Unit 2 - Deductive Reasoning PDF

UNIT 2 DEDUCTIVE REASONING Thought and Language María Vélez, PhD. Bachelor’s degree in Psychology Theoretical teaching programme Bibliography Minda, J. P. (2015). The psychology of thinking: reasoning, decision-making & problem-solving (2nd ed.). SAGE. Chapter 7: The Psychology of Thinking (pp. 144...

UNIT 2 DEDUCTIVE REASONING Thought and Language María Vélez, PhD. Bachelor’s degree in Psychology Theoretical teaching programme Bibliography Minda, J. P. (2015). The psychology of thinking: reasoning, decision-making & problem-solving (2nd ed.). SAGE. Chapter 7: The Psychology of Thinking (pp. 144 - 166). Eysenck, M. W., & Keane, M. T. (2020). Cognitive psychology (th ed.). Psychology Press. Chapter 14. Reasoning and hypothesis testing (pp. 666-690). 2 INDEX CONTENTS 1. 2. 3. 4. 5. Introduction. Propositional reasoning (Conditional). Syllogistic reasoning (Categorical). Paradigms to study deductive reasoning. Theories of deductive reasoning. 3 Dilema One of them, will tell always the truth. One of them, will always lie. One door leads to death. One door leads to live. You only have one question 4 1. Introduction Reasoning: a process that allows conclusions to be drawn from previously given premises or events. Inductive reasoning: ○ Forming generalizations (that may be probable but are not certain) from examples or sample phenomena. ○ Outcomes are probabilistic. ○ Specific to general. ○ To discover something new via thinking. Deductive reasoning: ○ Reasoning to a conclusion from a set of premises or statements, where that conclusion follows necessarily from the assumption the premises are true. ○ General to specific. ○ Verifying if something is true (It depends on the truth of premises). ○ For example, the conclusion Tom is taller than Harry is necessarily true if we assume Tom is taller than Dick and Dick is taller than Harry. 5 1. Introduction Deductive reasoning: ○ Owes their origins to formal logic. Field of philosophy: Abstract study of propositions or statements. It abstracts from the content of these elements, the structures or logical forms they embody. E.g., All cats are mammals → All A are B. Formal reasoning: logic // Informal reasoning: knowledge and experience. ○ Aims to test the validity of arguments based on premises and their conclusion, independently from the content. Syllogisms If Nancy is angry, then I am upset If it’s raining, then Nancy gets wet I am upset. It is raining. Therefore, Nancy is angry. Therefore, Nancy gets wet. Premises 1 and 2 Conclusion Invalid Valid 6 2. Propositional reasoning ○ Not semantic: It does not consider the content of propositions. It is abstract and universal. ○ Formal language (symbols or letters) vs. Natural language (sentences). Symbols (P, Q, R, S, T) represent propositions, and operators are applied to them (modifying the truth value of propositions). ○ Propositional logic does not admit any uncertainty about the truth of P (TRUE OR FALSE). P = It’s raining Q = Me using umbrella. If it rains (P), then I’ll use the umbrella (Q) [P → Q]. If it rains (P), then I’ll use the umbrella (Q) [P → Q]. It is raining (P is true). I will use the umbrella (So, Q is true). P = Antecedent Q = Consequent We do not assume that A causes B. It is an implication relationship. 7 2. Propositional reasoning In psychology, propositional language is more than a means, it is extremely useful for analyzing reasoning situations and formalizing from a logical to analyze reasoning situations and to formalize from logic the answers of the subjects. Can you think of a situation in therapy? The procedures for estimating validity is: 1. Tables of truth: to describe all the possible combinations of truth values. 