1 / 13

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

peony
Download Presentation

Reasoning

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Reasoning

  2. 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.

  3. Deduction • Syllogisms • Conditional Reasoning

  4. 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

  5. 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.

  6. 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.

  7. 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 (If-Then)Prescription: Truth Tables

  8. 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

  9. 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? Clickhere for the correct answer and a frequent error.

  10. 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.

  11. 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

  12. Deviations from Correct Bayesian Reasoning • Neglecting Base Rates • Under-estimating the importance of new evidence

  13. Why do we make these mistakes? • Heuristics – mental shortcuts • Availability • Adjustment and Anchoring • Representativeness • Why do we use heuristics?

More Related