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?