This Element explores the relationship between phenomenology and mathematics. Its focus is the mathematical thought of Edmund Husserl, founder of phenomenology, but other phenomenologists and phenomenologically-oriented mathematicians, including Weyl, Becker, Gödel, and Rota, are also discussed. After outlining the basic notions of Husserl's phenomenology, the author traces Husserl's journey from his early mathematical studies. Phenomenology's core concepts, such as intention and intuition, each contributed to the emergence of a phenomenological approach to mathematics. This Element examines the phenomenological conceptions of natural number, the continuum, geometry, formal systems, and the applicability of mathematics. It also situates the phenomenological approach in relation to other schools in the philosophy of mathematics-logicism, formalism, intuitionism, Platonism, the French epistemological school, and the philosophy of mathematical practice.
Author(s): Michael Roubach
Series: Elements in the Philosophy of Mathematics
Publisher: Cambridge University Press
Year: 2023
Language: English
City: Cambridge
Cover
Title page
Copyright page
Phenomenology and Mathematics
Contents
1 Basic Concepts of Husserl’s Phenomenology
2 Husserl’s Path from Mathematics to Phenomenology
3 Phenomenology of Mathematics
3.1 Husserl’s Mathesis Universalis and Phenomenology
3.2 Intuition and Mathematics
3.2.1 Intuition Understood as Perception
3.2.2 Intuition Understood as Proof
3.2.3 Can the Two Understandings of Intuition Be Reconciled?
3.3 Transcendental Phenomenology and Mathematics
3.3.1 Constitution of Mathematical Concepts
Set
Continuum
Weyl on the Continuum
Oskar Becker on the Continuum
3.3.2 Modes of Constitution
Geometry and the Experience of Space
Mathematics and Time
Mathematics and Intersubjectivity
3.4 Phenomenology and the Application of Mathematics
4 Phenomenology and Philosophies of Mathematics
4.1 Phenomenology and Logicism
4.2 Phenomenology and Formalism
4.3 Phenomenology and Platonism in Mathematics
4.3.1 Gödel and Phenomenology
4.4 Phenomenology and Brouwer’s Intuitionism
4.4.1 Phenomenology and the Primordial Intuition of “Two-Oneness”
4.4.2 Choice Sequences and Phenomenology
4.4.3 Law of Excluded Middle
4.4.4 Is Phenomenology a Revisionist Position?
4.5 Mathematics, Phenomenology, and Ontology
4.5.1 Being and Time and the Foundations of Mathematics
4.5.2 Mathematics and the Externalist Interpretation of Phenomenology
4.6 Phenomenology and the French School of
Philosophy of Mathematics
4.7 Phenomenology and the Philosophy of Mathematical Practice
Abbreviations
References
Acknowledgments