2. DERIVATION: Algorithm or logical system that allows to infer or deduce a true statement from another one that is considered as validly true. Rule of “modus ponens” (MP) Affirming the consequent fallacy (ACF) Rule of “modus tollens” (MT) Denying the antecedent fallacy (DAF) ○ ○ Rules (MP and MT) allows us to infer a valid argument. Fallacies are reasoning errors when inferring and argument as valid when they are not. 8 2. Propositional reasoning: tables of truth P Q P Q R T T T T T T F T T F F T T F T F F T F F F T T F T F F Example: Tomorrow, I will eat rice (P) and (∧) melon (Q). P Q P∧Q T T T I will eat P and Q à True F T F F I will eat P but no Q à False F T F T F I will not eat P but Q à False F F F F F I will not eat P, nor Q à False 9 2. Propositional reasoning: tables of truth Example: The light can be ON (P) or (∨) OFF (Q). P Q P∨Q T T F à False T F T à True F T T à True F F F à False 10 2. Propositional reasoning: tables of truth The type of propositional reasoning that has received most attention from reasoning researchers has been conditional reasoning / implication [If…then…]. Example: If you understand this (P), ( → ) then you will pass the subject (Q). Conditional P Q P→Q T T T T F F F T T F F T The only condition established by the conditional is the impossibility of the antecedent being true and the consequent being false. If…then VS Only if… then. The fact that P is not present, does not mean the the implication If…then… is not valid anymore. In Only if arguments, P must be present for Q to be. P Q P⟷Q T T T T F F F T F F F T Example: ONLY IF you understand this (P), ( ⟷ ) then you will pass the subject (Q). Biconditional 11 2. Propositional reasoning: tables of truth How to describe all the possible combinations of truth values: TABLE OF TRUTH. Example: If it does not rain (P), then (→) I will go to the beach (Q). ¬P Q T T T F F T F F ¬P → Q 12 2. Propositional reasoning: tables of truth How to describe all the possible combinations of truth values: TABLE OF TRUTH. Example: If it does not rain (P), then (→) I will go to the beach (Q). ¬P Q ¬P → Q T T T T F F F T T F F T 13 2. Propositional reasoning The procedure for estimating validity is: 1. Tables of truth: to describe all the possible combinations of truth values. 2. DERIVATION: Algorithm or logical system that allows to infer or deduce a true statement from another one that is considered as validly true. Rule of “modus ponens” (MP) Affirming the consequent fallacy (ACF) Rule of “modus tollens” (MT) Denying the antecedent fallacy (DAF) ○ ○ Rules (MP and MT) allows us to infer a valid argument. Fallacies are reasoning errors when inferring and argument as valid when they are not. 14 2. 1. Conditional reasoning Example: If the dog is alone (P), ( → ) he will bark (Q). I know my dog is alone. Will the dog bark? Modus Ponens: affirming the antecedent P Q P→Q T T T YES, VALID DEDUCTION T F F We keep the truth of the argument. F T T F F T We know that the dog is alone. The conclusion logically follows from the two premises. 97% judge correctly. 15 2. 1. Conditional reasoning Example: If I study enough (P), I will pass (Q). I didn’t pass. Does it mean I didn’t study enough? Modus Tollens: denying the consequent P Q P→Q T T T T F F We keep the truth of the argument. F T T I didn’t have a good grade. F F T Yes, VALID DEDUCTION More difficult to understand: It runs counter to the confirmatory bias. 60% judge correctly. 16 2. 1. Conditional reasoning Example: If people do not want to study (P), ( → ) then they do politics (Q). Marcos is doing politics. What conclusion we can draw from Marcos doing politics? Didn’t he want to study? P Affirming the consequent fallacy → → Q P→Q T T T T F F F T T F F T 40% judge correctly. If we accept the truth of consequent, and the truth of the conditional, we cannot conclude that the argument/conclusion is valid. NOT VALID We keep the truth of the argument. We accept the truth of the consequent. 17 2. 1. Conditional reasoning Example: If I live in Murcia (P), ( → ) then I live in Spain(Q). I live in Spain. What conclusion we can draw from that? Do I live in Murcia? NOT VALID In Spain, you can live in many different cities other than Murcia. P Q P→Q Affirming the consequent fallacy T T T T F F F T T F F T 40% judge correctly. We keep the truth of the argument. We accept the truth of the consequent. 18 2. 1. Conditional reasoning Example: If I am helpful (P), then people will love me (Q). I wasn’t helpful. Therefore, people won’t love me? Denying the antecedent fallacy DAF→ P Q P→Q T T T We deny the truth of the antecedent (no helpful). T F F We keep the truth of the argument. F T T F F T 40% judge correctly. NOT VALID From the truth of conditional, and the falsity of the antecedent, we cannot conclude the falsity of the consequent. 19 2. 