Foundations Without Foundationalism - A Case for Second-Order Logic

Zusatztext Clearly written and well produced, making it a pleasure to read . . . Shapiro's excellent book is for just about everyone. Logicians and philosophers of mathematics will certainly want to read it; but metaphysicians and philosophers of science and of language will greatly benefit, too.^ The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed development of higher-order logic, including a comprehensive discussion of its semantics. Zusammenfassung The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed development of higher-order logic, including a comprehensive discussion of its semantics. Inhaltsverzeichnis PART I: ORIENTATION; Terms and questions; Foundationalism and foundations of mathematics; PART II: LOGIC AND MATHEMATICS; Theory; Metatheory; Second-order logic and mathematics; Advanced metatheory; PART III: HISTORY AND PHILOSOPHY; The historical triumph of first-order languages; Second-order logic and rule-following; The competition; Index.

Product details

• Authors: Stewart Shapiro, Stewart (Professor of Philosophy Shapiro, Shapiro Stewart
• Publisher: Oxford University Press
• Languages: English
• Product format: Hardback
• Released: 19.09.1991
• EAN: 9780198533917
• ISBN: 978-0-19-853391-7
• No. of pages: 300
• Series: Oxford Logic Guides; Oxford Logic Guides
• Subjects: Humanities, art, music > Philosophy > General, dictionaries; PHILOSOPHY / Logic, MATHEMATICS / History & Philosophy, MATHEMATICS / Logic, Philosophy of Mathematics, Mathematical logic, Philosophy: logic