Transcript Rules for Valid Syllogisms PPT

Deductive Reasoning
Rules for Valid Syllogisms
Rules for a valid categorical
syllogism
1. A valid syllogism must possess three, and
only three, unambiguous terms.


If any term is vague or has multiple meanings,
the syllogism is invalid.
Invalid Syllogism:

Major premise: In order to run something must have
feet
 Minor Premise: My nose is running
 Conclusion: Therefore, my nose must have feet.
(the term “run” has two different meanings)
Rules for a valid categorical
syllogism
2. The middle term must be universal and
unqualified in at least one premise.


The middle term (the one that appears in both
premises) must be universal, e.g. an “all,” “every”
or “no” statement in at least one premise
Invalid syllogism:

Major premise: Some charities represent religious
groups.
 Minor premise: Some religious groups represent
extremist groups.
 Conclusion: Therefore, some charities represent
extremist groups.
(both premises are particular or qualified)
Rules for a valid categorical
syllogism
3. The middle term must be “distributed” in
both premises. (Also, the middle term may
not appear in the conclusion)


The middle term must serve as the subject of one
premise (before the verb) and the predicate (after
the verb) of the other premise.
Invalid Syllogism:
 Major premise: Convicts have a lot of tattoos
 Minor premise: Favio has a lot of tattoos
 Conclusion: Therefore, Favio must be a convict
(the middle term “a lot of tattoos” is the predicate of each
premise)
Rules for a valid categorical
syllogism
4. Qualified premises require qualified
conclusions



No term may be universal in the conclusion that is not
universal in a premise.
If one premise is qualified or particular, the conclusion
must be qualified or particular.
Invalid Syllogism

Major premise: Some Italians are great cooks

Minor premise: Joey is Italian

Conclusion: Therefore, Joey is a great cook
(the major premise is qualified, so the conclusion must be
qualified too)
Rules for a valid categorical
syllogism
5. At least one premise must be affirmative



Both premises cannot be negative.
If either premise is negative the conclusion must
be negative.
Invalid Syllogism
 Major premise: no cat is a reptile
 Minor premise: no reptile is warm-blooded
 Conclusion: Therefore, no cat is warm-blooded
(both premises are negative)
Argument 1
• Major premise: Some
snakes are poisonous
• Minor premise: No
mammals are
poisonous
• Conclusion:
Therefore, no
mammals are snakes
• Valid or Invalid?
•Answer: Invalid. The
middle term is not
distributed
Argument 2
• Major premise:Left• Valid or Invalid?
handers are more prone
to occupational injuries
Answer: Valid.
• Minor premise: Jake is
left-handed
• Conclusion: Therefore,
Jake is more prone to
occupational injuries.
Argument 3
• Major premise:
Students who study
hard get good
grades
• Minor premise:
Loretta gets good
grades
• Conclusion:
Therefore, Loretta
studies hard
• Valid or Invalid?
•Answer: Invalid.
Undistributed
middle term, and the
fallacy of affirming
the consequent
Argument 4
• Major premise: Either • Valid or invalid?
the state must raise taxes
or cut social services
• Answer: Valid.
• Minor premise: The
state will not raise taxes
• Conclusion: Therefore,
the state must cut social
services.
Argument 5
• Major premise: No
dog likes cats
• Minor premise: all
cats like fish
• Conclusion:
Therefore, no dog
likes fish
•Valid or invalid?
Invalid
Argument 6
• Major premise: If
deforestation continues,
there will be more global
warming
• Minor premise: We can
see that there is more
global warming
• Conclusion: Therefore,
deforestation must be
continuing
•Valid or invalid?
• Invalid: the middle term
global warming isn’t
distributed, and the
syllogism commits the
fallacy of affirming the
consequent
Argument 7
• Major premise: some
chimpanzees can be
potty-trained.
• Minor premise:
Bonzo is a chimpanzee
• Conclusion:
Therefore, Bonzo can
be potty-trained.
• Valid or invalid?
Invalid: the middle term,
chimpanzees, isn’t
universal or unqualified
in the major premise.
Argument 8
• Three friends are trying
• What type of movie(s)
to decide what movie
to see. Their choices
can all three friends
are a foreign film, a
agree on seeing?
violent action
adventure, a mystery, a Answer: a mystery or a
gory sci fi, or a
comedy
comedy.
Trudy Mona Ozzie
• Trudy doesn’t want to
see a foreign film
• Mona prefers not to see
an action adventure
movie
• Ozzie doesn’t like
violent or gory movies
foreign
action
adventure
X
XX
mystery
science
fiction
comedy
X
Argument 9
Assume the following
statements are all true:
Nero, the Roman
emperor, regularly
drank from cups made
of pewter that
contained lead.
Anyone who regularly
ingests lead will
develop lead
poisoning. Lead
poisoning always leads
to insanity.
Which of the following
conclusions can be logically
deduced from the
statements at left?
A. insane people crave lead.
B. lead poisoning is the leading cause
of insanity.
C. The use of pewter was reserved
exclusively for Roman emperors.
D. Lead poisoning was common
among the citizens of the Roman
empire.
E. Nero must have been insane.