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Student Material

Chapter 4: Logic – inductive force

Students’ material

A

Indicate whether or not the following arguments are inductively forceful.
Note
To keep the exercise challenging, we have not inserted ‘Probably’ before any of the conclusions. 

  1. P1) Winnie the Pooh is a bear.
    P2) Almost all bears eat either jam or honey, but not both.
    P3) Winnie the Pooh eats honey.
    C) Winnie the Pooh does not eat jam.
  2. P1) Billy is a bus.
    P2) Buses usually run on petrol or diesel.
    C) Billy runs on petrol or diesel.
  3. P1) Closing hospital wards would save money.
    P2) Hospital managers should do most of the things that would save money.
    C) Hospital managers should close wards.
  4. P1) If Smith works in a hospital then he is a doctor.
    P2) Most doctors are perfectionists.
    P3) Virgos are perfectionists.
    C) Smith is a Virgo.
  5. P1) Smith works in a hospital.
    P2) Some people who work in hospitals are nurses.
    C) Smith is a nurse.
  6. P1) Most children like to eat sugar.
    P2) These mice are made of sugar.
    C) My children will like to eat these mice.
  7. P1) These snakes are made of sugar.
    P2)  If these snakes are made of sugar, almost all children would like to eat them.
    C) Your children would like to eat these snakes.
  8. P1) People who eat too much sugar are likely to develop dental cavities.
    P2) Bruce is a dentist.
    C) If your children eat too many of these sugar mice and sugar snakes, they will have to visit Bruce.
  9. P1) Soccer teams who wear a red home strip are almost always more successful when they play away than soccer teams who wear a white home strip.
    P2) Manchester Utd wear a red home strip.
    C) Manchester Utd are more successful when they play at home than Tottenham Hotspur.
  10. P1) Soccer teams who wear a red home strip are almost always more successful when they play away than soccer teams who wear a white home strip.
    P2) Spain wear a red home strip.
    P3) England wear a white home strip.
    C) Spain are more successful when they play at home than England are when they play at home.

B

For the purpose of calculating the probability of a conclusion, is the rough numerical value of each of these quantifier terms taken to be greater or less than (approximately) 51%?

  1. most
  2. few
  3. many
  4. almost all
  5. a majority of
  6. some
  7. every
  8. none of
  9. usually
  10. sometimes

C

For each of the following arguments, consider the combination of quantifiers and ‘probably’ in the premises and say whether or not the premises make the conclusion likely to be true, i.e. whether or not the argument is inductively forceful. 

  1. P1) If I don’t take my umbrella to the match it will probably rain.
    P2) I am not taking my umbrella to the match.
    C) It will probably rain.
  2. P1) Lying is almost always morally wrong.
    P2) We should avoid doing anything that is morally wrong.
    C) We should never tell lies.
  3. P1) Almost always when I don’t bring my umbrella to the match it rains.
    P2) I probably won’t bring my umbrella to the match.
    C) It will rain.
  4. P1) Most people in Kailua live in wooden houses.
    P2) Most wooden houses are unsafe in the event of an earthquake.
    P3) Ben lives in Kailua.
    C) Ben’s house is unsafe in the event of an earthquake.
  5. P1) Probably Said will become an architect like his father.
    P2) Almost all architects live in well-designed houses.
    C) Said will live in a well-designed house.
  6. P1) Some chefs are disrespectful towards their staff.
    P2) Linda will probably become a chef.
    C) Linda will be disrespectful towards her staff.
  7. P1) It is highly likely that john will get elected to Parliament.
    P2) Almost all Politicians remain honest once elected.
    C) John will remain honest once elected.
  8. P1) Helen will almost certainly get elected to the Senate.
    P2) Very few politicians remain honest once elected.
    C) Helen will remain honest once elected.
  9. P1) If the Stein family are watching TV, then they are probably watching the Simpsons.
    P2) The Stein family are watching TV.
    C1) The Stein family are watching the Simpsons.
    P3) Whenever the Stein family watch the Simpsons they eat popcorn.
    C2) The Steins are eating popcorn.
  10. P1) If the Stein family are watching TV, they are probably eating pizza.
    P2) The Stein family are eating pizza.
    C1) The Stein family are watching TV.
    P3) Whenever the Stein family watch TV they drink beer.
    C2) The Steins are drinking beer.

D

Pick the missing term(s) needed to make each of these arguments as inductively forceful as possible.