1. Conditional reasoning Example: If I live in Murcia (P), then I live in Spain (Q). I don’t live in Murcia. Therefore, I don’t live in Spain? Denying the antecedent fallacy DAF→ P Q P→Q T T T We deny the truth of the antecedent (no helpful). T F F We keep the truth of the argument. F T T F F T 40% judge correctly. NOT VALID From the truth of conditional, and the falsity of the antecedent, we cannot conclude the false of the consequent. 20 2. 1. Conditional reasoning P = Rain // Q = Going to cinema Argument (Premises) Conclusion Formal denomination Example If P, then Q P Then, Q Modus Ponens (MP) “It’s raining, then I’ll go to the cinema” Valid. If P, then Q No P Then, no Q Denying antecedent fallacy (DAF) “It’s not raining, then I’ll go to the cinema” (fallacy reasoning). If P, then Q Q Then, P Affirming the consequent fallacy (ACF) “I’ll go to the cinema, then it’s raining” (fallacy reasoning). If P, then Q no Q Then, no P Modus Tollens (MT) “I won’t go to the cinema, then it’s not raining” Valid. 21 2. 1. Conditional reasoning Antecedent Consequent Affirm Modus Ponens Fallacy Deny Fallacy Modus Tollens 22 2. 1. Conditional reasoning VALID DEDUCTION Modus ponens – Affirming the antecedent If I behave aggressively (P), then people will be angry with P Q P→Q T T T T F F F T T F F T me (Q). I behaved aggressively. Therefore, are people angry with me? 23 2. 1. Conditional reasoning INVALID DEDUCTION Denying the antecedent fallacy P Q P→Q T T T T F F F T T F F T If people call me (P), ( → ) then they like me (Q). They didn’t call me. Do they don’t like me? 24 2. 1. Conditional reasoning VALID DEDUCTION Modus tollens – denying the consequent P Q P→Q T T T T F F F T T F F T If I am bad person (P), ( → ) then I will harm people (Q). I didn’t harm people. Therefore, am I not bad? 25 2. 1. Conditional reasoning INVALID DEDUCTION Affirming the consequent fallacy If s/he is flirting with another person(P), ( → ) then I will be suspicious (Q). I am suspicious. Therefore, is s/he flirting with another person? P Q P→Q T T T T F F F T T F F T 26 2. Propositional reasoning People misstate premises, omit premises, and generally fall prey to cognitive biases. Reject valid conclusions / State invalid conclusions. Belief bias: tendency to assume that deductions we believe, or are more believable, are valid. Those that do not seem believable are less likely to be valid. Confirmation bias: tendency to search evidence that confirms our beliefs or that downplay information inconsistent with your belief. These bias are the result of not treating them as logical tasks. They focus on semantics, rather than the argument. Fundamental paradox of rationality (Johnson-Laird, 1999): Rationality should be a necessary condition for correct decision-making and a hallmark of formal, mature thinking, and yet it does not seem to be necessary at all (for basic decisions). In everyday situations or elementary decisions, other factors such as intuition, emotions, or less formal processes may significantly influence outcomes. 27 2. Propositional reasoning Relevant in Psychology: How we formulate the arguments, or make statements, influences the conclusion. The Wason four-card problem. By following logical reasoning, distorted ideas can be dismantled. Broadly speaking, the main idea of all experimental research in propositional/syllogism psychology is to determine to what extent: "Variations in the nature of arguments affect the ability to detect (or generate) deductively correct conclusions” (Rips, 1994). 28 Dilema One of them, will tell always the truth. One of them, will always lie. One door leads to death. One door leads to live. You only have one question Will he tell me if this door is the one that leads to live? Will he tell me if this door is the one that leads to life? If RED says the truth, then BLUE is the liar. If BLUE sayssays RED=LIVE, then it would lie. If RED the truth, then BLUE be is aaliar. If BLUE would say YES leads to life), it would be a lie. Therefore, RED(RED does not lead to live. Therefore, RED does not lead to life. BLUE = Live, = Death BLUE= Life.RED RED= Death. If RED is a liar, then BLUE says the truth. REDsays lies, RED=LIVE, then BLUEthen saysitthe truth.be a lie. IfIfBLUE would It is a lie that BLUE would say YES (RED to life). Therefore, BLUE does not leadleads to live. Therefore, BLUE would say that BLUE leads to life. BLUE = Live, REDDeath. = Death BLUE= Life. RED= 29 Deductive reasoning excercises Click on the icon to play the games. 