Logic: evaluating deductive arguments - the syllogism

1. Logic: evaluating deductive arguments - the syllogism • A 5th pattern of deductive argument • the categorical syllogism (cf. the disjunctive syllogism, the hypothetical syllogism) • Df. - a deductive argument which contains three simple subject-predicate sentences, which in turn contain a total of three terms, each appearing twice. Deduction: the categorical syllogism - 1

2. Logic: evaluating deductive arguments - the syllogism • e.g. • All of Shakespeare’s dramas are in blank verse, and some of Shakespeare’s dramas are great plays. Hence some great plays are in blank verse. Deduction: the categorical syllogism - 2

3. Logic: evaluating deductive arguments - the syllogism • The components of a categorical syllogism • the three terms • middle term - this is the basis of the logic of a syllogism • major term • minor term Deduction: the categorical syllogism - 3

4. Logic: evaluating deductive arguments - the syllogism • Illustration: the Shakespeare example again • All S are B. • Some S are G. • Therefore, some G are B. Deduction: the categorical syllogism - 4

5. Logic: evaluating deductive arguments - the syllogism • The 3 statements in a categorical syllogism • major premise • minor premise • conclusion Deduction: the categorical syllogism - 5

6. Logic: evaluating deductive arguments - the syllogism • Testing validity • The need for rules rather relying on patterns • 256 patterns; 19 of these are valid • (Each of the 3 sentences in a syllogism can have 4 possible forms; this yields 64 possibilities. [4 x 4 x 4 = 64] And the middle term has 4 possible locations, thus 64 x 4 = 256.) Deduction: the categorical syllogism - 6

7. Logic: evaluating deductive arguments - the syllogism • The four rules for testing the validity of the categorical syllogism • (1) In a valid cat. syllogism, the middle term must be distributed at least • Aside on the notion of distribution • Distribution - whether a term (not a statement) refers to all or some of the members of its class Deduction: the categorical syllogism - 7

8. Logic: evaluating deductive arguments - the syllogism • e.g., All whales are mammals. • The subject is ? (U or D) • The predicate is ? (U or D) • e.g., No Hawaiians love winter. • The subject is ? (U or D) • The predicate is ? (U or D) Deduction: the categorical syllogism - 8

9. Logic: evaluating deductive arguments - the syllogism • e.g., Some Hawaiians love the mainland. • The subject is ? (U or D) • The predicate is ? (U or D) • e.g., Some Hawaiians do not love the mainland. • The subject is ? (U or D) • The predicate is ? (U or D) Deduction: the categorical syllogism - 9

10. Logic: evaluating deductive arguments - the syllogism • Notice this pattern. • Distribution subject universal (all, no) - distributed particular (some) - undistributed predicate affirmative - undistributed negative - distributed Deduction: the categorical syllogism - 10

11. Logic: evaluating deductive arguments - the syllogism • Back to rule # 1 Some poisons have medicinal value. Some things which have medicinal value have negative side effects. Therefore, some poisons have negative side effects. Deduction: the categorical syllogism - 11

12. Logic: evaluating deductive arguments - the syllogism • An Euler diagram of the preceding syllogism. • The syllogism is invalid; it violates rule # 1 Deduction: the categorical syllogism - 12

13. Logic: evaluating deductive arguments - the syllogism • (2) A syllogism in which a term moves from undistributed in a premise to distributed in the conclusion is invalid. (In a valid syllogism, a term may not move from U in the premises to D in the conclusion.) Deduction: the categorical syllogism - 13

14. Logic: evaluating deductive arguments - the syllogism • U in premise  D in conclusion - invalid • U in premise  U in conclusion - valid • D in premise  D in conclusion - valid • D in premise  U in conclusion - valid • Reason why U to D is invalid: the conclusion goes beyond the evidence provided in the premises. This is okay in inductive arguments, but not in deductive. Deduction: the categorical syllogism - 14

15. Logic: evaluating deductive arguments - the syllogism • E.g., All Nazis are guilty persons. Some anti-semites are not Nazis. Some anti-semites are not guilty persons. Deduction: the categorical syllogism - 15

16. Logic: evaluating deductive arguments - the syllogism • (3) A valid cat. syllogism may not have two negative premises. (A cat. syllogism with two negative premises is invalid.) • e.g., No members of the Kiwanis like Sting. No Democrats are members of the Kiwanis. Thus no Democrats like Sting. Deduction: the categorical syllogism - 16

17. Logic: evaluating deductive arguments - the syllogism Deduction: the categorical syllogism - 17

18. Logic: evaluating deductive arguments - the syllogism • (4) In a valid cat. syllogism, if a premise is negative, the conclusion must be negative, & if the conclusion is negative, one premise must be negative. • e.g., Some physicians are members of the AMA. No members of the AMA are for National Health Insurance. Hence some physicians are for National Health Insurance. Deduction: the categorical syllogism - 18

19. Logic: evaluating deductive arguments - the syllogism Deduction: the categorical syllogism - 19

20. Logic: evaluating deductive arguments - the syllogism • FINIS the categorical syllogism • To inductive logic Deduction: the categorical syllogism - 20