Metamathematics And The Philosophical Tradition
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Metamathematics And The Philosophical Tradition
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Author : William Boos
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-12-17
Metamathematics And The Philosophical Tradition written by William Boos and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-17 with Philosophy categories.
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.
Recursive Functions And Metamathematics
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Author : Roman Murawski
language : en
Publisher: Springer
Release Date : 1999-09-30
Recursive Functions And Metamathematics written by Roman Murawski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-09-30 with Philosophy categories.
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.
The Essence Of Numbers
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Author : Frédéric Patras
language : en
Publisher: Springer Nature
Release Date : 2020-10-06
The Essence Of Numbers written by Frédéric Patras and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-06 with Mathematics categories.
This book considers the manifold possible approaches, past and present, to our understanding of the natural numbers. They are treated as epistemic objects: mathematical objects that have been subject to epistemological inquiry and attention throughout their history and whose conception has evolved accordingly. Although they are the simplest and most common mathematical objects, as this book reveals, they have a very complex nature whose study illuminates subtle features of the functioning of our thought. Using jointly history, mathematics and philosophy to grasp the essence of numbers, the reader is led through their various interpretations, presenting the ways they have been involved in major theoretical projects from Thales onward. Some pertain primarily to philosophy (as in the works of Plato, Aristotle, Kant, Wittgenstein...), others to general mathematics (Euclid's Elements, Cartesian algebraic geometry, Cantorian infinities, set theory...). Also serving as an introduction to the works and thought of major mathematicians and philosophers, from Plato and Aristotle to Cantor, Dedekind, Frege, Husserl and Weyl, this book will be of interest to a wide variety of readers, from scholars with a general interest in the philosophy or mathematics to philosophers and mathematicians themselves.
Language And Philosophical Problems
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Author : Sören Stenlund
language : en
Publisher: Routledge
Release Date : 2013-01-11
Language And Philosophical Problems written by Sören Stenlund and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-11 with Philosophy categories.
Language and Philosophical Problems investigates problems about mind, meaning and mathematics rooted in preconceptions of language. It deals in particular with problems which are connected with our tendency to be misled by certain prevailing views and preconceptions about language. Philosophical claims made by theorists of meaning are scrutinized and shown to be connected with common views about the nature of certain mathematical notions and methods. Drawing in particular on Wittgenstein's ideas, Sren Stenlund demonstrates a strategy for tracing out and resolving conceptual and philosophical problems. By a critical examination of examples from different areas of philosophy, he shows that many problems arise through the transgression of the limits of the use of technical concepts and formal methods. Many prima facie different kinds of problems are shown to have common roots, and should thus be dealt and resolved together. Such an approach is usually prevented by the influence of traditional philosophical terminology and classification. The results of this investigation make it clear that the received ways of subdividing the subject matter of philosophy often conceal the roots of the problem.
Recursion Theory For Metamathematics
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Author : Raymond M. Smullyan
language : en
Publisher: Oxford University Press
Release Date : 1993-01-28
Recursion Theory For Metamathematics written by Raymond M. Smullyan and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-01-28 with Mathematics categories.
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.
Introduction To Metamathematics
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Author : Stephen Cole Kleene
language : en
Publisher:
Release Date : 2012-07-01
Introduction To Metamathematics written by Stephen Cole Kleene and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-01 with categories.
Logic Semantics Metamathematics
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Author : Alfred Tarski
language : en
Publisher: Hackett Publishing
Release Date : 1983-01-01
Logic Semantics Metamathematics written by Alfred Tarski and has been published by Hackett Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-01-01 with Philosophy categories.
Philosophy Of Mathematics
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Author : Paul Benacerraf
language : en
Publisher: Cambridge University Press
Release Date : 1983
Philosophy Of Mathematics written by Paul Benacerraf and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.
Seminal articles in the philosophy of mathematics by Russell, Quine, Gödel and other major thinkers.
Philosophical Papers Volume 1 Mathematics Matter And Method
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Author : Hilary Putnam
language : en
Publisher: Cambridge University Press
Release Date : 1979-04-30
Philosophical Papers Volume 1 Mathematics Matter And Method written by Hilary Putnam and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979-04-30 with Mathematics categories.
This volume deals with the philosophy of mathematics and of science and the nature of philosophical and scientific enquiry.
From Dedekind To G Del
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Author : Jaakko Hintikka
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
From Dedekind To G Del written by Jaakko Hintikka and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Philosophy categories.
Discussions of the foundations of mathematics and their history are frequently restricted to logical issues in a narrow sense, or else to traditional problems of analytic philosophy. From Dedekind to Gödel: Essays on the Development of the Foundations of Mathematics illustrates the much greater variety of the actual developments in the foundations during the period covered. The viewpoints that serve this purpose included the foundational ideas of working mathematicians, such as Kronecker, Dedekind, Borel and the early Hilbert, and the development of notions like model and modelling, arbitrary function, completeness, and non-Archimedean structures. The philosophers discussed include not only the household names in logic, but also Husserl, Wittgenstein and Ramsey. Needless to say, such logically-oriented thinkers as Frege, Russell and Gödel are not entirely neglected, either. Audience: Everybody interested in the philosophy and/or history of mathematics will find this book interesting, giving frequently novel insights.