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.

This book is a collection of fifteen essays that deal with issues at the intersection of phenomenology, logic, and the philosophy of mathematics. The book is divided into three parts. Part I, Reason, Science, and Mathematics contains a general essay on Husserl's conception of science and logic, an essay of mathematics and transcendental phenomenology, and an essay of phenomenology and modern pure geometry. Part II is focused on Kurt Godel's interest in phenomenology. It explores Godel's ideas and also some work of Quine, Penelope Maddy and Roger Penrose. Part III deals with elementary, constructive areas of mathematics. These are areas of mathematics that are closer to their origins in simple cognitive activities and in everyday experience. This part of the book contains essays on intuitionism, Hermann Weyl, the notion of constructive proof, Poincave and Frege.

This collection of new essays offers a "state-of-the-art" conspectus of major trends in the philosophy of logic and philosophy of mathematics. A distinguished group of philosophers addresses issues at the center of contemporary debate: semantic and set-theoretic paradoxes, the set/class distinction, foundations of set theory, mathematical intuition and many others. The volume includes Hilary Putnam's 1995 Alfred Tarski lectures published here for the first time. The essays are presented to honor the work of Charles Parsons.

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.

Offering a collection of fifteen essays that deal with issues at the intersection of phenomenology, logic, and the philosophy of mathematics, this 2005 book is divided into three parts. Part I contains a general essay on Husserl's conception of science and logic, an essay of mathematics and transcendental phenomenology, and an essay on phenomenology and modern pure geometry. Part II is focused on Kurt Godel's interest in phenomenology. It explores Godel's ideas and also some work of Quine, Penelope Maddy and Roger Penrose. Part III deals with elementary, constructive areas of mathematics. These are areas of mathematics that are closer to their origins in simple cognitive activities and in everyday experience. This part of the book contains essays on intuitionism, Hermann Weyl, the notion of constructive proof, Poincare and Frege.

This collection of new essays offers a "state-of-the-art" conspectus of major trends in the philosophy of logic and philosophy of mathematics. A distinguished group of philosophers addresses issues at the center of contemporary debate: semantic and set-theoretic paradoxes, the set/class distinction, foundations of set theory, mathematical intuition and many others. The volume includes Hilary Putnam's 1995 Alfred Tarski lectures published here for the first time. The essays are presented to honor the work of Charles Parsons.