rules for valid syllogisms

8/17/2019 Rules for Valid Syllogisms

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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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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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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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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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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.

rules for valid syllogisms

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