Reasoning

1. Reasoning http://www.toothpastefordinner.com/012408/circular-reasoning.gif

2. Types of Reasoning • Deductive Reasoning • deductive validity • Inductive Reasoning • inductive strength

3. Types of Reasoning • Deductive Reasoning • Syllogistic reasoning Basic syllogism: Premise 1: All A are B. Premise 2: All B are C. Conclusion: Therefore, all A are C.

4. Types of Reasoning • Deductive Reasoning • Syllogistic reasoning Syllogism example: All red books are astronomy books. All astronomy books are large. All red books are large.

5. Types of Reasoning • Deductive Reasoning • Syllogistic reasoning • Categorical syllogisms • Conditional syllogisms

6. 1. All Beagles are dogs All dogs have fur. Therefore: 2. Some teachers are women. All women are human. Therefore: 3. No elephants are carnivorous. Some dogs are carnivorous. Therefore:

7. 4. Some cats are grey. Some cats like dogs. Therefore: 5. All ghost stories are scary. No jokes are scary. Therefore: 6. No documentary films make money. No nonfiction books make money. Therefore:

8. Types of Reasoning • Deductive Reasoning • Principles of validity and truth in syllogisms • Principle 2: the validity of a syllogism is determined only by its form, not its content. • All birds are ants. • All ants have four legs. • Therefore, all birds have four legs.

9. Types of Reasoning • Deductive Reasoning • Principles of validity and truth in syllogisms • Principle 1: if two premises are true, the conclusion of a valid syllogism must be true. • All birds are animals. • All animals eat food. • Therefore, all birds eat food.

10. Types of Reasoning • Deductive Reasoning • Using Euler circles to determine validity

11. Types of Reasoning • Deductive Reasoning • Studying Syllogisms • Normative Approach • Descriptive Approach

12. Types of Reasoning • Deductive Reasoning • Studying Syllogisms • Normative Approach • Descriptive Approach

13. Illustrations of possible meanings of “Some bers are sabs.” Reasoning Performance • Premise phrasing

14. Illustration of possible meanings of “All daxes are wugs.” Reasoning Performance • Alternation of premise meaning

15. Reasoning Performance • Failure to consider all possibilities

16. Reasoning Performance • Believability effects All of the students are tired. Some tired people are irritable. Some of the students are irritable. All of the men are tired. Some tired people are women. Some of the men are women. All of the students are tired. Some tired people are irritable. Some of the students are irritable. All of the men are tired. Some tired people are women. Some of the men are women.

17. Types of Reasoning • Deductive Reasoning • Conditional syllogisms • An example of a logical argument Premise p  q If “p,” then “q” Existing condition p p is true Conclusion \q therefore, q is true

18. Types of Reasoning • Deductive Reasoning • Formal Logic • Inference rules • Modus Ponens (valid) p  q If “p,” then “q” p p is true \ ¬ p therefore, q is true

19. Types of Reasoning • Deductive Reasoning • Formal Logic • Inference rules • Modus Tollens (valid) p  q If “p,” then “q” ¬ q q is not true \ ¬ p therefore, p is not true

20. Types of Reasoning • Deductive Reasoning • Formal Logic • Fallacies • Denying the antecedent (invalid) p  q If “p,” then “q” ¬ p p is not true \ ¬ q therefore, q is not true

21. Types of Reasoning • Deductive Reasoning • Formal Logic • Fallacies • Affirming the consequent (invalid) p  q If “p,” then “q” q q is true \ p therefore, p is true

22. Summary of Conditional Syllogisms

23. Wason’s selection task (or four-card task) Types of Reasoning • Deductive Reasoning

24. Check 1 Check 3 $35 $20 Check 4 Check 2 initials no initials

25. Types of Reasoning • Inductive Reasoning

26. Types of Reasoning • Inductive Reasoning • Analogical reasoning Examples of verbal and pictorial analogies.

27. Example of a matrix completion problem. Types of Reasoning • Inductive Reasoning • Analogical reasoning

28. Types of Reasoning • Inductive Reasoning • Hypothesis testing • Confirmation bias

29. Approaches to Studying Reasoning • Fallacies in Reasoning • Equivocation • Illicit contrast • Argument by innuendo • Loaded question • Fallacy of the continuum • Fallacy of composition