After Godel

Platonism and Rationalism in Mathematics and Logic
1. Auflage 2011
ISBN: 978-0-19-960620-7
Verlag: OUP UK

Buch, Englisch, 258 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 555 g

Richard Tieszen presents an analysis, development, and defense of a number of central ideas in Kurt Gödel's writings on the philosophy and foundations of mathematics and logic. Tieszen structures the argument around Gödel's three philosophical heroes - Plato, Leibniz, and Husserl - and his engagement with Kant, and supplements close readings of Gödel's texts on foundations with materials from Gödel's Nachlass and from Hao Wang's discussions with Gödel. As well as providing discussions of Gödel's views on the philosophical significance of his technical results on completeness, incompleteness, undecidability, consistency proofs, speed-up theorems, and independence proofs, Tieszen furnishes a detailed analysis of Gödel's critique of Hilbert and Carnap, and of his subsequent turn to Husserl's transcendental philosophy in 1959. On this basis, a new type of platonic rationalism that requires rational intuition, called 'constituted platonism', is developed and defended. Tieszen shows how constituted platonism addresses the problem of the objectivity of mathematics and of the knowledge of abstract mathematical objects. Finally, he considers the implications of this position for the claim that human minds ('monads') are machines, and discusses the issues of pragmatic holism and rationalism.

Zielgruppe

Philosophers of logic and mathematics, historians of modern philosophy and mathematics, mathematicians and logicians interested in the philosophical foundations of their subject.

Autoren/Hrsg.

Tieszen, Richard

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Geisteswissenschaften Philosophie Philosophie der Mathematik, Philosophie der Physik
• Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
• Geisteswissenschaften Philosophie Philosophische Logik, Argumentationstheorie

Inhaltsverzeichnis

Preface
1: Setting the Stage
2: Consistency, and the Ascent to Platonic Rationalism
3: Gödel's Path From Hilbert and Carnap to Husserl
4: A New Kind of Platonism
5: Consciousness, Reason, and Intentionality
6: Constituted Platonism, Reason, and Mathematical Knowledge
7: Minds and Machines
8: Reason, Science, and Evidence
Bibliography
Index

Über Autor(innen)

Tieszen, Richard
Richard Tieszen is the author of Phenomenology, Logic, and the Philosophy of Mathematics and Mathematical Intuition, along with numerous papers and reviews on the philosophy of mathematics, philosophy of logic, and phenomenology. He co-edited Between Logic and Intuition: Essays in Honor of Charles Parsons, and is Professor of Philosophy at San José State University in California.