  1. P1) XXXXX when the Government enacts new legislation, the opposition tries to take the credit.
    P2) The Government is enacting new road safety legislation.
    C) Probably the opposition will try to take the credit for the new road safety legislation.
    a) Almost always
    b) In the majority of cases
    c) Sometimes
  2. P1) Noah’s animals are hungry.
    P2) XXXX hungry animals are noisy.
    C) Noah’s animals are probably noisy.
    a) Most
    b) Almost all
    c) Few
  3. P1) If Dan is a conservative, then he XXXX believes that the free market should be permitted to operate without regulation.
    P2) Dan is a conservative.
    C) Probably Dan believes that the free market should be permitted to operate without regulation.
    a) mostly
    b) sometimes
    c) probably
  4. P1) Tahua is visiting Tallahassee.
    P2) XXXX who visit(s) Tallahassee travels there either by plane or by car.
    P3) Tahua did not travel there by car.
    C) Probably Tahua travelled there by plane.
    a) Most people
    b) Someone
    c) Probably
  5. P1) Angus lives in Glasgow.
    P2) Men who live in Glasgow XXXX wear a kilt on Burns Night.
    P3) Tonight is Burns Night.
    C) Angus will probably wear a kilt tonight.
    a) usually
    b) almost always
    c) never
  6. P1) Xian is making pizza.
    P2) Pizza is XXXX made with cheese and tomato.
    C) Probably Xian is making pizza with cheese and tomato.
    a) almost always
    b) sometimes
    c) generally
  7. P1) XXXX countries in the EU use the Euro as their currency.
    C) If Greece is in the EU, then, probably, it Greece uses the Euro as its currency.
    a) Some
    b) A majority of
    c) A lot of
  8. P1) If Vanuatu beat New Zealand, they will win the Oceania group of the Football World Cup Qualifying Round.
    P2) Vanuatu will probably beat New Zealand.
    C1) Probably Vanuatu will win the Oceania group of the Football World Cup Qualifying Round.
    P3) XXXX the winners of the Oceania group of the Football World Cup Qualifying Round fail to progress beyond the first round of the World Cup Final.                                                                             
    C2) Probably Vanuatu will fail to progress beyond the first round of the World Cup Final.
    a) Usually
    b) Sometimes
    c) Almost always
  9. P1) Keats is more famous than Goethe.
    P2) XXXX if a writer is more famous than Goethe they are more famous than Dickens.
    C) Probably Keats is more famous than Dickens.
    a) Probably
    b) It is highly likely that
    c) It is unlikely that
  10. P1) Those roses won’t grow unless you fertilize them.
    P2) You XXXX won’t remember to fertilize them.
    C) Probably those roses won’t grow.
    a) almost certainly
    b) probably
    c) sometimes

E

Indicate whether or not the inductive inferences in the following passages are warranted.

  1. My sister is obsessed with celebrities – what they wear, who they are dating, how much weight they’ve lost or gained. It must be the same with all women.
  2. Beauty products that are clinically proven to give results! Results of clinical tests showed that, among 38 women who used Miracle Cream twice a day for a month, 30 saw a reduction in fine lines and other imperfections.
  3. Support for the Conservatives is growing after the latest round of Government budget cuts. We polled 100,000 voters in 100 constituencies and our results show 70 per cent support for the Conservatives across all age groups of voters, apart from 18- to 25-year-olds, where support was less at 55 per cent.
  4. The floor is probably wet because the roof is leaking. Since we had that new chimney installed last year, the roof has leaked every time it’s rained.
  5. I bet he’s going to give me chocolates for my birthday again. I’ve known him for 30 years and he’s given me chocolates on my birthday at least 25 times.
  6. You’re going to buy a Porsche? I wouldn’t do that. My sister and my cousin both drive Porsches and they’ve both had their cars vandalised. Porsches are very vulnerable if you have to park them out on the streets.
  7. Remind me never to eat his homemade pie again. Every time I’ve eaten it (which must be at least ten times now), I’ve had terrible indigestion.
  8. If history is any guide, this latest incursion into Smalland’s territory will not lead to a cessation of violence. Bigland has attacked Smalland eight times this century under very similar circumstances and each time the violence just gets worse and more and more innocent people are killed or maimed.
  9. I doubt that the All Blacks stand a good chance of winning the 2011 Rugby World Cup even though they’ll have a home advantage and they won the first World Cup in 1987. After all, they failed to repeat that success in 1991, 1995, 1999, 2003 and 2007.
  10. I expect I’ll enjoy the new Woody Allen movie. I’ve enjoyed all of his previous movies.

F

Reconstruct the following arguments to be deductively valid or inductively forceful. Put them in standard form. You can change or add premises, and you can change the conclusion. These arguments can be made deductively valid or inductively forceful in more than one way. Try not to diverge from the original argument too much, but keep the principle of charity in mind.

