# Logical Reasoning Deductive reasoning Inductive reasoning

## Presentation on theme: "Logical Reasoning Deductive reasoning Inductive reasoning"— Presentation transcript:

Logical Reasoning Deductive reasoning Inductive reasoning
key words: logical reasoning; deductive reasoning; inductive reasoning

Deductive Reasoning Reasoning from the general to the specific
For example, start with a general statement: All cars have tires. You can apply this general statement to specific instances and deduce that a Ford Escort, a Toyota Camry, and a Mercedes Benz must have tires. key words: deductive reasoning

Common deductive reasoning problems
Series problems Syllogisms key words: deductive reasoning; series problems; syllogisms

Series problems review series of statements
arrive at a conclusion not contained in any single statement For example: Robin is funnier than Billy Billy is funnier than Sinbad Whoopi is funnier than Billy Q: Is Whoopi funnier than Sinbad key words: deductive reasoning; series problems

Syllogisms Present two general premises that must be combined to see if a particular conclusion is true key words: deductive reasoning; syllogisms

Syllogism Example All Intro to Psychology students love their instructor. You are all Intro to Psychology students. Must you love your instructor? key words: deductive reasoning; syllogisms This is one example of a syllogism. The next slide contains an alternate example of a syllogism.

Syllogism Example All chefs are violinists. Mary is a chef.
Is Mary a violinist? key words: deductive reasoning; syllogisms This is one example of a syllogism. Theprevious slide contains an alternate example of a syllogism.

Ways to solve syllogisms
Mental model theories Pragmatic reasoning theories key words: deductive reasoning; syllogisms; mental model theories; pragmatic reasoning theories

Mental models theories
To solve a syllogism, you might visualize the statements All Intro to Psychology students love their instructor. Psych- ology Bi- ology Bi- ology You are all Intro to Psychology students. key words: deductive reasoning; syllogisms; mental model theories This slide applies the mental model theory to the syllogism encountered in Slide 6. If you used the syllogism on Slide 7 as your example, use Slide 11 to illustrate the mental models theory The first set of drawings illustrates that all Intro to Psychology students must love their instructor. The second set of drawings illustrates that students of other disciplines may love their instructor, but they don't necessarily have to love their instructor Must you love your instructor? YES! YES! YES!

Mental models theories
All Intro to Psychology students love their instructor. Psych- ology You are all Biology students. Bi- ology Bi- ology key words: deductive reasoning; syllogisms; mental model theories This slide applies the mental model theory to the syllogism encountered in Slide 6. If you used the syllogism on Slide 7 as your example, use Slide 11 to illustrate the mental models theory Must you love your instructor? NO! NO! NO!

Mental models theories
Syllogisms that are easy to visualize are more readily solved than more abstract syllogisms Psych- ology key words: deductive reasoning; syllogisms; mental model theories This slide adds to the information in Slide 9 and applies the mental model theory to the syllogism encountered in Slide 6. If you used the syllogism on Slide 7 as your example, use Slide 11 to illustrate the mental models theory. Bi- ology Bi- ology

Mental model theories To solve a syllogism, you might visualize the statements Syllogisms that are easy to visualize are more readily solved than more abstract syllogisms key words: deductive reasoning; syllogisms; mental model theories This slide applies the mental model theory to the syllogism encountered in Slide # 7. If you used the syllogism encountered in Slide #6, then use Slides 9 & 10 to illustrate the mental model theory

Pragmatic reasoning theories
Solve syllogisms by applying information to pre-existing schemas Problem difficulty related to importance of problem to our lives and survival as a species More relevant = easier to solve key words: deductive reasoning; syllogisms; pragmatic reasoning theories

Inductive reasoning Reasoning from the specific to the general
key words: inductive reasoning

Inductive reasoning 18 16 14 ?? ?? 12 10 Rule? Decrease by 2
?? ?? 12 10 Rule? Decrease by 2 Q: Why inductive reasoning? Answer: Take SPECIFIC numbers (i.e. 18,16,14) and come up with a GENERAL rule (i.e. decrease by 2) key words: inductive reasoning

Inductive Reasoning Sherlock Holmes is perhaps a better example of INDUCTIVE reasoning than deductive reasoning He takes specific clues and comes up with a general theory key words: inductive reasoning

Inductive reasoning problems

Inductive reasoning problems
?? ?? ?? ?? ?? ?? ?? ?? 20 25 30 35 40 45 50 55 Rule? Increase by five WRONG!!!!! key words: inductive reasoning; confirmation bias This slide is about confirmation bias. To prevent being misleading, the intsructor should be very careful with wording. The intsructor should say something like, " Here is another number problem. I want you to shout out answers and raise your hand when you know what the rule is." This problem, on the surface, seems very easy. Virtually all students will come up with the hypothesis " Increase numbers by 5". Notice that every response they give will be a multiple of 5. That is, students will only give responses that confirm their hypothesis. They fail to recognize that the best way to test their hypothesis is to give an answer that violates their hypothesis. For instance, if they said 68 or 124 or 1,989, they would have been told that these responses were also correct. The correct rule for this problem is "any increasing number." By only sticking to multiples of 5, most students arrived at the wrong rule. What is the correct rule? Any increasing number - the next number could be 87 or 62 or 1,000,006 Why did everyone guess the wrong rule?

