
After Goedel
Platonism and Rationalism in Mathematics and Logic
Richard Tieszen(Author)
Oxford University Press
Published on 2. May 2013
Book
Paperback/Softback
258 pages
978-0-19-968061-0 (ISBN)
Description
Richard Tieszen presents an analysis, development, and defense of a number of central ideas in Kurt Goedel's writings on the philosophy and foundations of mathematics and logic. Tieszen structures the argument around Goedel's three philosophical heroes - Plato, Leibniz, and Husserl - and his engagement with Kant, and supplements close readings of Goedel's texts on foundations with materials from Goedel's Nachlass and from Hao Wang's discussions with Goedel. As well as providing discussions of Goedel'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 Goedel'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.
Reviews / Votes
Tieszen has long been one of the bridge builders in contemporary philosophy, who is engaged by the philosophical issues and studies them with a broad background and an open mind. There is much to be learned by this, and I am eagerly looking forward to Tieszen's continuation of this interesting and very valuable work. * Dagfinn Follesda, Philosophia MathematicaJuliette Kennedy, Notre Dame Philosophical Reviews *More details
Language
English
Place of publication
Oxford
United Kingdom
Target group
College/higher education
Dimensions
Height: 234 mm
Width: 156 mm
Thickness: 14 mm
Weight
398 gr
ISBN-13
978-0-19-968061-0 (9780199680610)
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Schweitzer Classification
Other editions
Additional editions

Book
05/2011
1st Edition
Oxford University Press
€129.70
Shipment within 15-20 days
Person
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 Jose State University in California.
Content
Preface ; 1. Setting the Stage ; 2. Consistency, and the Ascent to Platonic Rationalism ; 3. Godel'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