Logic: evaluating deductive arguments - the syllogism

Deduction: the categorical 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.



• 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.



– 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



– Illustration: the Shakespeare example again• All S are B.• Some S are G.• Therefore, some G are B.



– The 3 statements in a categorical syllogism • major premise• minor premise• conclusion



– 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.)



– 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



– 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)



– 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)



– Notice this pattern.

• Distribution subject

universal (all, no) - distributedparticular (some) - undistributed

predicateaffirmative - undistributednegative - distributed



– 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.



– An Euler diagram of the preceding syllogism.

– The syllogism is invalid; it violates rule # 1



• (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.)



– 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.



– E.g., All Nazis are guilty persons. Some anti-semites are not Nazis. Some anti-semites are not guilty

persons.



• (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.



»



• (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.



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• FINIS the categorical syllogism

– To inductive logic

Logic: evaluating deductive arguments - the syllogism

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