Confirmation bias Only search for information confirming one’s hypothesis Example: reading newspaper columnists who agree with our point of view and avoiding those who don’t key words: inductive reasoning; confirmation bias

Chris story Chris is 6’7”, 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. Is Chris more likely to be a man or a woman? A motorcycle gang member or a priest? How did you make your decision? key words: representativeness heuristic This slide presents a story problem to demonstrate how people will use a representativeness heuristic. Give the students the problem first and then ask them how they arrived at their conclusion. Students will most likely answer that the traits listed seem more characteristic of a man than a woman and of an outlaw motorcycle gang member than a priest. One problem you might encounter is that students might guess what you're trying to do and might try to give the answer they think you're looking for (i.e. they might say Chris is more likely to be a woman or a priest if they think that's what you want them to say.) Before asking students to give their answer, you might want to tell students to give their gut response, rather than trying to overthink the problem.

Steve story Steve is meek and tidy, has a passion for detail, is helpful to people, but has little real interest in people or real-world issues. Is Steve more likely to be a librarian or a salesperson? How did you come to your answer? key words: representativeness heuristic This slide presents a second story problem that demonstrates how people will use a representativeness heuristic. Give the students the problem first and then ask them how they arrived at their conclusion. Students will most likely answer that the traits listed seem more characteristic of a librarian than a salesman. Again, one problem you might encounter is that students might guess what you're trying to do and might try to give the answer they think you're looking for (i.e. they might say Steve is more likely to be a salesman than a librarian if they think that's what you want them to say). Before asking students to give their answer, you might want to tell students to give their gut response, rather than trying to overthink the problem. The next slide contains a second example of a how students might use a representativeness heuristic

Representativeness Judge probability of an event based on how it matches a prototype Can be good But can also lead to errors Most will overuse representativeness i.e. Steve’s description fits our vision of a librarian key words: representativeness heuristic

Most will underuse base rates
Base rate - probability that an event will occur or fall into a certain category Did you stop to consider that there are a lot more salespeople in the world than librarians? By sheer statistics, there is a greatly likelihood that Steve is a salesperson. But very few take this into account key words: base rates

Guess the probabilities
How many people die each year from: Heart disease? Floods? Plane crashes? Asthma? Tornados? Stop key words: availability bias The purpose of this demo is to show that people will, in general, dramatically overestimate the number of deaths from natural disasters or accidents and underestimate deaths from asthma. Most people will say that more people die each year from floods or tornados or plane crashes than asthma - even though approximately 16 times as many people in the US die from asthma each year than die from floods, tornados and plane crashes combined. Approximate death rates per year in the US for the following: 1. Heart disease: 960,592 2. Flash floods: 108 3. Plane crashes: 147 4. Asthma: 5,000 5. Tornados: 52 Heart Disease: - According to the the American Heart Association, 960,592 people in the US died of heart disease in In 1993, the death rate from heart disease was 954,138. - Heart disease information was obtained at the following websites: 1) ) 3) Flash Floods: - The 108/year death rate from flash floods represents the average deaths per year in the US during the 1980's. From , a total of 1,083 people died as the result of flash floods. - In the state of Ohio, from , a total of 368 people died during flash flooding. - This data was obtained at the following website: Plane crashes: - The 147/year death rate from plane crashes reflects an average of fatalities from The number of deaths vary year to year (from lows of 0 deaths in 1993 and 1 in 1984 to highs of 319 in 1996 and 486 in 1985). - The 147/year death rate from plane crashes only represents fatalities of the major US air carriers. It does not include fatalities from commuter plane crashes (approximately fatalities per year) or from non-commercial flights of smaller planes. - This data was obtained from the website of the National Transportation safety Board at - An important point ot bring up is that, although 147/year mortality rate may seem high, it accounts for an extremely small percentage of fliers. For instance, in 1997 there were only 2 fatalities out of 625 million passengers ( % of all passengers) who boarded flights of the major US carriers. - This is an interesting statistic to bring up to your class. People who have a fear of flying will often feel flying is more dangerous than driving a car because planes crashes are more heavily reported on national news and in national newspapers and magazines (that is, they are falling prey to an availability bia). However, they will underestimate base rates (that statistically, driving isactually more dangerous than flying) Asthma: - According to the Dec. 8, 1994 issue of the New England Journal of Medicine, in the US, approximately 5,000 people die each year from asthma - This information was obtained at the following websites: 1) 2) 3) Tornados: The 108/year death rate from tornados represents the average deaths per year in the US during the 1980's. From , a total of 521 people died as the result of tornados. - In the state of Ohio, from , a total of 171 people died during tornados. Although not currently represented on this slide, you might choose to add any of the following: Lightning: - Approximately 73 people per year - The 73/year death rate from lightning represents the average deaths per year in the US during the 1980's. From , a total of 726 people died as the result of lightning. Diabetes: approximately 187,880 deaths per year in the US Cancer: approximately 500,000 deaths per year in the US The diabetes and cancer statistics were obtained from the Center for Disease Control at the following website:

