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Memory and Cognition

Memory and Cognition. PSY 324 Topic: Reasoning Dr. Ellen Campana Arizona State University. Reasoning. Reasoning is Process of drawing conclusions Cognitive process by which people start with information and come to conclusions that go beyond that information

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Memory and Cognition

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  1. Memory and Cognition PSY 324 Topic: Reasoning Dr. Ellen Campana Arizona State University

  2. Reasoning • Reasoning is • Process of drawing conclusions • Cognitive process by which people start with information and come to conclusions that go beyond that information • Using those definitions we’ve already seen many examples of reasoning – can you think of some?

  3. Reasoning • Focus today on two specific types of reasoning • Deductive reasoning (Aristotle) • Sequences of statements (syllogisms) • What can logically be concluded? • Definite conclusions • Inductive reasoning • Based on evidence • What is probably true in the world? • Probable conclusions • Both types tell us about cognition in general

  4. Deductive Reasoning

  5. Deductive Reasoning • Deductive reasoning is all about logic • This is logic as mathematicians, philosophers and computer scientists define it • As we’ll see, it doesn’t always match up with common sense • Note for tests: When you encounter a logic problem, be careful. It’s asking for very specific things. I’ll give you a strategy later.

  6. Deductive Reasoning • Basic form of deductive reasoning is syllogism • Includes 2 or more statements (premises), followed by a conclusion • Categorical syllogisms are a type of syllogism • Premises and conclusion describe the relationship between categories • Words like all, no, and some are used

  7. Categorical Syllogisms • This is an example of a categorical syllogism: Premise 1: All birds are animals Premise 2: All animals eat food Conclusion: (Therefore) all birds eat food • In “perfect form” this can be written as Premise 1: All A are B Premise 2: All B do C Conclusion: (Therefore) all A do C

  8. Validity and Deductive Reasoning • Syllogisms can be valid or not valid • Here valid means something very specific – be careful! • Valid syllogisms • The conclusions follow logically from the premises • If all premises are true, then the conclusion is true • What if one premise is not true? • Syllogism can still be valid if the form is valid • Truth and validity are NOT the same • This is difficult for people!

  9. Validity and Deductive Reasoning • Let’s practice…. Valid or not? Premise 1: All red cars are sports cars Premise 2: All sports cars are fast Conclusion: All red cars are fast VALID!

  10. Validity and Deductive Reasoning • Let’s practice…. Valid or not? Premise 1: All red cars are sports cars Premise 2: All red cars are fast Conclusion: All sports cars are fast NOT VALID!

  11. Validity and Deductive Reasoning • Let’s practice…. Valid or not? Premise 1: All of the students are tired Premise 2: Some tired people are irritable Conclusion: Some of the students are irritable NOT VALID!

  12. Validity and Deductive Reasoning • Let’s practice…. Valid or not? Premise 1: All of the men are tired Premise 2: Some tired people are women Conclusion: Some men are women NOT VALID!

  13. Validity and Deductive Reasoning • Let’s practice…. Valid or not? Premise 1: All lava lamps are lamps Premise 2: All lamps are furniture Conclusion: All lava lamps are furniture VALID!

  14. Validity and Deductive Reasoning • This practice was intended to illustrate that truth and validity are not the same • Truth depends on consistency with the world • Validity depends on the form of the statements • Does it follow a logical progression? • Do people think logically? • Philosophers say yes, errors are due to carelessness • Cognitive Psychologists say no, errors tell us how people really think in everyday situations

  15. Studying Deductive Reasoning • Two methods have been used • Evaluation method: present premises and conclusion, ask people to judge validity • Production method: present premises, ask what can logically be concluded, if anything • Most research has used the evaluation method • People make lots of errors (70-80%) • Error rate determined by many factors, including whether problem is abstract or concrete

  16. Problem Statement • A categorical syllogism that’s concrete: Premise 1: All robins are birds Premise 2: All birds are animals Conclusion: (Therefore) all robins are animals • A categorical syllogism that’s abstract: Premise 1: All A are B Premise 2: All B are C Conclusion: (Therefore) all A are C • Lower error rates for abstract statements • Here’s my tip: convert to abstract for the test

  17. Errors and Concrete Problems • When logic problems are stated in concrete terms, error rate goes up • Part of this effect is due to biases that people bring to the task of reasoning • Atmosphere effect • Belief bias • Biases are another example of heuristics • Much faster, often right • Sometimes cause errors

  18. Atmosphere Effect • Atmosphere effect: the words all, some, no in the premises create an overall “mood” or “atmosphere” that can influence judgement • Alls in premise suggest all in conclusion • Nos in premise suggest no in conclusion • Somes in premise suggest some in conclusion • This is sometimes, but not always, correct • Be careful of this bias in the test!

