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2019　Philosophy of Science B

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Academic unit or major
Humanities and social science courses
Instructor(s)
Higashi Katsuaki 
Class Format
Lecture     
Media-enhanced courses
Day/Period(Room No.)
Mon1-2(H121)  Thr1-2(H121)  
Group
-
Course number
LAH.T207
Credits
2
Academic year
2019
Offered quarter
3Q
Syllabus updated
2019/3/18
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

Reasoning from one or more premises to reach a logically certain conclusion is called deductive reasoning. The 20th century began, and the deductive reasoning was formalized and progressed very much. Today, the field of study dealing with formalized deductive reasoning is called logic. This course covers the fundamentals of logic. In the first part focuses on propositional logic, and in the second part focuses on predicate logic. For each logic, students will learn formal languages, translation of Japanese sentences into symbolic sentences, inference rules, derivation, and meta-logic (completeness and soundness).The concept of logic is essential in order to understand how computers work. In addition to the practical aspect, logic is essential for rationality of human beings and rationality of science. This course facilitates students’ learning the concept of logic and understanding philosophical problems concerning logic.

Student learning outcomes

At the end of this course, students will be able to:
1) Symbolize deductive reasoning and understand the structure of deductive reasoning.
2) Derive the conclusion from the premise by using of the inference rules.
3) Understand the two methods of deciding whether or not reasoning is valid, and understand that the judgements of those methods are always coincident.

Keywords

Propositional logic, predicate logic, reasoning, argument, derivation, completeness, soundness.

Competencies that will be developed

✔ Specialist skills Intercultural skills Communication skills ✔ Critical thinking skills ✔ Practical and/or problem-solving skills

Class flow

After explanation of each topic, students are given exercise problems related to it. At the beginning of the next class, solutions to the exercise problems assigned during the previous class are reviewed.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Inductive reasoning and deductive reasoning, symbolic language and sentences in propositional logic. Understand the definition of symbolic sentences. Answer whether or not the given expressions are (informal) symbolic sentences.
Class 2 Translation of Japanese sentences into symbolic sentences in propositional logic. Translate given japanese sentences into symbolic sentences.
Class 3 Derivations I - The Inference rules and the forms of derivation in propositional logic. Understand the inference rules and the forms of derivation.
Class 4 Test level of understanding with exercise problems (translation of Japanese sentences into symbolic sentences). Derivations II - Use of subsidiary derivations. Review translation of Japanese sentences into symbolic sentence. Understand how to use subsidiary derivations.
Class 5 Exercise of derivation in propositional logic. Derive the conclusion from the premisses of given arguments by using inference rules.
Class 6 Syntactic and semantic validity of arguments. Determine whether or not given arguments are valid by using truth-value analysis. Explanation of the difference between semantic and syntactic methods
Class 7 Completeness and soundness in propositional logic. Explain the relation between syntactic and semantic validity.
Class 8 Test level of understanding with exercise problems (derivation in propositional logic). An introduction to predicate logic. Review derivation in propositional logic. Explain why predicate logic is required in addition to propositional logic.
Class 9 Symbolic languages and symbolic sentences in predicate logic. Understand the definition of symbolic sentences in predicate logic. Decide wheter or not given expressions are (informal) symbolic sentences in predicate logic.
Class 10 Translation of Japanese sentences into symbolic sentences in monadic predicate logic. Translate given sentences including the words ``all" or ``some" into symbolic sentences.
Class 11 Symbolization of Japanese sentences including multiple quantification. Derivations in predicate logic - The inference rules and the forms of derivation. Understand the inference rules and the forms of derivation in predicate logic.
Class 12 Test level of understanding with exercise problems (translation of Japanese sentences into symbolic sentences). Derivations - Important theorems and their use. Review translation of Japanese sentences into symbolic sentences in predicate logic. Understand the important theorems in predicate logic and their use.
Class 13 Exercise of derivation in predicate logic. Derive the conclusion from the premises of given arguments by using inference rules.
Class 14 Semantics in predicate logic - Model and decidability in predicate logic. Understand the definition of models. Explain that the semantic validity in monadic predicate logic is decidable, but in (general) predicate logic not always decidable.
Class 15 Test level of understanding with exercise problems (derivation in predicate logic). Completeness, soundness, and consistency in predicate logic. Rreview derivation in predicate logic. Explain the relation between syntactic and semantic validity in predicate logic.

Textbook(s)

None required.

Reference books, course materials, etc.

Course materials are provided during class.

Assessment criteria and methods

Students’ course scores are based on 4 exams (30 minutes each time) and final report. (4 exams: 70％；the final report: 30%).

Related courses

  • LAH.T106 ： Philosophy of Science A
  • LAH.T306 ： Philosophy of Science C

Prerequisites (i.e., required knowledge, skills, courses, etc.)

No prerequisites.

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