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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.
Basic Concepts of Husserl’s Phenomenology
Husserl’s Path from Mathematics to Phenomenology
Phenomenology of Mathematics
Husserl’s Mathesis Universalis and Phenomenology
Intuition and Mathematics
Intuition Understood as Perception
Intuition Understood as Proof
Can the Two Understandings of Intuition Be Reconciled?
Transcendental Phenomenology and Mathematics
Constitution of Mathematical Concepts
Set
Continuum
Weyl on the Continuum
Oskar Becker on the Continuum
Modes of Constitution
Geometry and the Experience of Space
Mathematics and Time
Mathematics and Intersubjectivity
Phenomenology and the Application of Mathematics
Phenomenology and Philosophies of Mathematics
Phenomenology and Logicism
Phenomenology and Formalism
Phenomenology and Platonism in Mathematics
Gödel and Phenomenology
Phenomenology and Brouwer’s Intuitionism
Phenomenology and the Primordial Intuition of “Two-Oneness”
Choice Sequences and Phenomenology
Law of Excluded Middle
Is Phenomenology a Revisionist Position?
Mathematics, Phenomenology, and Ontology
Being and Time and the Foundations of Mathematics
Mathematics and the Externalist Interpretation of Phenomenology
Phenomenology and the French School of
Philosophy of Mathematics
Phenomenology and the Philosophy of Mathematical Practice
Abbreviations
References
Acknowledgments