Slide Logic học C3 - Logic Học UEL

Introduction to LOGIC Chapter 3: Categorical Syllogisms (Tam đoạn luận đơn) (Ref.: Chapter 5) Hà Văn Hiếu Faculty of Economic Mathematics, University of Economics and Law Outline Standard Form, Mood, and Figure Venn Diagram Rules and Fallacies (Các quy tắc và ngụy biện) Enthymemes Sorites (Tam đoạn luận liên kết) Categorical Syllogism (Tam đoạn luận đơn) ▶ A syllogism (tam đoạn luận) is a deductive argument consisting of two premises and one conclusion. Provisionally, we will define a categorical syllogism (tam đoạn luận đơn) as a syllogism consisting of three categorical propositions and containing a total of three different terms, each of which appears twice in distinct propositions. Example All soldiers are patriots. No traitors are patriots. Therefore, no traitors are soldiers. ▶ The major term (Đại từ, thuật ngữ lớn) is defined as the predicate of the conclusion, ▶ The minor term (Tiểu từ) is defined as the subject of the conclusion, and ▶ The middle term (Trung từ) is the term that occurs once in each premise, and does not occur in the conclusion. Example In the above example, the major term is “soldiers,”, the minor term is “traitors,” and the middle term is “patriots.” Standard-form Categorical Syllogism ▶ The major premise (đại tiền đề), by definition, is the one that contains the major term, and ▶ the minor premise (tiểu tiền đề) is the one that contains the minor term. Standard-form categorical syllogisms A categorical syllogism is said to be in standard-form if it satisfies the following four conditions: 1. All three statements are standard-form categorical propositions. 2. The two occurrences of each term are identical. 3. Each term is used in the same sense throughout the argument. 4. The major premise is listed first, the minor premise second, and the conclusion last. Example In standard-form: All soldiers are patriots. No traitors are patriots. Therefore, no traitors are soldiers. Not in standard-form: All watercolors are paintings. Some watercolors are masterpieces. Therefore, some paintings are masterpieces. ▶ Major term: “soldiers”, minor term: “traitors”, middle term: “patriots”. Mood (Kiểu) and Figure (hình) ▶ The mood (kiểu) of a categorical syllogism refers to the types of categorical propositions (A, E, I, O) that make up the syllogism. Example If the major premise is an A proposition, the minor premise is an O proposition, and the conclusion is an E proposition, the mood is AOE. ▶ The figure (hình) of a categorical syllogism is determined by the location of the two occurrences of the middle term M in the premises. Example Let’s consider the following argument: “No painters are sculptors. Some sculptors are artists. Therefore, some artists are not painters.” ▶ This argument is a categorical syllogism. ▶ This syllogism is in standard form. ▶ The major term is “painters”. The major premise is “No painters are sculptors.” ▶ The minor term is “artists”. The minor premise is “Some sculptors are artists.” ▶ The middle term is “sculptors”. ▶ The mood is EIO. ▶ The figure is four. ▶ The form is EIO-4.. Validity of standard syllogisms - Exercise 5.1 (p. 235) ▶ For both Boolean and Aristotelian standpoints: ▶ For the Aristotelian standpoint only: