Metamathematics and the Philosophical Tradition / / William Boos; Florence S. Boos.

• Superior document: Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE DG 2019 English
• VerfasserIn: Boos, William,
• TeilnehmendeR: Boos, Florence S.,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2018]; ©2019
• Year of Publication: 2018
• Language: English
• Physical Description: 1 online resource (492 p.)

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.

Table of Contents

Frontmatter -- Contents -- Preface -- Editorial Remarks -- 1. Introduction: Boundaries of Experience -- 2. "Was Blind, But Now I See": Ramifications of Plato's "Line" -- 3. The Stoics, the Skeptics and Aporetic Autonomy: Is "What Is In Our Power" In Our Power? -- 4. Anselm, Fides Quaerens Interpretationem, and Grenzideen as Generators of Metatheoretic Ascent -- 5. "Parfaits Miroirs de l'Univers": A "Virtual" Interpretation of Leibnizian Metaphysics -- 6. Berkeleyan Metalogical "Signs" and "Master Arguments" -- 7. The Second-order Idealism of David Hume -- 8. Kantian Ethics and "the Fate of Reason" -- 9. Metamathematical Interpretations of Free Will and Determinism -- 10. Time-Evolution in Random "Universes" -- Bibliography -- Index of Names -- Main Index -- Foreign Words Index