Deductive ReasoningDeductive Reasoning

Rules for Valid Syllogisms

Rules for a valid categorical Rules for a valid categorical syllogismsyllogism

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 Rules for a valid categorical syllogismsyllogism

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 Rules for a valid categorical syllogismsyllogism

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 Rules for a valid categorical syllogismsyllogism

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 lovers Minor premise: Joey is Italian Conclusion: Therefore, Joey is a great lover(the major premise is qualified, so the conclusion must be

qualified too)

Rules for a valid categorical Rules for a valid categorical syllogismsyllogism

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 1Argument 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 2Argument 2• Major premise:Left-

handers are more prone to occupational injuries

• Minor premise: Jake is left-handed

• Conclusion: Therefore, Jake is more prone to occupational injuries.

• Valid or Invalid?

Answer: Valid.

Argument 3Argument 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 4Argument 4

• Major premise: Either the state must raise taxes or cut social services

• Minor premise: The state will not raise taxes

• Conclusion: Therefore, the state must cut social services.

• Valid or invalid?

• Answer: Valid.

Argument 5Argument 5

• Major premise: No dog likes cats

• Minor premise: all cats like fish

• Conclusion: Therefore, no dog likes fish

•Valid or invalid?

Invalid

Argument 6Argument 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

• Invalid: the middle term global warming isn’t distributed, and the syllogism commits the fallacy of affirming the consequent

•Valid or invalid?

Argument 7Argument 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 8Argument 8• Three friends are trying

to decide what movie to see. Their choices are a foreign film, a violent action adventure, a mystery, a gory sci fi, or a comedy. • 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

• What type of movie(s) can all three friends agree on seeing?

Answer: a mystery or a comedy

Trudy Mona Ozzie

foreign X

action adventure

XX

mystery

science fiction

X

comedy

Argument 9Argument 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.

correctcorrect