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 • Using those definitions we’ve already seen many examples of reasoning – can you think of some?

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

Deductive Reasoning

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.

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

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

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!

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!

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!

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!

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!

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!

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

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

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

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

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!

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

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!

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!

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.

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

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

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.

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.

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.

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.

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.

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.

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.

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.

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

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

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

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

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

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

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

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

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

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

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

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

The Wason Four-Card Problem

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

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

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

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

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

Memory and Cognition