Philosophy of mathematics - ALGV19004

• Title: Philosophy of mathematics
• Guaranteed by: Department of Logic (21-KLOG)
• Faculty: Faculty of Arts
• Actual: from 2022
• Semester: winter
• Points: 5
• E-Credits: 5
• Examination process: winter s.:
• Hours per week, examination: winter s.:2/0, Ex [HT]
• Capacity: unlimited / unknown (unknown)
• Min. number of students: unlimited
• 4EU+: no
• Virtual mobility / capacity: no
• State of the course: taught
• Language: English
• Teaching methods: full-time
• Teaching methods: full-time
• Note: course can be enrolled in outside the study plan; enabled for web enrollment
• Guarantor: Mgr. Vít Punčochář, Ph.D.
• Teacher(s): Mgr. Vít Punčochář, Ph.D.

Annotation

Last update: Mgr. Vít Punčochář, Ph.D. (03.02.2021)

The course will provide an introduction into the modern philosophy of mathematics. It will focus on some essential texts of the field. The three big schools that emerged at the beginning of 20th century (logicism, formalism, and intuitionism) will be discussed together with the traditional topics, like, for example, the problem of the existence of mathematical objects and the nature of mathematical truth.

Course completion requirements

Last update: Mgr. Vít Punčochář, Ph.D. (03.02.2021)

active participation, presentation of a selected text, oral exam 

Literature

Last update: Mgr. Vít Punčochář, Ph.D. (10.11.2023)

A tentative reading plan: 

10.10.: Frege: Begriffsschrift (preface); Frege: Foundations of Arithmetic (Introduction + paragraphs 1-4)

17.10.: Frege: Foundations of Arithmetic, paragraphs 55-83 (pages 67-96)

14.11.: Frege: Foundations of Arithmetic, paragraphs 45 (pp. 58-59), 53 (pp. 64-65), 84-109 (pp. 96-119)

21.11.: Hilbert: On the Infinite

28.11.: Field: Realism and Anti-Realism about Mathematics

5.12.: Heyting: Disputation (from Intuitionism. An Introduction); Bishop: A constructivist Manifesto (from Foundations of Constructive Analysis)

12.12.: Martin-Löf: Sets, Types, and Categories; Kolmogorov: On the Interpretation of Intuitionistic Logic

19.12.: Benacerraf: Mathematical Truth

2.1.: Benacerraf: What Numbers Could Not Be

9.1.: Lakatos: Infinite Regress and Foundations of Mathematics

 

Further recommended literature:

Benacerraf, P. & Putnam, H. (eds.), 1983. Philosophy of Mathematics: Selected Readings, Cambridge University Press, 2nd edition.

Shapiro, S. (2000). Thinking about Mathematics, Oxford.