Transcript Reasoning
Reasoning 2 Types of Reasoning • Deduction – Deductive arguments: If the premises are true (and the argument's form is valid) then the conclusion must be true. • Induction – Inductive arguments: The premises support the conclusion, but do not guarantee that it is true. Deduction • Syllogisms • Conditional Reasoning Categorical Syllogisms • Major premise, minor premise, conclusion • Can be represented with Venn diagrams (all, some, none) • Aristotle: Prescriptions for reasoning correctly with syllogisms • Empirical observations: Descriptions of actual reasoning with syllogisms Reasoning with Syllogisms • "Atmosphere effect" – "Some parents are scientists; All scientists are drivers, therefore:" 1. Some parents are drivers 2. Some drivers are parents – Both conclusions are valid, but the first is more likely to be drawn. – One explanation: Johnson-Laird & Steedman (1979) model of syllogistic reasoning; checking validity of arguments is done by checking for a "path" from premises to conclusion. Reasoning with Syllogisms • High-imagery and high-relatedness syllogisms are solved more accurately than more abstract syllogisms (Cement & Falmagne, 1986) – High relatedness: Some politicians are lawyers. – Low relatedness: Some politicians are farmers. Conditional Reasoning (If-Then) Prescription: Truth Tables A (It rained today) B (The sidewalk is wet) If A then B (If it rained today then the sidewalk is wet) True True True True False False False True True False False True Conditional Reasoning: Prescriptive Rules • Propositional Logic • Modus Ponens – If A, then B – A – Therefore B • Modus Tollens – If A, then B – Not B – Therefore not A Conditional Reasoning: the Wason Selection Task o Subject is shown 4 cards: E F 4 7 o Each card has a letter on one side, a number on the other. o Hypothesis: "If a card has a vowel on one side, it has an even number on the other." o Task: Choose the cards you should turn over to test this hypothesis o Which cards would you turn over? Click here for the correct answer and a frequent error. Hypothesis Testing and the Confirmation Bias (Wason, 1960) • “2, 4, 6” – What is the rule? • Generate lists of 3 numbers to test your rule. • Subjects hypothesised the rule "ascending by 2" and generated test lists that fit the rule to test it. • The actual rule was "any ascending sequence"; so 2, 4, 5 would fit the rule also, but subjects never tried this. • The tendency to construct tests consistent with our hypotheses is the confirmation bias. Inductive Reasoning • Estimating probabilities -- because inductive reasoning involves having evidence that supports but does not prove a conclusion, correct inductive reasoning is a matter of correctly estimating the probability that the conclusion is true based on the available evidence. • Bayes' Theorum – a prescriptive rule Deviations from Correct Bayesian Reasoning • Neglecting Base Rates • Under-estimating the importance of new evidence Why do we make these mistakes? • Heuristics – mental shortcuts – Availability – Adjustment and Anchoring – Representativeness • Why do we use heuristics?