Print

2022　Philosophy of Science B

Font size  SML

Register update notification mail Add to favorite lecture list
Academic unit or major
Humanities and social science courses
Instructor(s)
Higashi Katsuaki 
Class Format
Lecture    (Face-to-face)
Media-enhanced courses
Day/Period(Room No.)
Mon1-2(W331)  Thr1-2(W331)  
Group
-
Course number
LAH.T207
Credits
2
Academic year
2022
Offered quarter
3Q
Syllabus updated
2022/4/20
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. In the 20th century, 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. The first part focuses on propositional logic, and the second part focuses on predicate logic. For each logic, students will learn formal languages, translation of Japanese sentences into formal sentences, inference rules, derivation, and meta-logic (e.g. 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 the rationality of human beings and the 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) Formalize deductive reasoning and understand the structure of the reasoning.
2) Derive the conclusion from the premise by using the inference rules.
3) Understand the two methods of deciding whether or not reasoning is valid, and make sure that the judgments 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 an explanation of each topic, students are given exercises related to it. At the beginning of the next class, solutions to the exercises are reviewed. Also, in order to check the degree of understanding of the learning content, three times comprehension-checks will be given, and in the next class, the lack of understanding found in the answers will be reviewed. In addition, at the end of the semester, a test will be conducted to check the level of understanding of the entire lecture.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Inductive reasoning and deductive reasoning, formal language 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 The 1st comprehension-check (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 The 2nd comprehension-check (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 quantifications. Derivations in predicate logic - The inference rules and the forms of derivation. Review translation of Japanese sentences into symbolic sentences in predicate logic. Understand the important theorems in predicate logic and their use.
Class 12 The 3rd comprehension-check (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. Semantics in predicate logic. Derive the conclusion from the premises of given arguments by using inference rules. Understand the definition of models.
Class 14 Model and decidability in predicate logic. Completeness, soundness, and consistency in predicate logic. Explain that the semantic validity in monadic predicate logic is decidable, but in (general) predicate logic not always decidable. Explain the relation between syntactic and semantic validity in predicate logic.
Class 15 Summary and final exam (predicate logic). Review (i) the symbolization of Japanese sentences and (ii) derivations in predicate logic.

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterward (including assignments) for each class.
They should do so by referring to course materials.

Textbook(s)

None required.

Reference books, course materials, etc.

Lecture materials can be downloaded from OCW-i.

Assessment criteria and methods

Students' scores are based on 3 times comprehension-checks [45%], final exam [35%], and a report on meta-logic [20%].

Related courses

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

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

No prerequisites.

Page Top