2. Reasoning -deductive versus inductive reasoning -two basic types of deductive reasoning task: conditional (propositional) and syllogistic

3. 1. Conditional (propositional) reasoning: If p, then q. P. Conclusion: q? If it snows a lot, then school is cancelled. It snows a lot. Therefore, school is cancelled.

4. Valid versus sound arguments If it rains, the road is dry It rains. The road is dry? Valid, but not sound.

5. 1. Modus Ponens (affirming the antecedent): If p, then q p! Conclusion: q! If it is Wednesday, then we have cognition. It is Wednesday. Therefore, we have cognition. 2. Modus Tollens (denying the consequent): Valid arguments: If p, then q Not q! Conclusion: not p! If it is Wednesday, then we have cognition. We don’t have cognition! Therefore, it is not Wednesday!

6. Logical fallacies: Denying the Antecedent: If p then q Not p! Not q? If it is Friday, then we have a test It isn’t Friday! Invalid arguments: We don’t have a test? Affirming the consequent: If p then q q! p? If it is Friday, then we have a test We have a test! It’s Friday?

7. Logical Fallacies Anecdotal evidence Argumentum ad antiquitatem Argumentum ad novitatem Argumentum ad hominem Argumentum ad ignorantiam Argumentum ad misericordiam Argumentum ad nauseam Argumentum ad numerum Argumentum ad verecundiam Bifurcation Circulus in demonstrando Fallacies of composition Cum hoc ergo propter hoc Post hoc ergo propter hoc Non sequitur Red Herring Slippery-slope argument Straw man Tu quoque No True Scotsman fallacy

8. 2. Syllogistic reasoning: Two premises, asked to evaluate a conclusion e.g.: Premise 1: All men are animals. Premise 2:Some animals are aggressive. Conclusion: Some men are aggressive. e.g.2: Premise 1: All students are bright. Premise 2: All bright people complete assignments on time. Conclusion: All students complete assignments on time. Most people agree with 1 st, disagree with 2 nd, but the 2 nd is logically valid, 1 st isn’t. Can evaluate using Venn diagrams: if you can come up with a diagram that fits the premises, but not the conclusion, then it is not a valid conclusion.

9. Syllogisms 1. All A’s are B’s. 2. Some B’s are C’s. Therefore, some A’s are C’s. 1. All men are animals. 2. Some animals are aggressive. Therefore, some men are aggressive. women

10. Syllogisms 1. All A’s are B’s. 2. Some B’s are C’s. 1. All men are animals. 2. Some animals are aggressive. ANIMALS MEN AGGRESSIVE Therefore, some A’s are C’s.Therefore, some men are aggressive.

11. Syllogisms 1. All A’s are B’s. 2. Some B’s are C’s. 1. All men are animals. 2. Some animals are aggressive. 1. All students are bright. 2. All bright people complete assignments on time. ANIMALS MENAGGRESSIVE BRIGHT PEOPLE STUDENTS COMPLETE ASSIGNMENTS ON TIME Therefore, some A’s are C’s.Therefore, some men are aggressive. Therefore, all students complete assignments on time.

12. “Some A’s are B’s” “No B’s are C’s” No A’s are C’s? A B C A B C “No A’s are B’s” “All B’s are C’s” No A’s are C’s? A B C A B C “Some dogs chase cars” “No cats are dogs” No cats chase cars? dogs Chase cars Cats

13. “Some A’s are B’s” “Some B’s are C’s” Some A’s are C’s? A B A B C C AB C A B C A B C A B C Why are we terrible at these? Difficult to generate alternatives

14. Syllogistic reasoning: Why are we terrible at this type of reasoning? 1) Rarely ever face one, so no practice at them 2) Belief bias 3) Misunderstanding the premises: if A=B, B=A not true here 4) Milieu of the question: all/all/all, none/none/none e.g.: No oranges are apples. No lemons are oranges. Therefore, no apples are lemons. Not a logical conclusion: 3. Formal logical reasoning:

15. Wason card task EJ76EJ76 Rule: If it has a vowel on one side, it has an even number on the other.

16. Wason card task 1724beercoke Rule: If a person is under 21, then they should be drinking something nonalcoholic.