30 3. Syllogistic reasoning Based on formal logic as well. Logical systems of syllogistic inference are characterized by their prescriptive character (indicating "what to do/conclude") and tell us when we can deduce a conclusion from the information contained in the premises. Conditional (propositional) – connective propositions. Categorical (syllogisms) – categories within propositions. Premise 1: All McDonald’s coffee (A) is hot (B). AB Premise 2: This coffee is from McDonald’s (A) Conclusion: This coffee is hot (B). 31 3. Syllogistic reasoning Structure of categorical syllogisms All McDonald’s coffees are hot. Major premise This coffee is from McDonald’s Minor premise This coffee is hot. Conclusion Statement of facts about something. We used them to make precise conclusions. In a deductive statement, they are considered true. Facts: Descriptions, statements and predicates of premises. Operators: Add meaning to premises (OR, AND, NOT, IF, ALL, SOME, NONE, etc.) Valid argument: the conclusion is the only possible conclusion given the premises. If these true premises allow for alternative conclusions, then the deduction is not valid. Sound argument: valid argument/conclusion (the only possible) and true premises. If it is not a sound deduction, we cannot trust the conclusions. E.g., if we have evidence that not all McDonald’s coffee is hot, the conclusion (The coffee is hot) can still be valid, but it is not a sound deduction. So, we may not trust the conclusions. There might be valid, but unsound. 32 3. 1. Syllogistic reasoning: Categorical reasoning Classical reasoning: when we make conclusions on the basis of category membership. Major premise: Statement about the category. Minor premise: Offers specific information. Major premise: All men (A) are mortal (B). [A] Minor premise: Socrates is a man (A). [A] Conclusion: Therefore, Socrates is mortal (B). Different varieties of formal classical syllogisms, according to quality and quantity: UNIVERSAL PARTICULAR Affirmative All A are B [A] Some A are B [I] Negative No A is B [E] Some A are not B [O] 33 3. 1. Syllogistic reasoning: Categorical reasoning. Classification of categorical syllogisms UNIVERSAL PARTICULAR Affirmative All A are B [A] Some A are B [I] Negative No A is B [E] Some A are not B [O] Figure: Figure 1 M–T t-M t-T Figure 2 T -M t–M t–T Figure 3 M–T M-t t-T Figure 4 T–M M–t t-T Type: AAA Figure 1 Major premise: All men (A) are mortal (B). [A] M-T Minor premise: Socrates is a man (A). [A] t-M Conclusion: Therefore, Socrates is mortal (B). [A] t-T Medium term (M) / Major term (T) / Minor Term (t) Medium term (M): Term that appears in both premises but not in the conclusion. Link between major and minor terms. Major term (T): Predicate of the conclusion. Minor Term (t): Subject of the conclusion. 34 3. 1. Syllogistic reasoning: Categorical reasoning. Classification of categorical syllogisms UNIVERSAL PARTICULAR Affirmative All A are B [A] Some A are B [I] Negative No A is B [E] Some A are not B [O] Figure: Figure 1 M–T t-M t-T Figure 2 T -M t–M t–T Figure 3 M–T M-t t-T Type: AAA Figure 4 T–M M–t t-T Figure 1 Major premise: All men (A) are mortal (B). [A] M-T Minor premise: Socrates is a man (A). [A] t-M Conclusion: Therefore, Socrates is mortal (B). [A] t-T Medium term (M) / Major term (T) / Minor Term (t) There are 256 possible combinations (A, E, I, O; 1, 2, 3, 4), BUT just 24 combinations produce valid conclusions. Figure 1 Figure 2 Figure 3 Figure 4 AAA AEE AAI AII AAI AEO AII AEE AII AOO EAI AEO EAE EAE EIO EAO EAO EAO IAI EIO EIO EIO OAO IAI 35 3. 1. Syllogistic reasoning: Categorical reasoning. Universal affirmative Statement in which the relationship between the two categories is universal for all the members, as stated. “All A are B”. B AB A Reflexive Hierarchical 36 3. 1. Syllogistic reasoning: Categorical reasoning. Particular affirmative Statement in which some members of one category can also be members of another category. “SOME A are B”. In formal logic (not everyday usage), Some = at least 1, and possibly all (’Some cats –A- are friendly -B-’ it’s also true if all cats are friendly). B AB A B A B A 37 3. 