Instructor Manual

Chapter 5: The practice of argument-reconstruction

Students’ material: solutions

The exercises provided in the students’ section can be extended for classroom or assessment use as follows.

Exercise A
Ask students to make their own valid/inductively forceful arguments that mirror the structures of the arguments given.

Exercise C
Ask students to construct valid arguments in which the covering generalisations serve as connecting premises.

Exercise D
Ask students to construct sound arguments using one of each of the pairs of generalisations, where possible (some of the generalisations given aren’t true). Where it is not possible to use either of the generalisations as they stand, ask students to narrow the scope of one of the generalisations so that the argument in which it is used is sound.

Exercise E/F

Ask students to represent the arguments in exercise E as argument trees.

 

Further exercises

A
Reconstruct the following arguments to make them valid or inductively forceful as appropriate adding the missing premise.

  1. If it is the case that life would be dull without its little challenges, it is clear we are in the most exciting of times!
  2. This economic crisis doesn’t just affect individuals. It has the power to devastate whole economies. We must act to ensure that it does not do so.
  3. Raising the level at which the top tax rate will apply is welcome because essential public servants such as teachers, nurses and police officers will no longer pay the top tax rate.
  4. The global rise in food prices is an opportunity for the more affluent to fight obesity. If we buy less food, we’ll eat less food.
  5. Our armed forces deployed overseas no longer fight but are engaged in rebuilding infrastructure. There is no longer any reason not to introduce compulsory military service for young men and women.
  6. A roadside sign advertising Christmas trees for sale earned its owner a £10,000 fine. But the many roadside vans selling fireworks at New Year are exempt. This is grossly unfair. The lesser offences should not be tackled first just because the perpetrators are less easy targets.
  7. While out shopping this Christmas I haven’t been elbowed nor had anyone be rude to me and complete strangers have smiled and passed the time of day. The economic downturn is probably not such a bad thing.
  8. It’s a good thing that Mica the Clown won The X-Factor. None of the other acts deserved to win; they didn’t appeal to the whole family.
  9. The United Nations has become increasingly irrelevant to today’s geopolitical situation. It seems unable to do anything to reduce hunger and suffering, to clean up the environment or to maintain a lasting peace in any ongoing conflict.
  10. Our Finance Minister should offer tax incentives to companies that invest in Research and Development. Most other developed economies have some form of tax incentives for Research and Development.

B
The following passages offer material for argument-reconstruction. If you are using these in a classroom situation, our experience is that it is most productive to take students through each stage of the reconstruction.