  1. John Keys said that he wouldn’t sell Kiwibank, but at another time he said that he won’t sell it on his first term as prime minister. He also said NZ should help more in Iraq, and later changed his mind. He can’t be trusted. He shouldn’t be the prime minister.
  1. The vast majority of Kiwi parents are decent, loving, law abiding people who want the very best for their children. They smack their children sparingly, and as a necessary correction of bad behaviour. The anti-smacking bill will make these good people criminals, so it should not be passed.
  1. The whole business with Tiger Woods shows that men can’t be trusted. He looked like such an honest, faithful and hard-working person, and even he couldn’t resist cheating.
  1. Some countries are developing cyberweapons. So we need to invest in cyberweapons too, as well as in defences against cyberattackes.
  1. Sudan is one of the most volatile countries in Africa. Now there is going to be a vote in southern Sudan which may see it break away from the rest of the country, which means that there is probably going to be another civil war there.
  1. Religions are almost certainly false. Without moderate religious faith there would be no radical religious faith, so in order to stop terrorism we need to show people that religions are almost certainly false.
  1. American Muslims are assimilated to American culture which prevents them from being radicalized. So they present no terrorist threat.
  1. Greece has an ever-growing deficit that may cause it to default on its loans. Greece’s credit rating should be lowered.
  1. If China softens its iron grip on its people it is likely to disintegrate into many ethnic groupings in a process that will spark civil unrest and wars similar to what happened in the Balkans. At the moment, then, China is not ready for all the freedoms which we enjoy in the West.
  1. Letting people vote to choose their leaders can have the disastrous consequence of electing a dictator. Democracies are not good political systems.
  1. People who are accused of political dissidence in China normally get sentenced to three to eight years in prison. Mr. Liu is in trouble.
  1. The relationship between Cuba and the US is warming up. So soon US sanctions will be abandoned.
  1. Attacks on Taliban fighters in Afghanistan using drones have been blamed for some civilian casualties so they should not be used.
  1. Pakistan is either unwilling or unable to deal with Al Qaeda and Taliban forces within its boarders. So the US should go in and do the job for them.
  1. Iran has been building an atomic fuel enrichment plant in secret. A month ago it agreed to send most of its atomic fuel to be enriched outside its borders – a measure that would prevent it from enriching its atomic fuel to the level needed to produce an atomic bomb – but now it has changed its mind. Iran is probably after nuclear weapons – not just power-plants. It has also threatened to wipe Israel off the map. Iran should not be allowed to possess nuclear weapons. (Hint: Try reconstructing this into two arguments.)
  1. Serious change on global warming demands concerted action by all the powerful and populous nations. But such changes are likely to have big negative economic effects, which governments are reluctant to cause for fear of loosing their power. So it is unlikely that the needed actions will be taken by governments without a worldwide popular outcry.
  1. The industrial nations of the first world like the US, Britain, Japan, Germany and France have built their success and prosperity on practices which caused enormous pollution. Now these countries want industrializing nations like China and India to curb their own pollution. But this demand will be very costly to India and China, and will likely slow their development. To be fair, the industrial nations should help industrializing nation carry the burden of cutting pollution.
  1. Most of the growth in greenhouse emissions in the next two decades is predicted to come from China and India so they should not be allowed to renege on environmental agreements.
  1. Many small island nations and peoples will be completely destroyed by the predicted sea level rise. These people should be given choice of citizenship in any and all the countries that are most responsible for global warming, as well as all the money and resources they will need to immigrate and integrate into those countries.
  1. The ethnic majority in Telangana, India, are a minority in their state, and they are discriminated against. Telangana should be made into a different state.
  1. Granting Telangana statehood would cause numerous other ethnic minorities to demand statehood. The problem of discrimination against Telangana should be resolved by other means.
  1. Ms. Weinstein chose and paid a sperm donor, she chose and paid an egg donor, and she chose and paid a surrogate mother to be a gestational carrier and to deliver the baby. Ms. Weinstein had a contract with the surrogate mom in which the baby is agreed to belong to Ms. Weinstein. The surrogate mom should not have any rights over the baby – it belongs to Ms. Weinstein.
  1. Although I gave Spencer & Jutland exclusive publishing rights to my book, this was before e-books existed. So they don’t have a right to publish my novel electronically.
  1. Out of about 30,000 Islamic schools in Pakistan, only 50 schools are connected with terrorists. These schools must be indoctrinating children into extremism.
  1. In our culture property and honour follow the male line of the family. We value the honour of the male lineage more than anything, and we trace it for many generations. If a woman commits adultery she puts the legitimacy of her sons in question and so dishonours the family. If we cannot trust our women to stay faithful, our whole culture will disintegrate. It is therefore necessary for us to punish adultery harshly in order to deter misbehaviour. So for us, it is necessary to put adulterous women to death.
  1. Credit cards offered by the major retailers offer big discounts and no interest repayments. But they punish you harshly for missing a payment. Consumers should be wary of them.
  1. We live in a celebrity obsessed global culture, in which those who get the most attention are often people who have done nothing of real importance. We should stop idolizing sports and pop stars and start appreciating and funding real culture.
  1. Over half of Europeans believe that Islam is an intolerant religion. Before we allow Islam to continue to spread throughout Europe, we need to make sure it has done enough to curb intolerance.
  1. President Obama did not make any peace so he shouldn’t have been awarded the Nobel peace prize.
  1. Tom is socially awkward and takes things too literally. He rarely gets a joke. I have a friend that behaves similarly and he said it is because he has aspergers. Tom probably has aspergers too.
  1. The news media is so often unfair, superficial and incorrect. If it wants to be protected by freedom of the press it needs to shapeup and start delivering on the promise of keeping the public well-informed, the same promise that freedom of the press is premised on.
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