Instructor Manual

Chapter 4: Logic – inductive force

Instructors’ material

All of the exercises provided in the students’ self-assessment section lend themselves to extension by instructors.

Exercise A

Students can be asked a) to explain why the arguments are/are not inductively forceful, and/or b) for those arguments that are not inductively forceful, how they could be amended to make them so.

Exercise B
Students can be asked to construct inductively forceful arguments using the quantifying terms that have an approximate value of greater than 51% probability.

Exercise C
Students can be asked to explain why the arguments are/are not inductively forceful.

Exercise D
Students can be asked to explain their choices to explain whether any of the other options for each question would have preserved the inductive force of the argument.

Exercise E
Students can be asked a) to explain why the inductive inferences are/are not warranted and/or b) in the case of the unwarranted inferences, what evidence would be required to make such an inference warranted.

Exercise F

This exercise brings together most of chapters three and four and may be difficult to some. It can be used to illustrate to students the malleability of argument interpretation and reconstruction. Students will see that arguments can be interpreted in many ways, but that some interpretations are still better than others. This exercise also highlights the difficulties involved in balancing the requirements of the principle of charity and the need to be faithful to the arguer’s intention.

Further exercises

The following arguments include a premise with a missing quantifying term. Write them in standard form supplying the missing quantifier. Make the arguments as inductively forceful as possible.

  1. If we don’t leave now, we won’t find a parking space. If we don’t find a parking space, we’ll be late. If we are late, we will miss the start of the movie. If we miss the start of the movie, I can’t follow the plot. I won’t be able to follow the movie plot.
  2. Children today are out of control and something must be done. If we don’t bring them under control now, they will become out of control adults incapable of contributing to society and this is a scenario that must be avoided.
  3. Unless we invest in driver education more people will die needlessly on our roads. Drivers take risks occasionally and that is enough to cause accidents. Only better and more regular driver education will stop people from taking those risks and we should pursue the only sensible solution that is open to us.
  4. Plagiarism is a major challenge in colleges today and something must be done to stop it. Students pass off another person’s work as their own. In examinations students cannot plagiarise. So to stop plagiarism we should end internal assessment and return to assessing by examination only.
  5. If the Patriots beat the Bears, they will be at the top of the league. If the Patriots stay top of the league for more than two weeks they make it to the Super Bowl. If the Patriots beat the Bears, they will make it to the Super Bowl.
  6. Teenagers use the internet to access social networking sites. Those sites carry advertising. If you want to expose your product to the teen market, social networking sites are a good place to advertise.
  7. Next week the UN Security Council will vote on whether to impose sanctions on Anyland. China and Russia vote against sanctions whatever the circumstances. So it’s said they’ll probably oppose sanctions at next week’s meeting.
  8. I’ve lost my grandmother’s recipe for Angel Cake. Let me see if I can remember it … Recipes for cake use either self-raising or plain (wheat) flour. My grandmother’s recipe doesn’t use plain (wheat) flour. Probably, then, I need to use self-raising (wheat) flour.
  9. Although no true vegetarians eat meat, vegetarians eat cheese. My friend Jannick is a vegetarian and he’s coming to dinner. If I make macaroni cheese, he will eat it.
  10. If we don’t limit our air travel, carbon emissions will continue to increase at a dangerously high rate. People fly more than they need to. People who fly more than they need to could easily limit their air travel. We all have a responsibility to reduce carbon emissions. People who fly more than they need to should limit their air travel.

The following arguments are valid but deductively unsound. Change a premise to make them inductively forceful and inductively sound. If you are unsure of the truth values of the premises, change the premise to make it likely to be true and explain what you would need to know to be sure of the truth value.

