Post on 04-Jan-2016
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?