Wason’s selection task

Wason’s selection task • E K 4 7 <- four cards • Each card in a deck of cards has a letter on one side and a number on the other • Claim: If there is an even number one side, then there is a vowel on the other side

problem and solution • E K 4 7 • If there is an even number on one side, then there is a vowel on the other side. • Determine which cards need to be turned over to verify that the rule or claim holds • answer: “4,” “K,” but not “E,” “7” • only ~10% of population gets the right answer

another selection problem • You serve drinks in a bar. Every patron of the bar has an age and a beverage. • 16 22 beer water • If you are drinking alcohol, then you have to be at least 21 years of age. • Which patrons do you need to know more about to see if the law is being observed? • Answer: check out 16-year old and the beer drinker; leave others alone • most of the population gets the answer right

differences in problems • connection to everyday life • EK47 version has no connection to everyday life; whereas, the bar problem does • difference in content: abstract version (EK47) and the realistic version (bar version)

logical structure of bar problem • 16 22 beer water • If someone is drinking alcohol, then they must be 21 years or older. • “p” = drinking alcohol • “q” = being 21 years or older • If p, then q

replace content with terms • 16 22 beer water • If p, then q (p = drinking alcohol; q = 21 years or older) • 16  “not q” beer  “p” • 22  “q” water  “not p”

logical structure • not q q p not p • If p, then q • exactly the same logical structure with EK47 version

conditions of naturally good critically thinking skills • more likely when we have realistic content in the problem • explanation: minds have a natural ability to solve logic problems, but only in situations of realistic content • deontic content: situations involving social rules (laws, detecting cheaters, etc.)

Implicit statements • If Michael Jackson is a normal guy, then I’m a monkey’s uncle. • (I’m not a monkey’s uncle.) • (Michael Jackson is not a normal guy.) • Implicit = unstated (indicate implicit statements by using parentheses)

logical structure of implicit statements • If Michael Jackson is a normal guy, then I’m a monkey’s uncle. • If p, then q (p = MJ normal guy, q = monkey’s uncle) • not q (I’m not a monkey’s uncle.) • not p (MJ is not a normal guy.) •  denial of the consequent (modus tollens)

realistic vs. abstract versions • If p, then q <- alone, no particular implications • If MJ is a normal guy, then I’m a monkey’s uncle <- adding words, particular implication is that MJ is not a normal guy

logical operators • If…then (conditional) • = if p, then q  under the condition that p is true, q is true • not (negation) “~” • = not p  p is not true • and (conjunction) • = p and q  both p and q are true

Disjunction • OR (disjunction) • = p or q  either p or q is true • logical operators allow you to combine information (premises) into logical statements

Interpretation of disjunction • p OR q  either p or q is true • but what about “I am male or female.” •  you are one or the other but not both (exclusive OR) excludes both (XOR) • what about “I am happy or smart.” •  you are one or the other or both • (inclusive OR) includes both

Interpretation of OR • p or q • could mean, p is true or q is true but not both • alternatively, could mean, p is true or q is true or both • unless specifically stated, either interpretation is possible

Disjunctive Reasoning • doing reasoning or critical thinking involving the word “or” • Start paying attention to me or I’ll kick you out of the class. (p or q) disjunction • means, If you don’t pay attention to me, then I’ll kick you out of the class. (If p, then q) conditional

Wason’s selection task