1. Syllogistic reasoning: Categorical reasoning. Universal negative Statement in which there is a relationship between two concepts for which there is absolutely no overlap. “NO A are B”. (No cats are dogs). A B 38 3. 1. Syllogistic reasoning: Categorical reasoning. Particular negative Statement in which some members of one category are not members or another category. “SOME A are NOT B”. (Some cats –A- are not friendly –B-). Some = at least 1, possibly all. A B B A B A 39 3. 1. Syllogistic reasoning: Categorical reasoning. Context errors in categorical reasoning People often make errors because of the ambiguity and complexity of these relationships. Many of the errors are made as a result of conflating personal beliefs and knowledge with the notion of logical validity. Syllogistic reasoning performance is better if the conclusions are believable. Worse – unbelievable (Figure; Klauer et al., 2000). Using these circles (Euler circles) help avoiding making errors: If there is more than one configuration that allows premises to be true, but that lead to different conclusions, then it is not a valid deduction. 40 3. 1. Syllogistic reasoning: Categorical reasoning. Context errors in categorical reasoning All doctors are professional people. Some professional people are rich. Therefore, some doctors are rich. Rich Doctors INVALID ARGUMENT Belief bias (We know that some doctors are rich, but from the logical perspective, this might not be true) Prof Professionals Rich Reflexive Rich Doc Hierarchical 41 3. 1. Syllogistic reasoning: Categorical reasoning. Context errors in categorical reasoning All frogs are mammals. No cats are mammals. Therefore, no cats are frogs. VALID ARGUMENT, BUT UNSOUND. The conclusion direct follows from the premises, but it is unacceptable because the premises are false. Cats Cats Frogs Frogs / Mammals Mammals 42 3. 1. Syllogistic reasoning: Categorical reasoning. Context errors in categorical reasoning All cats are mammals. No mammals are birds. Therefore, no cats are birds. VALID ARGUMENT, AND SOUND. Birds Birds Cats The conclusion direct follows from the premises, and the premises are true. Cats / Mammals Mammals 43 Propositional VS Syllogistic reasoning Propositional Syllogistic Unit of analysis Involves propositions or statements that can be true or false. Involves categorical statements and relationships between categories. Logical Connectiveness Utilizes logical connectives (AND, OR, NOT) to form compound propositions. Typically involves categorical statements using terms like "all," "some," or "none." Focus on generality Emphasizes logical relationships between general statements. Focuses on deriving specific conclusions from more general premises. 44 4. Paradigms to study deductive reasoning. In Psychology, the aim of studying syllogisms is to determine in what extent variations in the premises affect the ability to detect or generate correct deductive conclusions (Rips, 1994). For this purpose, there are several types of paradigms to study syllogisms: Classic paradigms: Verification or evaluation paradigm. Selection paradigm. Production or elaboration paradigm. Experimental paradigms: Euler circles: to test the comprehension of premises. Paradigm: a set of assumptions, attitudes, concepts, values, procedures, and techniques that constitutes a generally accepted theoretical framework within, or a general perspective of, a discipline. Venn’s diagrams. Contextualized syllogisms. 45 4. Paradigms to study deductive reasoning. Classic paradigms: Verification or evaluation Verification or evaluation paradigms: Subjects are displayed completed syllogisms for them to determine if they are valid or not. Some actors are singers Some actors are not artists [I] [O] Therefore, some artists are not singers [O] VALID [ ] INVALID [ X ] 46 4. Paradigms to study deductive reasoning. Classic paradigms: Verification or evaluation Selection paradigms: Subjects are displayed premises and several conclusions for them to select the valid one. Therefore, 1. 2. 3. 4. 