Epistemology of the Mathematical Processes
A.Y. 2026/2027
Learning objectives
The course aims at introducing the students to the epistemological study of mathematical processes, by means of a detialed analysis of some significant examples stemming from various mathematical disciplines.
Expected learning outcomes
At the end of the course, students will have acquired some basic knowledge about the construction of mathematical theories, and about their epistemological meaning.
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
1) Philosophical Aspects in Mathematical Practice
· On the Genesis of Mathematical Concepts
· The Critical Role of Mathematical Thought in the Problem of the Self-Foundation of Reason
· Against Logical Equivalence
· Beauty in Mathematics
2) Comparative Analysis of Foundational Systems in Mathematics
· Historical Schools: Logicism, Formalism, Intuitionism
· The set-theoretic foundation
· The categorical foundation: elementary toposes and Lawvere's category of sets
· Dependent types and Voevodsky's univalent foundation
· On the Genesis of Mathematical Concepts
· The Critical Role of Mathematical Thought in the Problem of the Self-Foundation of Reason
· Against Logical Equivalence
· Beauty in Mathematics
2) Comparative Analysis of Foundational Systems in Mathematics
· Historical Schools: Logicism, Formalism, Intuitionism
· The set-theoretic foundation
· The categorical foundation: elementary toposes and Lawvere's category of sets
· Dependent types and Voevodsky's univalent foundation
Prerequisites for admission
Good general background i mathematics
Teaching methods
Teacher lectures
Teaching Resources
Course notes written by the teachers. Extra references as indicated in Ariel platform,
Assessment methods and Criteria
Oral colloquium
MATH-01/A - Mathematical Logic - University credits: 3
MATH-01/B - Mathematics Education and History of Mathematics - University credits: 3
MATH-01/B - Mathematics Education and History of Mathematics - University credits: 3
Lessons: 42 hours
Professors:
Ghilardi Silvio, Rigoli Marco
Professor(s)