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 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 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 1Valid or Invalid?

• Major premise: Some snakes are poisonous.

• Minor premise: No mammals are poisonous.

• Conclusion: Therefore, no mammals are snakes .

Answer: Invalid. The middle term is not distributed.

Argument 2Valid or Invalid?

• 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.

Answer: Valid.

Argument 3Valid or Invalid?

• Major premise: Students who study hard get good grades.

• Minor premise: Loretta gets good grades.

• Conclusion: Therefore, Loretta studies hard.

Answer: Invalid. Undistributed middle term, and the fallacy of affirming the consequent.

Argument 4Valid or invalid?

• 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.

Answer: Valid.

Argument 5Valid or invalid?

• Major premise: No dog likes cats.• Minor premise: All cats like fish.• Conclusion: Therefore, no dog likes fish.

Answer: Invalid.

Why?

Argument 6Valid or invalid?

• 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.

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

Argument 7Valid or invalid?

• Major premise: some chimpanzees can be potty-trained.

• Minor premise: Bonzo is a chimpanzee.• Conclusion: Therefore, Bonzo can be

potty-trained.

Answer: Invalid. The middle term, chimpanzees, isn’t universal or unqualified in the major premise.

Argument 8Valid or Invalid

• 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: Invalid. Answer: a mystery or a comedy

Trudy Mona Ozzie

foreign X

action adventure XX

mystery

science fiction X

comedy

Argument 9Assume 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.

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.

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.

correct