Course for international guest/part time students
- Faculty
- Faculty of Humanities
- Organization
- BTK Institute of Philosophy
- Code
- BMI-LOTD-317E.06
- Title
- Philosophy of mathematics III: History and Philosophy of Constructive Mathematics
- Usual semester
- Spring
- ECTS
- 4
- Language
- en
- Learning outcomes
- This is a reading seminar. You’re expected to complete the assigned readings and submit a short mini-essay (<500 words) every week before class except Week 1 and Week 12. There will be 10 assignments in total and which will be graded 0–4: two points for argumentative structure and two points for use of sources. The exam will be based on the material covered in class and your submitted assignments. A detailed reading list and the finalised syllabus will be distributed after the first class. The class is in-person by default; you will be notified in advance of any changes to the schedule or mode of delivery.
- Course content
- Tentative course outline: 1. What Does It Mean to Be Constructive? Existence, Meaning, and Method 2. Kant: Objectivity and Mathematics and Construction in Pure Intuition 3. Cantor and Hilbert: Formalism and the Challenge of Constructive Meaning 4. Kronecker and Poincaré: Finitism, Predicativity, and the Vicious Circle Principle 5. Brouwer: Ur-Intuition, Two-ity, and Flow of Time 6. Heyting: Formalising Intuitionistic Logic as a Theory of Proof 7. BHK Interpretation: Meaning Explanations for Connectives and Quantifiers 8. Church and Turing: Effectivity, Formal Systems, and Machines 9. Markov: Recursive Mathematics, Unbounded Search, and Markov’s Principle 10. Bishop: Constructive Analysis and Numerical Meaning 11. Martin-Löf: Type Theory, Judgement, and Proofs-as-Programmes 12. Comparing Constructivisms: A Philosophical Map of Programmes
- Assessment method
- Evaluation: Class Participation (10%) + Weekly Assignments (40%) + Oral Exam (50%)