Numbering Code	U-LET01 25141 SJ34	Year/Term	2022 ・ First 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	The ultimate goal of this class is to familiarize students with logical and clear thinking. It is to clarify the basis on which a proposition is asserted, and this helps to make the argument to be easily verifiable. The subject of this class is "philosophical logic": we especially focus on the problem of "What is logic?". We do our day-to-day reasoning and we often use the word "logical". Of course, we are required to be "logical". But what is to be "logical", and why we need to be? It is one of the important tasks of philosophy to reconsider the meaning of daily concepts that are used without reflection. In the class, we introduce some symbolic systems ("formal system") that can simulate proving a theorem in mathematics. Specifically, we explain the system of natural deduction of minimum predicate logic and conduct problem exercises.
Course Goals	Students are required to be who can prove easy propositions by Natural Deduction of "minimal logic". Through this, students understand how deduction in a formal system proceeds, as well as how everyday reasoning is simulated in formal systems.
Schedule and Contents	The minimal predicate logic is one of the basic logical systems that has only the introduction rule and the elimination rule of logical connectives. The first half of the first half introduces the natural deduction of minimal predicate logic. The goal is to be able to prove easy propositions by natural deduction. In the latter half, many proofs in mathematics is shown to be performed with the minimum logic, taking an example of a system "the minimal arithmetic Q" of arithmetic within minimum logic. At the same time, basic concepts of computation such as primitive recursion are introduced. Specific lesson plans are as follows. 1. What does logic do? 2. formal language 3. the minimum-propositional logic - the implication and its introduction and elimination rules 4. Conjunction, disjunction nad their introduction and elimination rules 5. exercise of minimal propositional logic 6. proof without detour 7. quantifiers and minimal predicate logic 8. the universal quantifier - its introduction and elimination rules 9. the existential quantifier - its introduction and elimination rule 10. minimal predicate logic problem exercise 11. formal natural number theory 12. primitive recursive functions and the proof of "2 + 2 = 4" 13. numerical representability of recursive functions 14. comprehensive exercise 15. the philosophy of formal logic and language
Evaluation Methods and Policy	Students are evaluated by the cumulative results of homework almost every time.
Course Requirements	Nothing in particular (Note, however, that the later half of the class requires the completion of this first half class.)
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.