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ADVANCED STUDIES IN PHILOSOPHY AND ETHICS 1I
| Subtitle | Gödel's Incompleteness Theorem and its Philosophical Significance |
|---|---|
| Lecturer(s) | MINESHIMA, KOJI; AKIYOSHI, RYOUTA |
| Credit(s) | 2 |
| Academic Year/Semester | 2023 Spring |
| Day/Period | Tue.2 |
| Campus | Mita |
| Class Format | Face-to-face classes (conducted mainly in-person) |
| Registration Number | 04569 |
| Faculty/Graduate School | LETTERS |
| Department/Major | HUMANITIES AND SOCIAL SCIENCEPHILOSOPHY |
| Year Level | 2, 3, 4 |
| Field | SPECIALIZED SUBJECTS |
| K-Number | FLT-PH-34112-211-01 |
| Course Administrator | Faculty/Graduate School | FLT | LETTERS |
|---|---|---|---|
| Department/Major | PH | HUMANITIES AND SOCIAL SCIENCEPHILOSOPHY | |
| Main Course Number | Level | 3 | Third-year level coursework |
| Major Classification | 4 | Specialist Education Applied/Developmental Course | |
| Minor Classification | 11 | Common to All Philosophy Majors - Advanced Philosophy | |
| Subject Type | 2 | Elective required subject | |
| Supplemental Course Information | Class Classification | 2 | Lecture |
| Class Format | 1 | Face-to-face classes (conducted mainly in-person) | |
| Language of Instruction | 1 | Japanese | |
| Academic Discipline | 01 | Philosophy, art, and related fields | |
Course Contents/Objectives/Teaching Method/Intended Learning Outcome
The course will delve into Gödel's 1931 Incompleteness Theorem and its philosophical implications. We will review a set of issues in the philosophy of logic and mathematics, focusing on Hilbert's formalism (the Consistency Program), which is the background of the Incompleteness Theorem, and carefully explain the proof of the Incompleteness Theorem in arithmetic.
The primary goal of the spring semester will be to provide background knowledge on computability theory (Turing machines and recursive functions). This will serve as the foundation for philosophical discussions on Gödel's theorem.
In the fall semester, we will introduce Cantor's diagonal argument and axiomatization of arithmetic, followed by coding and diagonal complementation, which are key to the proof of the incompleteness theorem, and finally the first and second incompleteness theorems, as well as Tarski's theorem. In the remaining sessions, I will introduce the impact of these mathematical theorems on Hilbert's program and contemporary topics related to them.
The primary goal of the spring semester will be to provide background knowledge on computability theory (Turing machines and recursive functions). This will serve as the foundation for philosophical discussions on Gödel's theorem.
In the fall semester, we will introduce Cantor's diagonal argument and axiomatization of arithmetic, followed by coding and diagonal complementation, which are key to the proof of the incompleteness theorem, and finally the first and second incompleteness theorems, as well as Tarski's theorem. In the remaining sessions, I will introduce the impact of these mathematical theorems on Hilbert's program and contemporary topics related to them.
Course Plan
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Method of Evaluation
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Textbooks
Lecture notes and presentation slides will be distributed during each class session.
Reference Books
スチュワート・シャピロ『数学を哲学する』（金子洋之訳, 筑摩書房, 2012年）
飯田隆編『リーディングス 数学の哲学ーゲーデル以後』（勁草書房, 1995年）
M.ジャキント『確かさを求めて』（田中一之訳, 培風館, 2007年）
トルケル・フランセーン『ゲーデルの定理―利用と誤用の不完全ガイド』（田中一之訳, みすず書房, 2011）
飯田隆編『リーディングス 数学の哲学ーゲーデル以後』（勁草書房, 1995年）
M.ジャキント『確かさを求めて』（田中一之訳, 培風館, 2007年）
トルケル・フランセーン『ゲーデルの定理―利用と誤用の不完全ガイド』（田中一之訳, みすず書房, 2011）
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