Exam 4 Deductive Reasoning

Exam 4 Deductive Reasoning - Deductive Reasoning Reasoning...

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Unformatted text preview: Deductive Reasoning Reasoning • The process of drawing conclusions • The cognitive processes by which people start with information and come to conclusions that go beyond that information • Two types: – Deductive reasoning – Inductive reasoning Deductive Reasoning A solution must absolutely be correct if it follows and agrees with the given premises • Involves syllogisms in which a conclusion logically follows from premises General to specific: Given premises, conclusion MUST follow Deductive Reasoning • What kinds of errors do people make in reasoning? – Syllogisms – Conditional reasoning 1 Deductive Reasoning Syllogisms • A series of three statements: Two premises followed by a conclusion – Categorical syllogism • Premise 1: All birds are animals. • Premise 2: All animals eat food. • Conclusion: All birds eat food. – Is this a valid conclusion? Syllogisms • Validity vs. truth – Premise 1: All birds are animals. – Premise 2: All animals have four legs. – Conclusion: All birds have four legs. – Is this a valid conclusion? • Belief-bias effect Syllogisms • Validity vs. truth validity-logical conclusion that is valid Truth-something that we actual see in our lives Can be valid conclusion but is not true based on our knowledge of the world Using rules of logic this would be valid but based on our knowledge it is not true. Belief-bias effect-making an incorrect conclusion when people reason according to their beliefs instead of relying on the rules of logic. This is a valid conclusion! but most people would say it is not because they rely on beliefs and knowledge that birds don’t have 4 legs Could be true but doesn’t have to be true. Because there is another conclusion it is not valid. – Premise 1: All of the students are tired. – Premise 2: Some tired people are irritable. – Conclusion: Some of the students are irritable. – Is this a valid conclusion? 2 Deductive Reasoning Why syllogism is not valid Syllogisms • Conditional syllogism – The first premise has the form “If…then…” – “If p, then q” • Syllogism 1: Affirming the antecedent • Syllogism 2: Denying the consequent • Syllogism 3: Affirming the consequent • Syllogism 4: Denying the antecedent (antecedent is p, consequent is q) Premise 1: if P, then Q “If I am a senior, then I have to register for classes today” Syllogism Premise 2 Conclusion Is It Valid? Judged Correctly? Affirming the antecedent I am a senior I have to register today Yes 97% Denying the consequent I do not have to register today I am not a senior Yes Antecedent-part after if (I am a senior) Consequent-part after then(I have to register today) Affirming antecedent or denying consequent always lead to valid conclusion(deductively valid) 60% Affirming the consequent I have to register today I am a senior No 40% Denying the antecedent I am not a senior I do not have to register today No 40% Affirming consequent or denying antecedentnot valid because it didn’t say only seniors register today, so juniors could meaning there is another conclusion 3 Deductive Reasoning Conditional Reasoning • Stating problems in real-world terms – “logic” problems – Wason four-card problem Logic Problems Given scenario and asked which of the choices is the solution • Example: – A farmer plants only five different kinds of vegetables -- beans, corn, kale, peas, and squash. Every year the farmer plants exactly three kinds of vegetables according to the following restrictions: Logic Problems • Example: – If the farmer plants corn, the farmer also plants beans that year – If the farmer plants kale one year, the farmer does not plant it the other year – In any year, the farmer plants no more than one of the vegetables the farmer planted in the other year 4 Deductive Reasoning Logic Problems C – Which of the following is a possible sequence for the farmer to plant in 2 successive years? a. b. c. d. e. Beans, corn, kale; corn, peas, squash Beans, corn, peas; beans, corn, squash Beans, peas, squash; beans, corn, kale Corn, peas, squash; beans, kale, peas Kale, peas, squash; beans, corn, kale Wason Four-Card Problem • Each card has a letter on one side and a number on the other side. Which cards would you need to turn over to test the following rule: If there is a vowel on one side, then there is an even number on the other side. Wason Four-Card Problem (Wason, 1968) • Results: 89% 16% 62% 25% – ___ correctly turned over the E • (affirm antecedent) – ___ incorrectly turned over the K • (deny antecedent) – ___ incorrectly turned over the 4 • (affirm consequent) – ___ correctly turned over the 7 • (deny consequent) 5 Deductive Reasoning Griggs & Cox (1982) • Each card has a person’s age on one side, and the beverage they are drinking on the other side • Given this rule: If a person is drinking beer, then the person must be over 19 BEER COKE 22 Beer- affirming antecedent make sure the person is over 21 Coke-denying antecedent, you can drink coke at any age 22-affirming consequent you can drink anything 16-denying consequent make sure they are not drinking beer 16 Griggs & Cox (1982) Beer and 16 • Results – 73% correctly turned over ____ and ____ • Conclusion – Reasoning about familiar problems is easier The role of “permissions” • Pragmatic reasoning schemas Have to look at do they have permission? Focuses attention on card that violates conditions and increases reasoning – A way of thinking about cause and effect in the world that is learned as part of experiencing everyday life • Example: permission schema (if you are 19 or older, then you get to drink beer) • Changes the goal of the reasoning task to look for violators 6 Deductive Reasoning Cheng & Holyoak (1985) • Tested involvement of permission schema in reasoning about the W ason card problem Cheng & Holyoak (1985) does not activate permission shemas • Group 1 read these directions: You are an immigration officer at the International Airport in Manila, capital of the Philippines. Among the documents you have to check is a sheet called Form H. One side of this form indicates whether the passenger is entering the country or in transit, and the other side of the form lists names of tropical diseases. You have to make sure that if the form says “Entering” on one side, the other side includes cholera among the list of diseases. Which of the following forms would you have to turn over to check? Indicate only those that you need to check to be sure. Cheng & Holyoak (1985) • Group 2 read these directions: You are an immigration officer at the International Airport in Manila, capital of the Philippines. Among the documents you have to check is a sheet called Form H. One side of this form indicates whether the passenger is entering the country or in transit, and the other side of the form lists inoculations the travelers had received in the past 6 months. You have to make sure that if the form says “Entering” on one side, the other side includes cholera among the list of diseases. This is to ensure that entering passengers are protected against the disease. W hich of the following forms would you have to turn over to check? Indicate only those that you need to check to be sure. Only changes are in green, added details that activates permission shemas. Are they allowed to enter country based on the inoculations that they had 7 Deductive Reasoning Cheng & Holyoak (1985) 62% 91% • Results – Group 1: ___ chose the correct cards (“Entering” and “Typhoid, Hepatitis”) – Group 2: ___ chose the correct cards • Performance was better when permissions were implied by the instructions Conclusions • The context within which conditional reasoning occurs is important – Familiar situations can often generate better reasoning than abstract statements, but not always 8 ...
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