  1. Residents of this city need to know who is responsible for desecrating it. Every new public building should have a plaque at its doorway showing the names of the financiers, the developers, the architects and the builders.
    This would deter the building of abominations; it might even make local body politicians think twice before giving the go-ahead. In fact, we could insist the mayor concerned have his or her name included on the plaque for the sake of historical evaluation.
    From a Letter to the Editor, New Zealand Herald, 07/05/07 (minor adaptations)
  2. A conversation
    Joanna: Do you think we’ll  be able to  find a parking space at the mall this afternoon?
    Donna: Of course not, it’s Saturday and it’s after lunch.
    Joanna: I don’t think we should bother to go then.
  3. Reducing household debt
    With the worldwide economic downturn and the plunge in house prices, offering advice to people having difficulty making mortgage repayments is a noble gesture. However, the list of options on the front page (December 21) has its priorities all wrong. The first three options (repayment holiday, interest only and mortgage term extension) all have the end result of increasing debt long-term, which is why they should be last resorts for people in trouble. The last three options (increasing income, decreasing expenditure and selling off unnecessary items) are more painful but by far more financially sound in that they decrease debt. They should have appeared first on the list.
    Stephen McBride, Auckland, ‘Letter to the Editor’, Sunday-Star Times, 28/12/08
  4. It’s the environment
    Given the gravity of the situation we face globally in the coming years, it would seem a good time to start reviewing a few of the paradigms that have guided us to where we, as the custodians of the planet, find ourselves. Left, Right, Centre, for instance. Surely these horizontal political categories are redundant in a world where communism is dead and capitalism has terminal cancer. Given that the new imperative for human survival is environmental responsibility a more appropriate gauge of commitment – by politicians, corporations, scientists and citizens alike – would be a vertical indicator  graded in shades of green, the environment being so glaringly the most important of all present considerations.
    Wayne O’Connell, Dunedin, Letter to the Editor, Sunday-Star Times, 08/12/08 (adapted)
  5. Here the reconstruction would be of the argument contained in the quotes from Barack Obama.
    Today, more than ever before, science holds the key to our survival as a planet and our security and prosperity as a nation’, Obama announced. ‘It's time we once again put science at the top of our agenda and ... worked to restore America's place as the world leader in science and technology.’
    Extracted from http://www.guardian.co.uk/world/2008/dec/21/obama-climate-change-john-holdren, accessed 21/12/08.
  6. Here’s a much longer piece, which could be used in its entirety or in parts. It also provides good practice in identifying and setting aside extraneous material.
    Spying police abuse their powers
    Something is amiss when a police informer spends a decade spying on protest groups. Rob Gilchrist has admitted he did so, forwarding information to the police not only about planned protests but about the personal lives of members. The police unit that ran him was the Special Investigation Group, whose job is to look after counterterrorism and national security. It is impossible to justify this kind of policing. It has exceeded its brief and infringed important human rights.
    The Labour government set up these groups following September 11, when the world was rightly obsessed with terrorism. No sensible person can object to the police taking a close interest in suspected terrorist groups: if they did not infiltrate the local al Qaeda cell, they would not be doing their job. But these are not terrorist groups. 
    It is true that Greenpeace and the peace groups and animal welfare lobbies that Gilchrist infiltrated sometimes break the law.  Greenpeace’s attempt to block the sailing of a coal ship from Lyttelton harbor may well have been illegal, and Greenpeace cheerfully agrees it sometimes breaks the law. So does the Happy Valley protest group. They plead a wider brief: they break the law to highlight some greater evil.
    Blockading coal ships and trains and digging up Solid Energy’s front lawn, in any case, do not amount to terrorism and nor are they a threat to national security. They are acts of civil disobedience that have for a long time been treated with a certain tolerance by the authorities. It may well infuriate politicians or officials when protesters sit down on a motorway, for example, and it might well cause annoyance to the public.  But most people recognise that these kinds of activities, provided they don’t go too far, are part of the life of a democracy.
    The right to protest is a fundamental part of that democracy, and infiltrating a protest group has a chilling effect not only on the members but on wider society. If people think police routinely place informers within these groups, many will be more reluctant to get involved and exercise their right to dissent. Long-term surveillance of protest groups is a fundamental breach of our rights to free speech and association. So police must not do it unless there is an extremely cogent reason that will stand up to outside scrutiny.
    Gilchrist himself has shown that there were no such grounds for his long stint as a police informer. After all that time, he concludes that the protesters were ‘good people trying to make a better world’, and he is sorry for what he has done. As an epitaph for this whole sorry episode, these words are hard to beat.
    What has happened, it seems, is that the local police have overreacted to the threat of terrorism, as politicians and officials have done in many other western countries. It’s a familiar pattern. Amid the understandable horror at the mass murder at the Twin Towers, governments sacrificed important liberties to an imagined ‘security’. Perhaps the worst excesses took place in the United States, where the Bush administration permitted torture of suspects and then denied it had done so. Waterboarding is torture: ask John McCain, who knows about torture. The Bush regime also permitted men to be held at Guantanamo Bay without benefit of habeas corpus and other basic parts of the western justice system, and incurred the wrath of the US Supreme Court.
    The case of Rob Gilchrist pales in comparison with these dreadful acts, but it is part of the same panicked over-reaction to genuine terrorism. The worrying thought remains: how many other such informers do the police have?
    Editorial, Sunday-Star Times, 14/12/08

C

Put the arguments below into standard form.  To do this, you will need to make explicit premises and/or conclusions (including intermediate conclusions) that are implicit in the argument as it is presented. The number of implicit propositions that you will need to make explicit is given after each argument.

 

1. The government should not subsidise the arts. Government funds should only be spent on things we need for our basic survival.
(One implicit premise.)

 

2. In his will, Alfred Nobel, the founder of the Nobel Prize, said that the Nobel Peace Prize should be awarded to the person who has done the most or best work promoting peace that year. Barack Obama was awarded the prize in 2009 so he did the most or best work promoting peace in that year.
(One implicit premise.)

 

3. In the Super 14 rugby union competition, the team based in Canberra are called the Brumbies. They are named after brumbies, a type of wild horse. The team based in Durban in the same competition are called the Sharks. It's clear that the Brumbies will beat the Sharks. This is because, unlike horses, sharks cannot live on dry land, which is where rugby is played.
(One  implicit premise.)

 

4. Hyenas are more closely related to cats than to dogs. So you probably can't train hyenas to fetch sticks.
(Three implicit premises.)