5. All dancers are lawyers [A] All dancers are singers [A] All lawyers are singers Some singers are lawyers No lawyers are singers Some lawyers are not singers None of the above 47 4. Paradigms to study deductive reasoning. Classic paradigms: Verification or evaluation Construction or production paradigms: Subjects have to generate the conclusion. Therefore, All psychologists are crazy people [A] No crazy people are happy people [E] No happy people are psychologists [E] …………………………………….. Some happy people are not psychologists [O] 48 4. Paradigms to study deductive reasoning. Experimental paradigms Euler’s circles and Venn’s diagrams: diagrammatic way to represent sets and their relationships. Contextualized diagrams: propositions are presented in a narrative way. 49 4. Paradigms to study deductive reasoning. Card Selection task Most-well known reasoning tasks in the psychological literature. They assess people’s ability to evaluate evidence and arrive at deductions. In previous examples, subjects had to say if conclusions were valid or not. In this type of task, individuals have to arrive at a conclusion based on the deduction, considering a set of rules. The rules refer to symbols, letters, numbers or facts presented in cards. To determine the validity, they select the card that should be investigated. Ecological validity = like everyday thinking. If you are given a series of facts, how do you go about verifying whether those facts are true? Wason selection task: hypothesis testing using a conditional rule. 50 4. Paradigms to study deductive reasoning. “If there is an R on one side of the card, then there is a 2 on the other side of the card” Select only those cards needing to be turned over to the decide if the rule is valid or not. What would be your solution? 51 4. Paradigms to study deductive reasoning. “If a person drinks alcohol, they must be over 18” Select only those cards needing to be turned over to the decide if the rule is valid or not. 21 Beer Coke 17 What would be your solution? 52 4. Paradigms to study deductive reasoning. Wason selection cards “If there is an R on one side of the card, then there is a 2 on the other side of the card” Select only those cards needing to be turned over to the decide if the rule is valid or not. What would be your solution? 53 4. Paradigms to study deductive reasoning. Wason selection cards Selecting the R first = affirming the antecedent [Modus Ponens] (If there is an R on one side”. You see if the rule is true with that card. Then, selecting 2 = affirming the consequent. Confirmation bias = looking for evidence to confirm the statement. Selecting 7 = Denying the consequent [Modus Tollens]. It would definitely disprove the rule if it had an R on the other side. Selecting G = Denying the antecedent. Fallacy 54 4. Paradigms to study deductive reasoning. Wason selection cards Findings: People committed Matching bias = tendency to select cards matching items mentioned in the rule (R and 2). Confirmation bias. It is less demanding. Denying the antecedent is to consider a premise that is not explicitly stated à working memory resources. The confirmation bias may be related to the notion of entrenchment. Culturally and linguistically set to think in terms of describing something that is. According to logic, we should test statements by searching contrary evidence. Choose confirmatory evidence. Penguins are black and white – Search penguins that are not black and white. Instead, we assume probabilistic approaches. The probabilities of different kinds of events or objects. 55 4. Paradigms to study deductive reasoning. Wason selection cards Findings: Influence of motivation: People are more likely to select the potentially falsifying cards if motivated to disprove the rule. Deontic rules: rules related to obligation and permission. Marrero et al., 2016: Individuals concerned about potential costs focus on disconfirming evidence, whereas those concerned about potential benefits focus on confirming evidence. DEONTIC SELECTION TASKS: When thinking about permission, it is easier to think about what you can do and what you cannot do. Cards have ages and beverages on either side. “If a person drinks alcohol, they must be over 18”. 