# Logic: evaluating deductive arguments - the syllogism

```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 subjectpredicate sentences, which in turn
contain a total of three terms, each
appearing twice.
Deduction: the categorical syllogism - 1
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
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
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
Logic: evaluating deductive arguments the syllogism
– The 3 statements in a categorical
syllogism
• major premise
• minor premise
• conclusion
Deduction: the categorical syllogism - 5
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
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
&raquo; Distribution - whether a term
(not a statement) refers to all
or some of the members of its
class
Deduction: the categorical syllogism - 7
Logic: evaluating deductive arguments the syllogism
– e.g., All whales are mammals.
&raquo; The subject is ? (U or D)
&raquo; The predicate is ? (U or D)
– e.g., No Hawaiians love winter.
&raquo; The subject is ? (U or D)
&raquo; The predicate is ? (U or D)
Deduction: the categorical syllogism - 8
Logic: evaluating deductive arguments the syllogism
– e.g., Some Hawaiians love the
mainland.
&raquo; The subject is ? (U or D)
&raquo; The predicate is ? (U or D)
– e.g., Some Hawaiians do not love
the mainland.
&raquo; The subject is ? (U or D)
&raquo; The predicate is ? (U or D)
Deduction: the categorical syllogism - 9
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
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
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
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
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
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
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
Logic: evaluating deductive arguments the syllogism
&raquo;
Deduction: the categorical syllogism - 17
Logic: evaluating deductive arguments the syllogism
• (4) In a valid cat. syllogism, if a
premise is negative, the conclusion
must be negative, &amp; 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
Logic: evaluating deductive arguments the syllogism
–
Deduction: the categorical syllogism - 19
Logic: evaluating deductive arguments the syllogism
• FINIS the categorical syllogism
– To inductive logic
Deduction: the categorical syllogism - 20
```