  19. Belief Bias • If a conclusion is true (meaning it matches the world) or consistent with a person’s belief, the whole syllogism will often be judged valid • It’s as if people skip the logic and move right to evaluating the conclusion

  20. Validity and Deductive Reasoning • Let’s practice…. Valid or not? Premise 1: No police dogs are vicious Premise 2: Some highly trained dogs are vicious Conclusion: Some police dogs are not highly trained NOT VALID!

  21. Validity and Deductive Reasoning • Let’s practice…. Valid or not? Premise 1: No addictive drugs are inexpensive Premise 2: Some cigarettes are inexpensive Conclusion: Some addictive drugs are not cigarettes NOT VALID!

  22. Thinking Conditionally • Much of the research on deductive reasoning has focused on conditional syllogisms • Conditional syllogisms are like categorical syllogisms, except the first premise is if… then.. • Common in everyday life Let’s say you lent your friend Steve $20, but he has never paid you back. Knowing Steve, you might say to yourself that you knew this would happen.

  23. Thinking Conditionally • Much of the research on deductive reasoning has focused on conditional syllogisms • Conditional syllogisms are like categorical syllogisms, except the first premise is if… then.. • Common in everyday life Premise 1: If I lend Steve $20, then I won’t get it back Premise 2: I lent Steve $20 Conclusion: I won’t get my $20 back

  24. Thinking Conditionally • The second premise can either affirm or deny either the antecedent or the consequent • This relationship is what determines validity • As before, validity is NOT the same as truth in the world p q If …… then …… antecedent consequent

  25. Valid Conditional Syllogisms • Affirming the antecedent is valid • Affirming the antecedent is when the second premise asserts that the antecedent of the first premise is true Premise 1: If p, then q. Premise 2: p. Conclusion: (Therefore), q.

  26. Valid Conditional Syllogisms • Affirming the antecedent is valid • Affirming the antecedent is when the second premise asserts that the antecedent of the first premise is true Premise 1: If I study, then I’ll get a good grade. Premise 2: I studied. Conclusion: (Therefore), I’ll get a good grade.

  27. Valid Conditional Syllogisms • Denying the consequent is valid • Denying the consequent is when the second premise asserts that the consequent of the first premise is NOT true Premise 1: If p, then q. Premise 2: not q. Conclusion: (Therefore), not p.

  28. Valid Conditional Syllogisms • Denying the consequent is valid • Denying the consequent is when the second premise asserts that the consequent of the first premise is NOT true Premise 1: If I study, then I’ll get a good grade. Premise 2: I didn’t get a good grade. Conclusion: (Therefore), I didn’t study.

  29. Invalid Conditional Syllogisms • Affirming the consequent is not valid • Affirming the consequent is when the second premise asserts that the consequent of the first premise is true Premise 1: If p, then q. Premise 2: q. Conclusion: (Therefore), p.

  30. Invalid Conditional Syllogisms • Affirming the consequent is not valid • Affirming the consequent is when the second premise asserts that the consequent of the first premise is true Premise 1: If I study, then I’ll get a good grade. Premise 2: I got a good grade. Conclusion: (Therefore), I studied.

  31. Invalid Conditional Syllogisms • Denying the antecedent is not valid • Denying the antecedent is when the second premise asserts that the antecedent of the first premise is NOT true Premise 1: If p, then q. Premise 2: not p. Conclusion: (Therefore), not q.

  32. Invalid Conditional Syllogisms • Denying the antecedent is not valid • Denying the antecedent is when the second premise asserts that the antecedent of the first premise is NOT true Premise 1: If I study, then I’ll get a good grade. Premise 2: I didn’t study. Conclusion: (Therefore), I didn’t get a good grade.