Availability heuristic
Judge probability of an event by how easy you can recall previous occurrences of that event. Most will overestimate deaths from natural disasters because disasters are frequently on TV Most will underestimate deaths from asthma because they don’t make the local news key words: availability heuristic

Word probabilities Is the letter “k” most likely to occur in the first position of a word or the third position? Answer: “k” is 2-3 times more likely to be in the third position Why does this occur? key words: availability heuristic This is another demonstration of the availability bias at work.

Class demonstration Name words starting with “k”
Name words with the letter “k” in the third position key words: availability heuristic

Availability heuristic
Because it is easier to recall words starting with “k” , people overestimate the number of words starting with “k” key words: availability heuristic

Finish the sequence problems
?? ?? ?? 12 6 Rule? Decrease by six ?? ?? ?? ?? 3 5 4 6 key words: inductive reasoning; mental sets; problem solving This slide gives some more inductive reasoning problems. However, the purpose is not merely to demonstrate inductive reasoning. Rather, the purpose is to set up a demonstration of how mental set can prevent you from solving problems. The two problems on this slide can be solved by applying a mathematical formula to the problems. However, if you try to solve the problem on the next slide by using a mathematical formula, you will never come up with the solution. To solve the problem on the next slide, you have to break out of your mental set and look at the problem from a new angle. Rule? Increase by two, decrease by 1

Finish the sequence problems
?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? 13 20 21 22 29 30 31 32 39 200 201 299 300 301 302 399 2000 Rule? Increasing numbers starting with the letter “t” key words: inductive reasoning; mental sets; problem solving - To solve this problem, you have to break out of the mental set. - Before revealing the true purpose of this slide (i.e. a demo of the megative effects of mental set ) I generally will go through the next 5 slides which give more examples of problems that require a person to break out of a mental set to come up with the correct solution. After going through the slides, I then generally ask people why they weren't able to come up with the solutions. Students will generally give an answer that segues into the discussion of mental set.

Chess problem Two 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? Solution: They didn’t play against each other. key words: mental sets; problem solving

Bar problem A 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? Solution: The man behind the bar wasn’t a bartender. He was a robber. key words: mental sets; problem solving

Bar problem # 2 A man who wanted a drink walked into a bar. Before he could say a word he was knocked unconscious. Why? Solution: He walked into an iron bar, not a drinking establishment. key words: mental sets; problem solving

Nine dots problem Without lifting your pencil or re-tracing any line, draw four straight lines that connect all nine dots key words: mental sets; problem solving; nine dots problem

key words: mental sets; problem solving; nine dots problem

Metal Set Q: Why couldn’t you solve the previous problems?
A: Mental set - a well-established habit of perception or thought

Strategies for solving problems
1. Break mental sets key words: mental sets; problem solving

Number problem mental set
?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? 13 20 21 22 29 30 31 32 39 200 201 299 300 301 302 399 2000 Most people get stuck in the same rhythm Only view problems in terms of math formulas Need to break out of this mental set to solve the problem key words: mental sets; problem solving

Nine dots mental set Most people will not draw lines that extend from the square formed by the nine dots To solve the problem, you have to break your mental set key words: mental sets; problem solving; nine dots problem

Mounting candle problem
Using 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 key words: functional fixedness, mental set; problem solving Although students can work on this problem by simply thinking and visualizing a solution in their heads, this demonstration works better by by bringing the actual materials to class and doing a live demonstration with your students, letting them attemtp to solve the problem through trial and error. To do this task you need the folllowing materials: 1. a cork bulletin board 2. a book of matches 3. a candle 4. a BOX of thumbtacks - make sure you keep the thumbtacks in a BOX - also make sure the thumbtacks aren't too big that they can pass through your candle. The smaller the thumb tack, the better