  1. P1) All animals eat standing up.
    P2) Elephants are animals.
    C) Elephants eat standing up.
  2. P1) Hens lay eggs.
    P2) Farmer Brown keeps hens.
    C) Farmer Brown’s hens lay eggs.
  3. P1) Trucks run either on petrol or on diesel.
    P2) Eddie Stobbard’s trucks run on diesel.
    C) Eddie Stobbard’s trucks do not run on petrol.
  4. P1) Kittens have tails.
    P2) Kittens chase their tails.
    C) Your new kitten will chase its tail.
  5. P1) Doctors are caring and competent.
    P2) My uncle Ralph is a doctor.
    C) My uncle Ralph is caring and competent.
  6. P1) If it rains in winter, the temperature drops.
    P2) It is winter.
    P3) It is raining.
    C1) The temperature will drop.
    P4) If the temperature drops, we have to turn on the heating.
    C2) We will have to turn on the heating.
  7. P1) Parisian football supporters support Paris St-Germain.
    P2) Jean-Luc is Parisian.
    P3) Jean-Luc is a football supporter.
    C) Jean-Luc supports Paris St-Germain.
  8. P1) We can only go sailing if the wind drops.
    P2) The wind drops around lunchtime.
    C) We can go sailing after lunch.
  9. P1) Women own at least one pair of high-heeled shoes.
    P2) High-heeled shoes are relatively difficult to walk in.
    C) Women own at least one pair of shoes that are relatively difficult to walk in.
  10. P1) If your shoes have high heels, you should not wear them when you are going on a protest march.
    P2) You are not going on a protest march today.
    C) You can wear your shoes with high heels today.

Explain why the inductive inferences in the following passages are unwarranted.

  1. My boyfriend’s sister is an artist. I met a few artists once. They were completely pretentious and self-absorbed, so I’m trying to avoid meeting his sister.
  2. My last husband was a disaster – couldn’t pick up after himself, couldn’t make himself a cup of coffee, couldn’t get his own beer from the fridge. I couldn’t even rely on him to take out the trash. I’m not going to bother getting married again; men are all the same.
  3. My last marriage was a catastrophe. My former wife was hopeless: always tidying up after me, wouldn’t let me into the kitchen to make a coffee or get a beer from the fridge. She wouldn’t even let me take out the trash. I’m never living with a woman again; they’re all the same.
  4. The British Government proposes to cut spending on welfare at a time of recession. The Thatcher Government did that in the 1980s and we ended up with four million unemployed. The Government must be made to see sense.
  5. Our food safety technicians have tested six samples of the allegedly contaminated meat, all from the same store, and they were all found to contain levels of toxin within the safe levels. The media should stop scaremongering – our meat is completely safe.
  6. A science degree is no longer a guaranteed path to well-paid employment. I have three friends and a cousin who all have degrees in Chemistry or Physics and they have all ended up working in call centres or waiting tables.
  7. Whatever you do, don’t buy that blue sweater. I had a blue one once and the moths ate it.
  8. So there I was, standing in the rain, getting soaked and I thought to myself, ‘I knew I should have brought my raincoat. Last time I didn’t bring may raincoat, it rained, I got soaked and I caught the flu and had to take a week of work.’
  9. In this time of need, compulsory vegetable growing is to be introduced throughout the country. We ran a pilot scheme in Duncanshire, which is a small, rural county, and it was successful. We now have evidence to support the roll-out of the scheme across the whole nation.
  10. There’s no point in taking nasi goreng to the pot-luck dinner. The guests won’t eat it. Last time I took a spicy dish to a pot-luck party, hardly anyone ate it.

Provide the missing premise(s) to make these arguments inductively forceful

  1. P1)
                                                                                                   
    C) Probably your children will enjoy the latest Pixlar movie.
  2. P1) If it is sunny today, you will probably get sunburnt at the beach.
    P2)
    ______________________________________________
    C) You will probably get sunburnt at the beach.
  3. P1) People who get badly sunburned as children usually have a higher risk of developing skin cancer as adults.
    P2)
                                                                                                   
    C) Probably you have a higher risk of developing skin cancer as an adult.
  4. P1) Either the Mets or the Lakers will win the final.
    P2)
                                                                                                   
    C) Probably the Mets will win the final.
  5. P1) Unless she works hard she won’t pass her exams.
    P2)
                                                                                       
    C) Probably she won’t be able to get a place at graduate school.
  6. P1) Unless Betty works hard she won’t pass her exams.
    P2)
    P3) If she doesn’t pass her exams, she won’t get a place at graduate school.
    C1) She probably won’t get a place at graduate school.
    P4) If she doesn’t get a place at graduate school she won’t be able to become a lawyer.
    P5)
                                                                                                                          
