5141002Philosophy (Seminars)
| Numbering Code | G-LET01 75141 SJ34 | Year/Term | 2022 ・ Second semester | |
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| Number of Credits | 2 | Course Type | special lecture | |
| Target Year | Target Student | |||
| Language | Japanese | Day/Period | Tue.5 | |
| Instructor name | YATABE SHUNSUKE (Part-time Lecturer) | |||
| Outline and Purpose of the Course |
We reason every day. Also, the word "logical" is always used with the word "reasoning". Philosophers' reasonings, of course, are required to be "logical". But what is "logic"? It is one of the important tasks of philosophy to reconsider the meaning of concepts that are used without reflection. The question of what "logic" is is a major problem today. This is because, since the 20th. century, many different systems of logic have been proposed in addition to classical logic. If these nonclassical systems are called logics, what properties do they need to be shared to be called "logic"? The purpose of this class is to start with an explanation of a system of natural deduction of minimum predicate logic, and to enable students to prove logically using minimum logic, intuitionistic logic, and classical logic. Throughout that, we consider the properties that a simple symbol processing system must have in order to be called a "logic". |
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| Course Goals | Students are required to be who can prove easy propositions by Natural Deduction of intuitionistic and classical logic. We also understand the proof of the completeness theorem of classical logic and the significance of model-theoretic semantics. | |||
| Schedule and Contents |
In the first half of this class, we consider the meaning of logical connectives from the standpoint called "proof theoretic semantics" by taking the minimum predicate logic introduced in the first half as an example. Specifically, using the example of "Tonk" as a subject, it aims to consider what the conditions of logical connectives are, and to understand basic concepts of logic such as the "harmony", of the introduction rule and the elimination rule, and the "normalization" of proofs. In the latter half of the class, we expand the minimal logic by adding new inference rules. In other words, by adding Law of Contradiction, we introduce the intuitionistic logic, and by adding the Law of Excluded Middle we introduce the classical logic. These examples show that as inference rules are added, the proofs become more difficult, but the model becomes simpler. It also seeks to understand the basic concepts of the relationship between symbols and models, such as the soundness and the completeness. Specific lesson plans are as follows. 1. What is the meaning of logical connectives, Theory of Meaning 1 and Theory of Meaning 2 2. Theory of meaning 2 and condition of logical connectives: "Tonk" and of Belnap`s conservative extension 3. Pravitz's "inversion principle" 4. Normalizability of proofs and the "harmony" of rules 5. "Sherlock Holmes argument", Law of Contradiction and intuitionistic logic 6. Intuitionistic logic Exercise 7. Law of Excluded Middle and Classical Logic 8 Demonstration and exercises in classical logic 9 Classical Logic and Truth Tables 10 Classical logic and the completeness theorem 11 Proof of the completeness theorem 12 General Exercises 13 (Extra Issues) Goedel's incompleteness theorem 14 (Extra Issues) Proof of Goedel's incompleteness theorem 15 Significance of the (Extra Issues) incompleteness theorem |
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| Evaluation Methods and Policy | Students are evaluated by the cumulative results of homework almost every time. | |||
| Course Requirements |
Complete previous exercises "Philosophical Logic 1" |
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| Study outside of Class (preparation and review) | I upload the class materials on this website in advance (1-2 days before) every time. Students should download the materials before class. | |||
| Textbooks | Textbooks/References | Distribute handouts each time. | ||
