Deductive Reasoning zReasoning from the general to the specific zFor example, start with a general statement: All cars have tires. zYou can apply this general statement to specific instances and deduce that a Ford Escort, a Toyota Camry, and a Mercedes Benz must have tires.
Common deductive reasoning problems zSeries problems zSyllogisms
Series problems zreview series of statements zarrive at a conclusion not contained in any single statement zFor example: zRobin is funnier than Billy zBilly is funnier than Sinbad zWhoopi is funnier than Billy zQ: Is Whoopi funnier than Sinbad
Syllogisms zPresent two general premises that must be combined to see if a particular conclusion is true
Syllogism Example zAll Intro to Psychology students love their instructor. zYou are all Intro to Psychology students. zMust you love your instructor?
Syllogism Example zAll chefs are violinists. zMary is a chef. zIs Mary a violinist?
Ways to solve syllogisms zMental model theories zPragmatic reasoning theories
Mental models theories zTo solve a syllogism, you might visualize the statements zAll Intro to Psychology students love their instructor. zYou are all Intro to Psychology students. zMust you love your instructor? Psych- ology Psych- ology Psych- ology Bi- ology Bi- ology Bi- ology Bi- ology
Mental models theories zAll Intro to Psychology students love their instructor. zYou are all Biology students. zMust you love your instructor? Psych- ology Psych- ology Psych- ology Bi- ology Bi- ology Bi- ology Bi- ology
Mental models theories zSyllogisms that are easy to visualize are more readily solved than more abstract syllogisms Psych- ology Psych- ology Psych- ology Bi- ology Bi- ology Bi- ology Bi- ology
Mental model theories zTo solve a syllogism, you might visualize the statements zSyllogisms that are easy to visualize are more readily solved than more abstract syllogisms
Pragmatic reasoning theories zSolve syllogisms by applying information to pre-existing schemas zProblem difficulty related to importance of problem to our lives and survival as a species zMore relevant = easier to solve
Inductive reasoning zReasoning from the specific to the general
Inductive reasoning z18 16 14 ?? ?? 12 10 zRule? Decrease by 2 zQ: Why inductive reasoning? zAnswer: Take SPECIFIC numbers (i.e. 18,16,14) and come up with a GENERAL rule (i.e. decrease by 2)
Inductive Reasoning zSherlock Holmes is perhaps a better example of INDUCTIVE reasoning than deductive reasoning zHe takes specific clues and comes up with a general theory
Inductive reasoning problems z 5 10 15 ?? ?? ?? ?? ?? ?? ?? ?? 2520304045505535 zRule? zIncrease by five WRONG!!!!! zWhat is the correct rule? zAny increasing number y- the next number could be 87 or 62 or 1,000,006 zWhy did everyone guess the wrong rule?
Confirmation bias zOnly search for information confirming ones hypothesis zExample: reading newspaper columnists who agree with our point of view and avoiding those who dont
zChris is 67, 300 pounds, has 12 tattoos, was a champion pro wrestler, owns nine pit bulls and has been arrested for beating a man with a chain. zIs Chris more likely to be a man or a woman? zA motorcycle gang member or a priest? zHow did you make your decision? Chris story
Steve story zSteve is meek and tidy, has a passion for detail, is helpful to people, but has little real interest in people or real- world issues. z Is Steve more likely to be a librarian or a salesperson? zHow did you come to your answer?
Representativeness zJudge probability of an event based on how it matches a prototype zCan be good zBut can also lead to errors zMost will overuse representativeness yi.e. Steves description fits our vision of a librarian
Most will underuse base rates zBase rate - probability that an event will occur or fall into a certain category yDid you stop to consider that there are a lot more salespeople in the world than librarians? yBy sheer statistics, there is a greatly likelihood that Steve is a salesperson. xBut very few take this into account
Guess the probabilities zHow many people die each year from: zHeart disease? zFloods? zPlane crashes? zAsthma? zTornados? Stop
Availability heuristic zJudge probability of an event by how easy you can recall previous occurrences of that event. zMost will overestimate deaths from natural disasters because disasters are frequently on TV zMost will underestimate deaths from asthma because they dont make the local news
Word probabilities zIs the letter k most likely to occur in the first position of a word or the third position? zAnswer: k is 2-3 times more likely to be in the third position zWhy does this occur?
Class demonstration zName words starting with k zName words with the letter k in the third position
Availability heuristic zBecause it is easier to recall words starting with k, people overestimate the number of words starting with k
Finish the sequence problems z 30 24 18 ?? ?? ?? 1260 z 1 3 2 4 ?? ?? ?? ?? zRule? zDecrease by six zRule? zIncrease by two, decrease by 1 6453
Finish the sequence problems z 2 3 10 12 ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? zRule? zIncreasing numbers starting with the letter t 1321 31 39200 201 299300301 202930 32 302 2000 399 22
Chess problem zTwo grandmasters played five games of chess. Each won the same number of games and lost the same number of games. There were no draws in any of the games. How could this be so? zSolution: They didnt play against each other.
Bar problem zA man walked into a bar and asked for a drink. The man behind the bar pulled out a gun and shot the man. Why should that be so? zSolution: The man behind the bar wasnt a bartender. He was a robber.
Bar problem # 2 zA man who wanted a drink walked into a bar. Before he could say a word he was knocked unconscious. Why? zSolution: He walked into an iron bar, not a drinking establishment.
Nine dots problem zWithout lifting your pencil or re-tracing any line, draw four straight lines that connect all nine dots
Answer to nine dots problem
Metal Set zQ: Why couldnt you solve the previous problems? zA: Mental set - a well-established habit of perception or thought
Strategies for solving problems z1. Break mental sets
Number problem mental set zMost people get stuck in the same rhythm zOnly view problems in terms of math formulas zNeed to break out of this mental set to solve the problem z 2 3 10 12 ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? 1321 31 39 200 201 299300301 202930 32 302 2000 399 22
Nine dots mental set zMost people will not draw lines that extend from the square formed by the nine dots zTo solve the problem, you have to break your mental set
Mounting candle problem zUsing only the objects present on the right, attach the candle to the bulletin board in such a way that the candle can be lit and will burn properly
Answer to candle problem zMost people do not think of using the box for anything other than its normal use (to hold the tacks) zTo solve the problem, you have to overcome functional fixedness
Functional fixedness ztype of mental set zinability to see an object as having a function other than its usual one
Two general classes of rules for problem solving z1. Algorithms z2. Heuristics
Two general classes of rules for problem solving zAlgorithms - things the vice- president might say zAlgorithms - rules that, if followed correctly, will eventually solve the problem
An algorithm example zProblem: List all the words in the English language that start with the letter q zIf using an algorithm, would have to go through every single possible letter combination and determine if it were a word yi.e. is qa a word; is qb a word etc. yThis would take a very long time zInstead, what rule could you use to eliminate these steps?
Rules for q problem zSkip ahead and assume the second letter is a u zAssume the third letter has to be a vowel zThese types of rules are called heuristics
Heuristics zAny rule that allows one to reduce the number of operations that are tried in problem solving za.k.a rules of thumb or shortcuts zAnother common heuristic: yProblem: List all the numbers from 1-100,000 that are evenly divisible by 5 yAnswer: Rather than divide each and every number, you would use the rule: Any number ending in 0 or 5 is evenly divisible by 5.
z1. Break mental sets z2. Find useful analogy z3. Represent information efficiently z4. Find shortcuts z5. Establish subgoals z6. Turn ill-defined problems into well- defined problems Strategies for solving problems