Deductive Reasoning

1. Deductive Reasoning Rules for Valid Syllogisms

2. Rules for a valid categorical syllogism • A valid syllogism must possess three, and only three, unambiguous terms. • There must be exactly three 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. • Every syllogism has two premises and a conclusion • 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. • A qualified or particular term in a premise cannot become a universal or unqualified term in the conclusion • 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. Major premise: Some snakes are poisonous Minor premise: No mammals are poisonous Conclusion: Therefore, no mammals are snakes Valid or Invalid? Argument 1 • Answer: Invalid. The middle term is not distributed

8. 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? Argument 2 Answer: Valid.

9. Major premise: Students who study hard get good grades Minor premise: Loretta gets good grades Conclusion: Therefore, Loretta studies hard Valid or Invalid? Argument 3 • Answer: Invalid. Undistributed middle term, and the fallacy of affirming the consequent

10. 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? Argument 4 • Answer: Valid.

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

12. 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 Argument 6 • Valid or invalid?

13. Major premise: some chimpanzees can be potty-trained. Minor premise: Bonzo is a chimpanzee Conclusion: Therefore, Bonzo can be potty-trained. Valid or invalid? Argument 7 Invalid: the middle term, chimpanzees, isn’t universal or unqualified in the major premise.

14. 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? Argument 8 • Answer: a mystery or a comedy

15. 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? 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. Argument 9 correct