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Deductive ReasoningDeductive Reasoning
Rules for Valid Syllogisms
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Rules for a valid categoricalRules for a valid categorical
syllogismsyllogism1. 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: a!or premise: In order to run something must have
feet
inor "remise: y nose is running #onclusion: $herefore, my nose must have feet.
%the term &run' has t(o different meanings)
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Rules for a valid categoricalRules for a valid categorical
syllogismsyllogism*. $he middle term must be universal and
un+ualified in at least one premise. $he 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:
a!or premise: Some charities represent religiousgroups.
inor premise: Some religious groups representetremist groups. #onclusion: $herefore, some charities represent
etremist groups.
%both premises are particular or +ualified)
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Rules for a valid categoricalRules for a valid categorical
syllogismsyllogism-. $he middle term must be &distributed' in both
premises. %Also, the middle term may notappear in the conclusion)
$he middle term must serve as the sub!ect of one premise %before the verb) and the predicate %after theverb) of the other premise.
Invalid Syllogism: a!or premise: #onvicts have a lot of tattoos
inor premise: avio has a lot of tattoos
#onclusion: $herefore, avio must be a convict
%the middle term &a lot of tattoos' is the predicate of each premise)
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Rules for a valid categoricalRules for a valid categorical
syllogismsyllogism/. 0ualified premises re+uire +ualified
conclusions o term may be universal in the conclusion that is not
universal in a premise. If one premise is +ualified or particular, the conclusion
must be +ualified or particular.
Invalid Syllogism a!or premise: Some Italians are great lovers
inor premise: 2oey is Italian #onclusion: $herefore, 2oey is a great lover
%the ma!or premise is +ualified, so the conclusion must be+ualified too)
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Rules for a valid categoricalRules for a valid categorical
syllogismsyllogism3. At least one premise must be affirmative
4oth premises cannot be negative.
If either premise is negative the conclusion must be negative. Invalid Syllogism
a!or premise: no cat is a reptile
inor premise: no reptile is (arm5blooded
#onclusion: $herefore, no cat is (arm5blooded
%both premises are negative)
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Argument 1Argument 1
6 Major premise: Some
sna7es are poisonous
6 Minor premise: omammals are
poisonous
6 Conclusion:
$herefore, no
mammals are sna7es
6 Valid or Invalid8
•Answer: Invalid. The
middle term is not
distributed
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Argument *Argument *
6 Major premise:9eft5
handers are more prone
to occupational in!uries
6 Minor premise: 2a7e is
left5handed
6 Conclusion: $herefore,
2a7e is more prone tooccupational in!uries.
6 Valid or Invalid8
Answer: Valid.
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Argument -Argument -
6 Major premise:
Students (ho study
hard get good grades6 Minor premise:
9oretta gets good
grades
6 Conclusion:
$herefore, 9oretta
studies hard
6 Valid or Invalid8
•Answer: Invalid.Undistributed
middle term, and the
fallacy of affirming
the consequent
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Argument /Argument /
6 Major premise: ither
the state must raise taes
or cut social services6 Minor premise: $he
state (ill not raise taes
6 Conclusion: $herefore,
the state must cut social
services.
6 Valid or invalid8
• Answer: Valid.
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Argument 3Argument 3
6 Major premise: odog li7es cats
6 Minor premise: allcats li7e fish
6 Conclusion: $herefore, no dog
li7es fish
•Valid or invalid?
Invalid
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Argument ;Argument ;
6 Major premise: If
deforestation continues,
there (ill be more global
(arming
6 Minor premise:
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Argument >Argument >
6 Major premise: some
chimpan?ees can be
potty5trained.6 Minor premise:
4on?o is a chimpan?ee
6 Conclusion:
$herefore, 4on?o can
be potty5trained.
6 Valid or invalid8
Invalid: the middle term,chimpanzees, isn’t
universal or unqualified
in the maor premise.
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Argument @Argument @
6 $hree friends are tryingto decide (hat movie tosee. $heir choices are aforeign film, a violent
action adventure, amystery, a gory sci fi,or a comedy. 6 $rudy doesn=t (ant to
see a foreign film
6 ona prefers not to seean action adventuremovie
6 ??ie doesn=t li7eviolent or gory movies
6
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Argument CArgument C
Assume the follo(ing
statements are all true:
ero, the Roman
emperor, regularly
dran7 from cups madeof pe(ter that
contained lead.
Anyone (ho regularly
ingests lead (ill
develop lead
poisoning. 9ead
poisoning al(ays leads
to insanity.
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