21 Beer Coke 17 Permission schema: reduce the number of options and makes it easier to consider what violates the rule. 56 5. Theories of deductive reasoning Dualprocess approach Mental model Traditional More recent and popular 57 5. Theories of deductive reasoning Johnson-Laird’s mental model theory Reasoning involves constructing mental models. An iconic representation of a possibility that depicts only those clauses in a compound assertion that are true. “A or B, but not both” à possibly A and possibly B Premises: The lamp is on the right of the pad. The book is on the left of the pad. The clock is below the book. The vase is below the lamp. Conclusion: The clock is to the left of the vase. Where is the clock with respect of the vase? 58 5. Theories of deductive reasoning Johnson-Laird’s mental model theory Assumptions: 1. A mental model describing the given situation is constructed and the conclusions that follow are generated. 2. An attempt is made to construct alternative models to falsify the conclusion by finding counterexamples to the conclusion. If a counterexample model is not found, the conclusion is deemed valid. 3. The construction of mental models involves the limited resources of working memory. 4. The principle of truth: “Mental models represent what is true, but not what is false” (Khemlani & Johnson-Laird, 2017, p. 16). Reasoning problems requiring the construction of several mental models are harder than those requiring only one mental model because the former impose greater demands on working memory. This minimizes demands on working memory. This can be counteracted by giving them explicit instructions. 59 5. Theories of deductive reasoning Johnson-Laird’s mental model theory Evidence: Kehmlani and Johnson-Laird (2017): They reviewed 20 studies testing the principle of truth, and how how illusory inferences were produced. People make illusory inferences because they ignore what is false. The mental model theory was best at predicting participants’ responses with a 95% success rate (Kehmlani and Johnson-Laird, 2012). 60 5. Theories of deductive reasoning Johnson-Laird’s mental model theory Evidence: 3 tion p m Assu 4 tion p m Assu Copeland and Radvansky (2004): Permitting additional mental models reduced successful reasoning. There’s a moderate correlation (+.42) between working memory capacity and syllogistic reasoning. Bell and Johnson-Laird (1998): People respond faster to possibility questions when the correct answer is “Yes” rather than “No”. People respond faster to necessity questions when the answer is “No” rather than “Yes”. 61 5. Theories of deductive reasoning Johnson-Laird’s mental model theory Strenghts: Accounts for reasoning performance across a wide range of problems. Many errors on deductive reasoning tasks occur because of the principle of truth. Reasoning may involve similar processes to normal comprehension. Limitations: People engage in deductive reasoning less than assumed. Processes involved in forming mental models are underspecified. Tends to ignore individual differences (Ford, 1995). People sometimes make no systematic attempt at falsification / counterexamples (Copeland & Radvansky, 2004; Newstead et al., 1999). 62 5. Theories of deductive reasoning Heuristic-Analytical Theory / Dual-process theories Evans and Stanovich (2013): Distinction between Type 1 and Type 2 systems: Type 1 – Autonomy: Mandatory or necessary when the appropriate triggering stimuli are encountered. Lack of involvement of working memory (independent of cognitive ability). Type 2: Correlated with cognitive ability. Its use reduce belief bias. The believability of the conclusion interfere with logic-based responses, but the reverse should not be the case. 63 5. Theories of deductive reasoning Heuristic-Analytical Theory / Dual-process theories Human reasoning (and hypothetical thinking) is based on: Evidence Belief bias reduced when: Instructions emphasize logical reasoning over heuristics (Evans, 2000). Time is strictly limited, reducing the chances of using analytic processes (Evans & Curtis-Holmes, 2005). Higher WM capacity holds no benefit for heuristic reasoning (De Neys, 2006). Dual-process theory provides a better overall fit to conditional reasoning data (Oberauer, 2006). Singularity principle: Only a single mental model is considered at any given time. Relevance principle: The most relevant mental model based on prior knowledge and current context is considered. Satisficing principle: The current mental model is evaluated by the analytic system and accepted if adequate. 