Essays on Gödel's reception of Leibniz, Husserl, and Brouwer
著者
書誌事項
Essays on Gödel's reception of Leibniz, Husserl, and Brouwer
（Logic, epistemology, and the unity of science / editors, Shahid Rahman, John Symons, v. 35）
Springer, c2015
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注記
Bibliography: p. 289-308
Includes indexes
内容説明・目次
内容説明
This volume tackles Goedel's two-stage project of first using Husserl's transcendental phenomenology to reconstruct and develop Leibniz' monadology, and then founding classical mathematics on the metaphysics thus obtained. The author analyses the historical and systematic aspects of that project, and then evaluates it, with an emphasis on the second stage.
The book is organised around Goedel's use of Leibniz, Husserl and Brouwer. Far from considering past philosophers irrelevant to actual systematic concerns, Goedel embraced the use of historical authors to frame his own philosophical perspective. The philosophies of Leibniz and Husserl define his project, while Brouwer's intuitionism is its principal foil: the close affinities between phenomenology and intuitionism set the bar for Goedel's attempt to go far beyond intuitionism.
The four central essays are `Monads and sets', `On the philosophical development of Kurt Goedel', `Goedel and intuitionism', and `Construction and constitution in mathematics'. The first analyses and criticises Goedel's attempt to justify, by an argument from analogy with the monadology, the reflection principle in set theory. It also provides further support for Goedel's idea that the monadology needs to be reconstructed phenomenologically, by showing that the unsupplemented monadology is not able to found mathematics directly. The second studies Goedel's reading of Husserl, its relation to Leibniz' monadology, and its influence on his publishe
d writings. The third discusses how on various occasions Brouwer's intuitionism actually inspired Goedel's work, in particular the Dialectica Interpretation. The fourth addresses the question whether classical mathematics admits of the phenomenological foundation that Goedel envisaged, and concludes that it does not.
The remaining essays provide further context. The essays collected here were written and published over the last decade. Notes have been added to record further thoughts, changes of mind, connections between the essays, and updates of references.
目次
Chapter 1. Introduction.- Part I Goedel and Leibniz.- Chapter 2 A note on Leibniz's argument against infinite wholes.- Chapter 3. Monads and sets: on Goedel, Leibniz, and the Reflection Principle.- Chapter 4. Goedel's Dialectica Interpretation and Leibniz.- Part II Goedel and Husserl.- Chapter 5. Phenomenology of mathematics.- Chapter 6. On the philosophical development of Kurt Goedel (with Juliette Kennedy).- Chapter 7. Goedel, mathematics, and possible worlds.- Chapter 8. Two draft letters from Goedel on self-knowledge of Reason.- Part III Goedel and Brouwer.- Chapter 9. Goedel and Brouwer: two rivalling brothers.- Chapter 10. Mysticism and mathematics: Brouwer, Goedel, and the common core thesis (with Robert Tragesser).- Chapter 11. Goedel and intuitionism.- Part IV A partial assessment.- Chapter 12. Construction and constitution in mathematics.
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