PS2111 - Reasoning2024 Part II.pptx

PS2111 – REASONING II DR CAREN FROSCH Overview of Reasoning II Deductive reasoning  focus on conditional reasoning Valid & invalid inferences Mental model theory Influencing logical reasoning Role of prior knowledge Belief bias in reasoning Dual systems theories of thinking (Heuristic analytic theo...

PS2111 – REASONING II DR CAREN FROSCH Overview of Reasoning II Deductive reasoning  focus on conditional reasoning Valid & invalid inferences Mental model theory Influencing logical reasoning Role of prior knowledge Belief bias in reasoning Dual systems theories of thinking (Heuristic analytic theory) Intuitive & deliberative systems Feeling of rightness Conflict detection Processing speed Deductive reasoning Reasoning to a conclusion from a set of premises or statements where that conclusion follows necessarily from the assumption that the premises are true. Conclusion can be drawn with certainty Based on formal logic Try this task Logical reasoning Major Premise (conditional statement) If I attend all of my lectures then I will do well on my exam! Minor premise I attend all of my lectures What can you conclude? Logical reasoning Major Premise If I attend all of my lectures then I will do well on my exam! Minor premise I do not attend all of my lectures What can you conclude? A. I do well on my exam B. I do not do well on my exam C. I may or may not do well on my exam Logical reasoning Major Premise If I attend all of my lectures then I will do well on my exam! Minor premise I do well on my exam What can you conclude? A. I attended all of my lectures B. I did not attend all of my lectures C. I may or may not have attended all of my lectures Logical reasoning Major Premise If I attend all of my lectures then I will do well on my exam! Minor premise I do not do well on my exam What can you conclude? A. I attended all of my lectures B. I did not attend all of my lectures C. I may or may not have attended all of my lectures Conditional Reasoning ‘If p then q’ The ‘if p’ part is the antecedent (e.g., If I attend all of my lectures) The ‘then q’ part is the consequent (e.g., I will do well on my exam) Distinguish four inference depending on which part appears in minor premise ‘p’ – modus ponens (attend lectures) ‘not q’ – modus tollens Logically valid inferences (not do well on exam) ‘not-p’ – denial of the antecedent (not attend all lectures) Logically invalid ‘q’ – affirmation of the consequent inferences (do well on exam) IF I ATTEND ALL OF MY LECTURES THEN I WILL DO WELL ON MY EXAM! Valid inferences Modus Ponens (p): Attend all lectures Conclude: Do well on exam Modus Tollens (not-q): Not do well on exam Conclude: Did not attend lectures Invalid inferences Denial of the Antecedent (not-p): Do not attend all lectures Conclude: Do not do well on exam Affirmation of the Consequent (q): Do well on exam Conclude: attended lectures How do people reason with conditionals? Distinguish logical reasoning from everyday meaning, e.g., ‘If you mow my lawn then you will get £10’ means you will only get £10 if you mow my lawn, i.e. Implies the biconditional ‘If and only if...’ Reasoning tasks with abstract materials (e.g., If there is a circle then there is a triangle) most make valid modus ponens (MP) inference fewer make valid modus tollens (MT inference) Many make the invalid denial of the antecedent (DA) and affirmation of the consequent (AC) inferences Theories of reasoning Mental model theory (e.g., Johnson-Laird, 1983) Mental models represent possibilities given premise information Only true possibilities are represented (principle of truth) Alternative models are created to identify counterexamples but if no counterexamples found then conclusion is valid Limited WM capacity means that sometimes not all possible models created Mental Models If I attend all of my lectures then I will do well on my exam! attend lectures... not attend lectures not attend lectures do well do well not do well Mental Models & inferences If I attend all of my lectures then I will do well on my exam! attend lectures do well not attend lectures do well not attend lectures not do well Valid inferences require 1 model: Modus ponens: attend lectures do well Modus tollens: not do well not attend lectures Invalid inferences require 2 models: Denial of the antecedent: not attend lectures do well not attend lectures not do well Affirmation of the consequent: do well do well attend lectures not attend lectures Mental models: evaluation Strengths Predictions have been confirmed experimentally Predict participants’ responses to a rate of 95% accuracy (Khemlani & JohnsonLaird, 2012) Weaknesses Assume more deductive reasoning occurs than actually does Underspecification of the process involved in mental model formation Do not account for ambiguous reasoning problems Can we influence reasoning? Ruth Byrne Alternative & Additional premises: Simple: If she meets her friend then she will go to a play Further premises: Alternative: If she meets her family then she will go to a play Additional: If she has enough money then she will go to a play Byrne 1989 Exp 1 - results Hindere d Improve d Counterexamples Wim De Neys Conditionals differed in terms of number of alternatives or disablers that can be generated Similar to Byrne Alternative & Additional Conditionals with few/ many alternatives/disablers Working memory tested (De Neys et al., 2005) COUNTEREXAMPLES Inference acceptance affected by number of counterexamples High WM-capacity better at reasoning (De Neys et al., 2005) Apply conditional reasoning Wason’s selection task https://youtu.be/6I5n2aZNoUU Standard version: Four cards Each card has a letter on one side and a number on the other (in the video it’s a number & colour) A rule applies to the four cards The task is to select only those cards that would need to be turned over to decide whether or not the rule is correct Wason’s selection task Matching bias – select cards named in rule Logical solution in conflict with what makes sense in real life (Oaksford, 1997) E.g. ‘All swans are white’, too time consuming to seek all swans and nonwhite birds Probabilistic approach better Jonathan Evans Improving performance 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, while 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, then the other side includes ‘CHOLERA’ among the list inoculations. Which of the following forms would you have to turn over to check? (Cheng & Holyoak, 1985) A) 1 & 3 B) 1& 4 C) 2 & 4 D) 2 & 3 1 2 3 4 PRIOR KNOWLEDGE CAN IMPROVE REASONING PERFORMANCE ALSO SEE PART 2 OF VIDEO ON BB BUT IT CAN ALSO HINDER PERFORMANCE!  SEE NEXT LECTURE Summary Conditional reasoning Role of additional information & counterexamples Mental Model Theory Wason’s selection task References Eysenck, M.W. & Keane, M.T. (2020). Cognitive psychology: A student's handbook. (8th ed.) Abingdon: Routledge.(ch.14 pp. 672-690 & 701-711) Eysenck, M.W. & Keane, M.T. (2015). Cognitive psychology: A student's handbook. (7th ed.) Hove: Erlbaum. (ch.14 pp. 594 – 611 & 622 - 631)[old edition contains useful material] Byrne, R.M.J. (1989). Suppressing valid inferences with conditionals. Cognition, 31, 61-83. Cheng, P.W., & Holyoak, K.J. (1985). Pragmatic reasoning schemas. Cognitive Psychology, 17, 391-416. Newman, I.R., Gibb, M., & Thompson, V.A. (2017). Rule-based reasoning is fast and belief-based reasoning can be slow: Challenging current explanations of belief-bias and base-rate neglect. Journal of Experimental Psychology: Learning, Memory, & Cognition, 43, 1154 – 1170. [especially Experiment 2] References you can find in E&K Evans et al. 1993 De Neys et al. 2005 Oaksford 1997 Johnson-Laird, 1983 Khemlani & Johnson-Laird 2012 Kahneman 2003 Evans 2006 De Neys 2012 Thompson et al. 2011 Camerer & Hogarth 1999 Brase et al. 2006 Tversky & Kahneman 1983