64 5. Theories of deductive reasoning Dual-process theories Strenghts: Wide applicability within cognitive research. Evidence for reasoning being based on singularity, relevance, and satisficing principles. Doesn’t over-emphasize deductive reasoning. Advance understanding of meta-reasoning processes. Evidence for distinguishing between heuristic and analytical processes is strong. Accounts for some individual differences based on the extent to which they use analytic processes. 65 5. Theories of deductive reasoning Dual-process theories Three models of how systems 1 and 2 mights combine (De Neys, 2012): a) Serial processing with intuitive (1) processing being followed by deliberate (2) (not necessarily). b) Parallel model: intuitive and deliberate processing are both involved from the outset. a) c) Wasteful of cognitive resources. Logical intuition model: deliberate processing (2) is triggered if there is a conflict between initial intuitive heuristic and intuitive logical response in parallel (two types of intuitive reasoning). a) Type 2 resolves the conflict. 66 5. Theories of deductive reasoning Dual-process theories Findings: Syllogistic tasks involving conflict between logical validity and believability of the conclusions (De Neys et al., 2010). 52% of accuracy – belief bias. Greater physiological arousal on conflict trials – some logical processing might be intuitive. “Logical intuition model” – Trippas et al., 2016. Sentences following logically from preceding sentences were rated more likeable than those that did not. Implicit sensitivity to logical structure involving Type 1 processes. 82 5. Theories of deductive reasoning Dual-process theories Findings: Syllogistic tasks involving conflict between logical validity and believability of the conclusions (Bago and De Neys, 2017). Two responses: fast, intuitive; slow and deliberate. Participants performed a secondary demanding task at the same time to reduce engagement in Type 2 analytic processing. 49% of fast responses were logically correct. Same task (Newman et al., 2017: Fast responses were often logically correct, and slow responses were often incorrect and exhibit belief bias. 83 5. Theories of deductive reasoning Dual-process theories If a child is happy, then it cries; Suppose a child laughs; does it follow that the child is happy? Findings: Thompson et al., 2018. Individual cognitive differences. Reasoning problems involving a conflict between belief and logic. More intelligent individuals generate logic-based responses faster than belief-ones. Less intelligent individuals generate belief-based response faster. 84 5. Theories of deductive reasoning Dual-process theories What cause Type 2 processing? Traditional series model: Type 2 monitor the output and intervene in case of conflict. Parallel model: Type 2 reasoning is triggered when conflict monitoring leads to conflict detection. Logical intuition model. Ackerman and Thompson (2017): Meta-reasoning: process that monitor the progress of reasoning and problem-solving activities, and regulate the time and effort devoted to them. This meta-reasoning assess the probability of success. Feeling of rightness: The degree to which the first solution that comes to mind feels right. Type 2 intervenes when the feeling of rightness is weak. Feeling of rightness is determined based on the familiarity of content. Higher when familiar content. Feeling of error. 85 5. Theories of deductive reasoning Dual-process theories Limitations of the model: Processes are individually based: they vary depending on their abilities and preferences, their motivation, and their task requirements. Isn’t clear what the analytic processes are or how people decide which to use. Difficult for researchers to test the dual-process theories. Fails to lay out how the heuristic and analytic processes interact. A rapid increase in the findings that require to be explained theoretically, but theories have not kept pace in this increase. Meta-reasoning. No theorists have integrated it into a comprehensive dual-process theory of reasoning. 86 María Vélez, PhD [email protected] UCAM Universidad Católica de Murcia © © UCAM UCAM