Reasoning.

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Presentation transcript:

Reasoning

2 Types of Reasoning Deduction Induction 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:" Some parents are drivers 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 False

Conditional Reasoning: Prescriptive Rules Propositional Logic Modus Ponens If A, then B A Therefore B Modus Tollens Not B Therefore not A

Conditional Reasoning: the Wason Selection Task Subject is shown 4 cards: E F 4 7 Each card has a letter on one side, a number on the other. Hypothesis: "If a card has a vowel on one side, it has an even number on the other." Task: Choose the cards you should turn over to test this hypothesis 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?