Metamathematics and the Philosophical Tradition

William Boos

Published by De Gruyter 2019

Metamathematics and the Philosophical Tradition

William Boos
Edited by: Florence S. Boos

https://doi.org/10.1515/9783110572452

Overview
Contents

About this book

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 / Editor information

William Boos (†), University of Iowa, USA.

Reviews

"For whom then is the book a suitably good investment? The researcher looking for topics which require a solid grounding in mathematics, and even more so in philosophy, will find this an excellent and comprehensive source of challenging ideas for further development and exposition."
Anthony G. Shannon in: Metascience 29 (2020), 163-166

Topics

Frontmatter Publicly Available Download PDF	I
Contents Publicly Available Download PDF	V
Preface Publicly Available Download PDF	IX
Editorial Remarks Publicly Available Download PDF	XI
1. Introduction: Boundaries of Experience Requires Authentication Unlicensed Licensed Download PDF	1
2. “Was Blind, But Now I See”: Ramifications of Plato’s “Line” Requires Authentication Unlicensed Licensed Download PDF	68
3. The Stoics, the Skeptics and Aporetic Autonomy: Is “What Is In Our Power” In Our Power? Requires Authentication Unlicensed Licensed Download PDF	105
4. Anselm, Fides Quaerens Interpretationem, and Grenzideen as Generators of Metatheoretic Ascent Requires Authentication Unlicensed Licensed Download PDF	131
5. “Parfaits Miroirs de l’Univers”: A “Virtual” Interpretation of Leibnizian Metaphysics Requires Authentication Unlicensed Licensed Download PDF	160
6. Berkeleyan Metalogical “Signs” and “Master Arguments” Requires Authentication Unlicensed Licensed Download PDF	186
7. The Second-order Idealism of David Hume Requires Authentication Unlicensed Licensed Download PDF	233
8. Kantian Ethics and “the Fate of Reason” Requires Authentication Unlicensed Licensed Download PDF	306
9. Metamathematical Interpretations of Free Will and Determinism Requires Authentication Unlicensed Licensed Download PDF	382
10. Time-Evolution in Random “Universes” Requires Authentication Unlicensed Licensed Download PDF	406
Bibliography Requires Authentication Unlicensed Licensed Download PDF	443
Index of Names Requires Authentication Unlicensed Licensed Download PDF	455
Main Index Requires Authentication Unlicensed Licensed Download PDF	459
Foreign Words Index Requires Authentication Unlicensed Licensed Download PDF	477

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Scholars, institutes, libraries
Pages
- Front matter: 12
- Main content: 480
Keywords: Scepticism; Kant; Immanuel; epistemology; self-reference

eBook

Published: December 17, 2018
ISBN: 9783110572452

Hardcover

Published: December 17, 2018
ISBN: 9783110572216

Paperback

Published: December 7, 2020
ISBN: 9783110736847