    C2) Probably If she doesn’t become a lawyer, her grandmother will be disappointed.
  7. P1)
    P2) Francine’s grandmother is disappointed.
    C) Probably Francine’s grandmother won’t leave her an inheritance.
  8. P1) Unless she tidies up the mess in her study, she’ll never find her assignment.
    P2)
                                                                                                               
    C) Probably she’ll never find her assignment.
  9. P1) The enemy must either commit to a cease fire immediately or we will continue the ground and air attacks.
    P2)
                                                                                                     
    C) Probably our ground and air attacks will continue.
  10. P1) If Edward drank all the wine, then the bottle is probably empty.
    P2)
                                                                                                  
    C) Probably Edward did not drink all the wine.


Reconstruct the following arguments into the standard form and make a tree diagram for each. Some material may have to be omitted or modified to make the argument clearer.

1.
The Fierce Nettle is a highly toxic plant. Coming into contact with it can make you very ill and even kill you. Some of the symptoms which it causes are heavy sweating, difficulty with breathing, loss of coordination, paralysis, blindness, and loss of consciousness. Kojiro had all these symptoms before he died according to his friends. Also, the Fierce Nettle is very common in the area where Kojiro was hiking the day he died. There is a good chance, then, that Kojiro died from a Fierce Nettle poinsoning.

2.
Alexis was seen walking up a wall by passers by. Only ninjas and spider-man can walk up walls. Alexis is probably not spider-man, but she did study martial arts when she was little, so she is most likely a ninja.

3.
Although viral videos and emails account for 94 hours of wasted time for the average office worker every year, they also boost workforce morale, and a happy workforce has been shown to be one of the most valuable qualities of successful businesses. Also, if internet usage was restricted employees are likely to be angered and performance would decrease. So businesses should think twice before they decide to tamper with internet access.

4.
A lot of people get abused, raped, and even killed in the prison system. Although they are considered criminals under the law, their punishment does not and should not include these abuses. The prison system needs to be overhauled to make sure these things don’t happen.

5.
Mr J was brutally attacked by an intruder in his own home. After being beaten into revealing the location of his safe and its key, Mr J had the opportunity to get a box cutting knife while the intruder was busy with the safe. The intruder then came back upstairs and into the bedroom. At this time Mr J was hiding behind the bedroom door. When the intruder entered the room, Mr J lunged at him with the knife, inflicting a mortal wound on his throat. Mr J admits he acted out of anger and the desire to revenge what he has just past through. Because of this Mr J should be prosecuted for murder.

6.
The airport tower experienced a blackout on Sunday for almost three hours. Luckily it wasn’t the busiest time of the day. As yet, the cause of the problem is unknown. If this happens again there is no way of telling how disastrous the consequences could be. A major crash with multiple fatalities can’t be dismissed out of hand. We should therefore invest what is left in this year’s budget to bring in professionals to try and figure out why our electrical system failed.

7.
Our planet can’t sustain so many people. If we don’t start seriously limiting population growth like the Chinese, chances are that nature and war will do it for us, and as unwelcome a one child policy would be, it is nowhere near as bad as starvation and war. The best thing to do is to tighten our belt now before our pants fall off!

8.
The latest summer blockbuster by Major Studios cost a quarter of a billion dollars to make, has a long line of stars, and is 3D and high definition. It is a good bet for two and a half hours of family fun this summer.

9.
Most of the clothing we wear is produced in sweatshops in India and China under conditions that we in the west would consider close to slavery. If we stop buying cloths from these countries people who depend on this work for a living would be destitute. The best thing to do is probably to demand that retailers only stock cloths that come from factories that are supervised to give their employees the worker rights that are considered minimum in the West.

10.
If you want to buy a computer the first choice you need to make is whether to buy a laptop or a desktop. Although laptops are “cooler” and good for people who need to use their computer in more than one place, they are not as good as desktop computers of the same price. Desktops are smarter and faster and capable of doing more things than laptops that cost the same. They are also cheaper to maintain and upgrade. So if you only really need a computer for home, and you are not a slave to fashion, the choice is clear.