Deductive Logic, Categorical Syllogism

1. Deductive Logic, Categorical Syllogism 5th Meeting

2. Deduction One of the two major types of argument traditionally distinguished, the other being induction. A deductive argument claims to provide conclusive grounds for its conclusion; if it does so it is valid, if it is does not it is invalid

3. Meaning of syllogism • Syllogism is a deductive argument in which a conclusion is inferred from two premises • A categorical syllogism is a deductive argument consisting of three categorical propositions that together contain exactly three terms, each of which occurs in exactly two of the constituent propositions. • This categorical syllogism is called as standar order

4. Major term, Minor term, middle term • Major term : predicate of conclusion • Minor term: subject of the conclusion • Middle term: third term appearing in both premises, but not in the conclusion

5. The mood of a syllogism A: Affirmative Universal proposition E: Negative Universal proposition I: Affirmative particular proposition O: Negative particular proposition

6. Figure of syllogism • The middle term is the subject term of the major premise and the predicate term of the minor premise(M_P,S-M, therefore S-P) • The middle term is the predicate term of both premises (P-M. S-M, therefore S-P) • The middle term is the subject term of both premises (M-P, M-S, therefore S-P • The middle term is the predicate term of the major premise and the subject term of minor premise (P-M, M-S, therefore S-P)

7. 6 Essential rules for standard-form syllogism • A standard-form categorical syllogism must contain exactly three terms, each of which is used in the same sense throughout the argument. Violation: fallacy of terms • In a valid standard-form categorical syllogism, the middle term must be distributed in at least one premise. Violation: fallacy of the undistributed middle • In a valid standard-form categorical syllogism, if either term is distributed in the conclusion, then it must be distributed in the premises. Violation: fallacy of the illicit major, or fallacy of the illicit minor

8. 4. No standard-form categorical syllogism having two negative premises is valid. Violation: fallacy of exclusive premises 5. No standard form categorical syllogism is negative, the conclusion must be negative. Violation: fallacy of drawing an affirmative conclusion from negative premise 6. No valid standard-form categorical syllogism with a particular conclusion can have two universal premises. Violation: Extensial fallacy

9. Exercises • AAA-2, • IEO-1, • AAA-3

10. Exercises • All textbooks are books intended for careful study Some reference books are books intended for careful study Therefore some reference books are textbooks 2. Some spaniels are not good hunters All spaniels are gentle dogs Therefore no gentle dogs are good hunters

11. All chocolate eclairs are fattening foods, because all chocolate eclairs are rich desserts, and some flattening foods are not rich desserts. • All people who live in London are people who drink tea, and all people who drink tea are people who like it. We may conclude, then, that all people who live in London are people who like it.

12. Exercises • Can any standard-form categorical syllogism be valid that contains exactly three terms, each of which is distributed in both of its occurence?