  33. Conditional Syllogisms • Let’s practice…. Type? Valid or not? Premise 1: If it’s a robin, then it’s a bird Premise 2: It’s not a robin. Conclusion: (Therefore) it’s not a bird. NOT VALID! Denying the Antecedent

  34. Conditional Syllogisms • Let’s practice…. Type? Valid or not? Premise 1: If it’s a robin, then it’s a bird Premise 2: It’s not a bird. Conclusion: (Therefore) it’s not a robin. VALID! Denying the Consequent

  35. Conditional Syllogisms • Let’s practice…. Type? Valid or not? Premise 1: If it’s a robin, then it’s a bird Premise 2: It’s a bird. Conclusion: (Therefore) it’s a robin. NOT VALID! Affirming the Consequent

  36. Conditional Syllogisms • Let’s practice…. Type? Valid or not? Premise 1: If it’s a robin, then it’s a bird Premise 2: It’s a robin. Conclusion: (Therefore) it’s a bird. VALID! Affirming the Antecedent

  37. Errors in Reasoning • If people used logical rules in reasoning there would be no effect of the problem statement • As we’ll see, there is an effect of problem statement • Errors can tell us how people represent the problem and reason about it • One task that has been used to study errors in reasoning is the Wason four-card problem • Different versions lead to different patterns

  38. Coglab Note If you have not done this week’s Coglab, the Wason Selection Task, do it now!

  39. The Wason Four-Card Problem • Four cards • Number on one side • Letter on the other side • Test the following rule • If there’s a vowel on one side, then there’s an even number on the other side • The cache: Flip the minimum number of cards

  40. The Wason Four-Card Problem • Rule: If vowel, then even number • Which card would you flip first? • Are there any other cards you would need to flip in order to be completely sure? E K 4 7

  41. The Wason Four-Card Problem • Rule: If vowel, then even number • Flipping the E directly tests the rule • Even number consistent with the rule • Odd number violates the rule • In this version 53% picked E (correct) E K 4 7

  42. The Wason Four-Card Problem • Rule: If vowel, then even number • What about flipping the 4? • Vowel consistent with the rule • Consonant does not violate the rule • In this version 46% picked 4 (incorrect/suboptimal) E K 4 7

  43. The Wason Four-Card Problem • Rule: If vowel, then even number • What about flipping the 7? • Consonant consistent with the rule • Vowel violates the rule • In this version 4% picked 4 (correct) E K 4 7

  44. The Wason Four-Card Problem • The correct answer to the problem is that in order to be 100% certain that the rule is correct you would need to flip a minimum of 2 cards • E (affirmation of antecedent) • 7 (denial of the consequent) • Key to solution is the falsification principle • Falsification principle: to test a rule it is necessary to look for situations that falsify (violate) that rule • This version is called the abstract version

  45. The Wason Four-Card Problem

  46. Real-world Four-card Problems • If we change the way the problem is stated, people change their behavior • Griggs and Cox did a version with drinking age • Imagine you are a police officer applying the following rule: if a person is drinking beer, then he or she must be over 19 years old • Each card has an age on one side and a drink on the other

  47. Griggs and Cox (1982) • Rule: If drinking beer, must be over 19 years old • Which card would you flip first? • Are there any other cards you would need to flip in order to be completely sure? Beer Soda 24 16

  48. Griggs and Cox (1982) • Rule: If drinking beer, must be over 19 years old • Correct answers are Beer and 16 (no others) • This is much easier for people than the abstract version of the task (73% correct vs. 0% correct) Beer Soda 24 16

  49. Real-world Four-card Problems • The beer version of the problem was easier for people because it was more concrete • Or could it have been experience with the situation described by the problem? • There’s another version of the problem that was used to investigate this possibility • Problem described in terms of postal regulations • Great Britain has different regulations than the US

  50. 5d 4d Johnson-Laird and Coworkers (1972) • Rule: If a letter is sealed, must have 5d stamp • This rule was familiar to people in Great Britain • Original experiment done in Great Britain • Easier for British people than the abstract version of the task (81% correct vs. 15% correct) • Griggs and Cox (1982) tested Americans, found that this was just as difficult as abstract

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