1. Rules for Valid Syllogisms
Deductive Reasoning
Rules for Valid Syllogisms

2. Rules for a valid categorical syllogism
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)

3. Rules for a valid categorical syllogism
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)

4. Rules for a valid categorical syllogism
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)

5. Rules for a valid categorical syllogism
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)

6. Rules for a valid categorical syllogism
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)

7. 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

8. Argument 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.

9. 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

10. Argument 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.

11. Argument 5 Major premise: No dog likes cats Valid or invalid?
Minor premise: all cats like fish
Conclusion: Therefore, no dog likes fish
Valid or invalid?
Invalid

12. Argument 6 Valid 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
Valid or invalid?
Invalid: the middle term global warming isn’t distributed, and the syllogism commits the fallacy of affirming the consequent

13. 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.

14. Argument 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
comedy

15. Argument 9 correct Assume the following statements are all true:
Which of the following conclusions can be logically deduced from the statements at left?
insane people crave lead.
lead poisoning is the leading cause of insanity.
The use of pewter was reserved exclusively for Roman emperors.
Lead poisoning was common among the citizens of the Roman empire.
Nero must have been insane.
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.
correct