Deduction: the categorical syllogism - 1 Logic: evaluating deductive arguments - the syllogism 4 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 - 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 - 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 - 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 - 5 Logic: evaluating deductive arguments - the syllogism –The 3 statements in a categorical syllogism major premise minor premise conclusion

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

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

Deduction: the categorical syllogism - 20 Logic: evaluating deductive arguments - the syllogism FINIS the categorical syllogism –To inductive logicTo inductive logic