8241006Philosophy and History of Science (Seminars)
| Numbering Code | G-LET32 78241 SJ34 | Year/Term | 2022 ・ Second semester | |
|---|---|---|---|---|
| Number of Credits | 2 | Course Type | Seminar | |
| Target Year | Target Student | |||
| Language | Japanese | Day/Period | Tue.5 | |
| Instructor name | YATABE SHUNSUKE (Part-time Lecturer) | |||
| Outline and Purpose of the Course |
We make deductions in daily life. We also often use the word "logical." It is of course necessary to be "logical" in philosophy. But what exactly is "logic"? Questioning once again the meaning of concepts we think we know, and which we use habitually and thoughtlessly, is an important task in philosophy. The question of what is "logic" is also a big issue for modern times. This is because, since the 20th century, many different logic systems have been proposed aside from that of the classical logic system. If these non-classical systems are called logic, what kinds of properties need to be satisfied in order for a system to be called "logical"? In this seminar, starting with an explanation of the system of natural deduction in minimal predicate logic, we will aim to be capable of doing logical proofs in minimal logic, intuitionist logic, and classical logic, as well as make arguments using these models. In doing this, we will examine the kinds of properties that need to be met in order for a system that merely processes notation to be called "logical." |
|||
| Course Goals | Be able to solve basic practice problems using natural deduction in intuitional logic and classical logic. Understand proofs in the Completeness Theorem of classical logic, as well as the significance of model theory semantics. | |||
| Schedule and Contents |
In the first half of the course, we will use examples from the minimal predicate logic introduced in the first semester, while also considering the meaning of logical connectors from the standpoint of "proof-theoretic semantics." Specifically, using the theme of Belnap's "tonk" example, we will consider the conditions for logical connectors and aim to cultivate an understanding of the fundamental logical concepts of conservation expansion and standardization. In the second half, we will introduce a logical system expanded by adding logical rules to minimal logic. In other words, we will add the logical rules of the law of contradiction and the law of the excluded middle to minimal logic to produce intuitionist logic and classical logic. From these examples, as we add logical rules the logical formula proofs will get more difficult, but we will show that their models get simpler. By examining these, we will aim to understand the basic concepts of the relationship between symbols and models seen in soundness and integrity. Finally, we will introduce Goedel's incompleteness theorem as a topic in the study of logic. The specific class organization will be as follows. 1. What Is the Meaning of Logical Connectors? Theory of Meaning 1 and Theory of Meaning 2 2. Theory of Meaning 2 and Logical Connector Conditions: Prior's "Tonk," Belnap's Preservation Expansion 3. Prawitz's "Reverse Principle" 4. Dummett and the Standardization Potential of Proofs 5. "Holmes Reasoning" and the Law of Contradiction, Intuitionist Logic 6. Intuitionist Logic Practice Problems 7. The Law of the Excluded Middle and Classical Logic 8. Proofs and Practice Problems in Classical Logic 9. Classical Logic and Truth Tables 10. Classical Logic and the Completeness Theorem 11. Completeness Theorem Proofs 12. Comprehensive Practice 13. (Extra Topics) Goedel's Incompleteness Theorem 14. (Extra Topics) Goedel's Incompleteness Theorem Proofs 15. (Extra Topics) The Meaning of the Incompleteness Theorem |
|||
| Evaluation Methods and Policy | Grades will follow the cumulative score of the homework that will be assigned nearly every class session. | |||
| Course Requirements | Must take the first semester seminar "Logic 1" | |||
| Study outside of Class (preparation and review) |
Handouts and other class materials will be uploaded to the website (the above class blog) in advance (1-2 days before class). Students should read over the materials before class. |
|||
| Textbooks | Textbooks/References | None; handouts will be distributed in each class session. | ||
| References, etc. | 戸次大介 『数理論理学』 (東大出版会), 小野寛晰 『情報科学における論理』 (日本評論社), Dag Prawitz 『Natural Deduction: A Proof-Theoretical Study』 | |||
| Related URL | http://d.hatena.ne.jp/kyoto_logic/ (授業Blog: 休講等の連絡、ハンドアウト配布) | |||
