Book contents
- Frontmatter
- Contents
- Acknowledgments
- Introduction: Themes and Issues
- PART I REASON, SCIENCE, AND MATHEMATICS
- PART II KURT GÖDEL, PHENOMENOLOGY, AND THE PHILOSOPHY OF MATHEMATICS
- PART III CONSTRUCTIVISM, FULFILLABLE INTENTIONS, AND ORIGINS
- 11 Intuitionism, Meaning Theory, and Cognition
- 12 The Philosophical Background of Weyl's Mathematical Constructivism
- 13 Proofs and Fulfillable Mathematical Intentions
- 14 Logicism, Impredicativity, Formalism: Some Remarks on Poincaré and Husserl
- 15 The Philosophy of Arithmetic: Frege and Husserl
- Bibliography
- Index
12 - The Philosophical Background of Weyl's Mathematical Constructivism
Published online by Cambridge University Press: 14 July 2009
- Frontmatter
- Contents
- Acknowledgments
- Introduction: Themes and Issues
- PART I REASON, SCIENCE, AND MATHEMATICS
- PART II KURT GÖDEL, PHENOMENOLOGY, AND THE PHILOSOPHY OF MATHEMATICS
- PART III CONSTRUCTIVISM, FULFILLABLE INTENTIONS, AND ORIGINS
- 11 Intuitionism, Meaning Theory, and Cognition
- 12 The Philosophical Background of Weyl's Mathematical Constructivism
- 13 Proofs and Fulfillable Mathematical Intentions
- 14 Logicism, Impredicativity, Formalism: Some Remarks on Poincaré and Husserl
- 15 The Philosophy of Arithmetic: Frege and Husserl
- Bibliography
- Index
Summary
My principal goal in this chapter is to describe the philosophical background of Weyl's mathematical constructivism. The most important phase of Weyl's work on the foundations of mathematics commenced with the development of his predicativism in Das Kontinuum (DK) in 1918 and proceeded through his alignment with Brouwerian intuitionism in the early twenties. The work of this period shows a deep commitment to constructivism. Around 1924 Weyl began to feel the need to account for parts of mathematics that could not be understood constructively. His views on constructivism would need to be supplemented in some way. I discuss this matter in § 7, but my primary focus will be on the central constructivist phase of Weyl's work. There is no indication in Weyl's comments on foundations that he was ever prepared to accept realism about mathematics, and, thus, the inclination toward constructivism is not completely absent even in Weyl's later comments. I will argue that Weyl's views on constructive foundations were shaped in a general way by a form of idealism, and in particular by a kind of transcendental idealism in the tradition of Kant.
I open the essay by reminding the reader of a few general themes from Kant's philosophy. Two other philosophers in this tradition are especially important for understanding Weyl's views: Fichte and Husserl. I will comment on a few themes in Fichte's work and then focus on Husserl's influence on Weyl. Weyl studied some of Husserl's writings and the two corresponded.
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- Phenomenology, Logic, and the Philosophy of Mathematics , pp. 248 - 275Publisher: Cambridge University PressPrint publication year: 2005
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