Most people do not think of using the box for anything other than it’s normal use (to hold the tacks) To solve the problem, you have to overcome functional fixedness key words: functional fixedness; mental sets; problem solving

Functional fixedness type of mental set
inability to see an object as having a function other than its usual one key words: functional fixedness; mental set; problem solving Some examples of overcoming functional fixedness include: 1. Using a dime to unscrew something when a screwdriver cannot be found. 2. Using a book to prop open a door when a doorstop cannot be found. 3. Before a baseball game, a rainstorm occurred. They wanted to dry the field a little before beginning play, so they had a helicopter hover above the field, and the rotating helicopter blades acted as a fan and helped dry up the field.

Strategies for solving problems
1. Break mental sets break functional fixedness 2. Find useful analogy key words: functional fixedness; mental sets; problem solving; finding analogies

Find useful analogy Compare unknown problem to a situation you are more familiar with Key words: analogies; problem solving For example, let's say you come across someone who has been in an accident and is bleeding badly. You've never had any medical experience at all, but still have to do something to help the person live. You think back to a similar problem at your home when a faucet burst, causing water to go everywhere. The first thing you did at home was to put your thumb up to the faucet to stop the leak. So, you might try to apply direct pressure on the person's wound to stop the bleeding. Unfortunately, just as with the leaking faucte at home, direct pressure does not stop the bleeding. Now, you have to think of what top do next. At home, you realized that you had to turn off the water to the house. Applying this to the current situation, you decide to apply a tourniquet to stop the bloodflow. You find that, just as at home with the lekay faucet, this does the trick and the person is no longer bleeding. Now what do you do with the person? Well, at home, you realized that the water had to be turned on eventually, just as the tourniquet will eventually have to be removed. At home, you called a plumber or other professional to provide a more long-term fix. Applying this to the new situation, you decide to call an ambulance to take care of the accident victim.

Strategies for solving problems
1. Break mental sets 2. Find useful analogy 3. Represent information efficiently 4. Find shortcuts (use heuristics) key words: functional fixedness; mental sets; problem solving; finding analogies; shortcuts; heuristics

Two general classes of rules for problem solving
1. Algorithms 2. Heuristics key words: problem solving; finding analogies; shortcuts; heuristics; algorithms

Two general classes of rules for problem solving
Algorithms - things the vice-president might say Algorithms - rules that, if followed correctly, will eventually solve the problem key words: algorithms; problem solving Give students the chance to write down the definition before reading it aloud to them. The purpose is to see how many students will write down the whole definition before realizing it is a bogus definition. How does this relate to algorithms? Well, assume a student's problem is that they want to do well and get an "A" in their Introduction to Psychology class. Now, if they memorized absolutely everything in the text book and wrote down and memorized each and every single word you said in class, they would most likely get an "A". This is a safe, sure way - an algorithm. However, this can lead to a lot of wasted effort. For instance, you might be writing down a lot of notes (such as the bogus definition) that will not appear on an exam. Also, unlike a computer which can readily process vast quantities of information, a task of this nature in not as feasible in a human. Instead, a student might choose to use a heuristic. For instance, always wait 20 seconds before writing down notes or don't write down the intructor's jokes and amusing anectdotes from the instructor's childhood that have no relevance to the lecture material.

An algorithm example Problem: List all the words in the English language that start with the letter “q” If using an algorithm, would have to go through every single possible letter combination and determine if it were a word i.e. is “qa” a word; is “qb” a word etc. This would take a very long time Instead, what rule could you use to eliminate these steps? key words: algorithms; problem solving

Rules for “q” problem Skip ahead and assume the second letter is a “u”
Assume the third letter has to be a vowel These types of rules are called heuristics key words: algorithms; problem solving; heuristics

Heuristics Any rule that allows one to reduce the number of operations that are tried in problem solving a.k.a rules of thumb or shortcuts Another common heuristic: Problem: List all the numbers from 1-100,000 that are evenly divisible by 5 Answer: Rather than divide each and every number, you would use the rule: Any number ending in 0 or 5 is evenly divisible by 5. key words: heuristic; problem solving; shortcuts Also see speaker notes for slide 46 for another example of a heuristic

Strategies for solving problems
1. Break mental sets 2. Find useful analogy 3. Represent information efficiently 4. Find shortcuts 5. Establish subgoals 6. Turn ill-defined problems into well-defined problems key words: functional fixedness; mental sets; problem solving; finding analogies; shortcuts; heuristics; subgoals; ill-defined problems; well-defined problems