.
Author: William Boos
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110572397
Category : Philosophy
Languages : en
Pages : 614
Get Book
Book Description
Metamathematics and the Philosophical Tradition is the first work to explore in such historical depth the relationship between fundamental philosophical quandaries regarding self-reference and meta-mathematical notions of consistency and incompleteness. Using the insights of twentieth-century logicians from Gödel through Hilbert and their successors, this volume revisits the writings of Aristotle, the ancient skeptics, Anselm, and enlightenment and seventeenth and eighteenth century philosophers Leibniz, Berkeley, Hume, Pascal, Descartes, and Kant to identify ways in which these both encode and evade problems of a priori definition and self-reference. The final chapters critique and extend more recent insights of late 20th-century logicians and quantum physicists, and offer new applications of the completeness theorem as a means of exploring "metatheoretical ascent" and the limitations of scientific certainty. Broadly syncretic in range, Metamathematics and the Philosophical Tradition addresses central and recurring problems within epistemology. The volume’s elegant, condensed writing style renders accessible its wealth of citations and allusions from varied traditions and in several languages. Its arguments will be of special interest to historians and philosophers of science and mathematics, particularly scholars of classical skepticism, the Enlightenment, Kant, ethics, and mathematical logic.
Author: Roman Murawski
Publisher: Springer
ISBN: 9780792359043
Category : Philosophy
Languages : en
Pages : 395
Get Book
Book Description
Recursive Functions and Metamathematics deals with problems of the completeness and decidability of theories, using as its main tool the theory of recursive functions. This theory is first introduced and discussed. Then Gödel's incompleteness theorems are presented, together with generalizations, strengthenings, and the decidability theory. The book also considers the historical and philosophical context of these issues and their philosophical and methodological consequences. Recent results and trends have been included, such as undecidable sentences of mathematical content, reverse mathematics. All the main results are presented in detail. The book is self-contained and presupposes only some knowledge of elementary mathematical logic. There is an extensive bibliography. Readership: Scholars and advanced students of logic, mathematics, philosophy of science.
Author: Alfred Tarski
Publisher: Hackett Publishing
ISBN: 9780915144761
Category : Philosophy
Languages : en
Pages : 542
Get Book
Book Description
Author: Hilary Putnam
Publisher: Cambridge University Press
ISBN: 9780521295505
Category : Mathematics
Languages : en
Pages : 380
Get Book
Book Description
This volume deals with the philosophy of mathematics and of science and the nature of philosophical and scientific enquiry.
Author: Thomas Bedürftig
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110468336
Category : Mathematics
Languages : en
Pages : 474
Get Book
Book Description
The present book is an introduction to the philosophy of mathematics. It asks philosophical questions concerning fundamental concepts, constructions and methods - this is done from the standpoint of mathematical research and teaching. It looks for answers both in mathematics and in the philosophy of mathematics from their beginnings till today. The reference point of the considerations is the introducing of the reals in the 19th century that marked an epochal turn in the foundations of mathematics. In the book problems connected with the concept of a number, with the infinity, the continuum and the infinitely small, with the applicability of mathematics as well as with sets, logic, provability and truth and with the axiomatic approach to mathematics are considered. In Chapter 6 the meaning of infinitesimals to mathematics and to the elements of analysis is presented. The authors of the present book are mathematicians. Their aim is to introduce mathematicians and teachers of mathematics as well as students into the philosophy of mathematics. The book is suitable also for professional philosophers as well as for students of philosophy, just because it approaches philosophy from the side of mathematics. The knowledge of mathematics needed to understand the text is elementary. Reports on historical conceptions. Thinking about today‘s mathematical doing and thinking. Recent developments. Based on the third, revised German edition. For mathematicians - students, teachers, researchers and lecturers - and readersinterested in mathematics and philosophy. Contents On the way to the reals On the history of the philosophy of mathematics On fundamental questions of the philosophy of mathematics Sets and set theories Axiomatic approach and logic Thinking and calculating infinitesimally – First nonstandard steps Retrospection
Author: Paul Benacerraf
Publisher: Cambridge University Press
ISBN: 9780521296489
Category : Mathematics
Languages : en
Pages : 604
Get Book
Book Description
Seminal articles in the philosophy of mathematics by Russell, Quine, Gödel and other major thinkers.
Author: David Corfield
Publisher: Cambridge University Press
ISBN: 1139436392
Category : Philosophy
Languages : en
Pages : 300
Get Book
Book Description
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: Raymond M. Smullyan
Publisher: Oxford University Press
ISBN: 9780195344813
Category : Mathematics
Languages : en
Pages : 184
Get Book
Book Description
This work is a sequel to the author's Gödel's Incompleteness Theorems, though it can be read independently by anyone familiar with Gödel's incompleteness theorem for Peano arithmetic. The book deals mainly with those aspects of recursion theory that have applications to the metamathematics of incompleteness, undecidability, and related topics. It is both an introduction to the theory and a presentation of new results in the field.
Author: Nikolay Milkov
Publisher: Bloomsbury Publishing
ISBN: 1350086444
Category : Philosophy
Languages : en
Pages : 292
Get Book
Book Description
This book investigates the emergence and development of early analytic philosophy and explicates the topics and concepts that were of interest to German and British philosophers. Taking into consideration a range of authors including Leibniz, Kant, Hegel, Fries, Lotze, Husserl, Moore, Russell and Wittgenstein, Nikolay Milkov shows that the same puzzles and problems were of interest within both traditions. Showing that the particular problems and concepts that exercised the early analytic philosophers logically connect with, and in many cases hinge upon, the thinking of German philosophers, Early Analytic Philosophy and the German Philosophical Tradition introduces the Anglophone world to key concepts and thinkers within German philosophical tradition and provides a much-needed revisionist historiography of early analytic philosophy. In doing so, this book shows that the issues that preoccupied the early analytic philosophy were familiar to the most renowned figures in the German philosophical tradition, and addressed by them in profoundly original and enduringly significant ways.