 

5. If Jack Plane had given evidence at Alan Key's trial, Key would have been found guilty of the murder of Pat Locke. And nothing short of death would have stopped Plane from spilling the beans at the the trial. Key wasn't found guilty of the murder of Locke, so Plane must have died before giving evidence at the trial.
(One implicit conclusion.)

 

6. It's clear that people should use aeroplanes less often. If God had wanted us to fly, he'd have sent us the tickets!
(Two implicit premises, one implicit conclusion.)

 

7. Toast is not the best breakfast: all those crumbs make a mess. And a cooked breakfast just takes too long to make. The only other option is cereal: it's the best breakfast.
(Two  implicit premises, one  implicit conclusion.)

 

8. If Macs were better than PCs then more people would have Macs than have PCs. Further, Macs are more expensive than PCs. And you should only buy a more expensive computer if it's better than a cheaper one.
(One implicit premise, two implicit conclusions.)

 

9. If he can't do it, then he should let someone who hasn't tried it have a go. And everybody else has had a go except me. So he should let me have a go.
(Two implicit premises, two implicit conclusions.)

 

10. If we concentrate on climate change, the world economy will collapse, leading to hardship and suffering for much of the world's population. But if we concentrate on the world economy, climate change will continue apace. Again, the result will be hardship and suffering for many millions of people. Whatever we do, then, hardship and suffering will be the fate of many, many people in the years ahead.
(One implicit premise, two implicit conclusions.)

 

Answers

(Propositions that have been made explicit are in italics.)

 

1.
P1) Government funds should only be spent on things we need for our basic survival.
P2) The arts are not needed for our basic survival.
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C) The government should not subsidise the arts.

 

2.
P1) In his will, Alfred Nobel, the founder of the Nobel Prize, said that the Nobel Peace Prize should be awarded to the person who has the most or best work promoting peace that year.
P2) Barack Obama was awarded the Nobel Peace Prize in 2009.
P3) In 2009 the Nobel Peace Prize was awarded to the person it should have been awarded to.
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C) Barack Obama did the most or best work promoting peace that year.

 

3.
P1) In the Super 14 rugby union competition, the team based in Canberra are called the Brumbies.
P2) The Brumbies are named after brumbies, a type of wild horse.
P3) In the Super 14 rugby union competition, the team based in Durban are called the Sharks.
P4) Unlike horses, sharks cannot live on dry land, which is where rugby is played.
P5) When two sports teams are named after animals, and one of the animals cannot live in the environment in which the sport is played while the other can, then the team named after animal which can live in the playing environment will beat the other team.
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C) The Brumbies will beat the Sharks.

 

4.
P1) Hyenas are more closely related to cats than to dogs.
P2) Cats can't be trained to fetch sticks.
P3) Dogs can be trained to fetch sticks.
P4) If an animal is more closely related to cats than to dogs, it is unlikely that it can be trained to fetch sticks.
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C) Probably, hyenas can't be trained to fetch sticks.

 

5.
P1) If Plane had given evidence at Key's trial, then Key would have been found guilty of the murder of Locke.
P2) Key wasn't found guilty of the murder of Locke.
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C1) Plane didn't give evidence at the trial.
P3) Nothing short of death would have stopped Plane from giving evidence at the trial.
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C2) Plane died before giving evidence at the trial.

 

6.
P1) If God had wanted us to fly, he'd have sent us the tickets.
P2) God didn't send us the tickets.
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C1) God doesn't want us to fly.
P3) If God doesn't want us to fly, we should fly by aeroplane less often.
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C) People should use aeroplanes less often.

 

7.
P1) Eating toast for breakfast makes a (crumby) mess.
P2) If a breakfast food makes a mess, it's not the best breakfast.
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C1) Toast is not the best breakfast.
P3) A cooked breakfast takes too long to make.
P4) If a breakfast food takes too long to make, it is not the best breakfast.
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C2) A cooked breakfast is not the best breakfast.
P5) The only options for breakfast are toast, a cooked breakfast, and cereal.
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C3) Cereal is the best breakfast.

 

8.
P1)  If Macs were better than PCs then more people would have Macs than have PCs.
P2) It is not the case that more people have Macs than have PCs.
--------------------------------------------------------------------
C1) Macs are not better than PCs.
P3) Macs are more expensive than PCs.
P4) You should only buy a more expensive computer if it's better than a cheaper one.
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C2) You should not buy a Mac.

 

9.
P1) If he can't do it, then he should let someone who hasn't tried it have a go.
P2) He can't do it.
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C1) He should let someone who hasn't tried it have a go.
P3) Everybody else has had a go except me.
P4) If everybody else has had a go except me, then I'm the only person who hasn't tried it.
--------------------------------------------------------------------
C2) I'm the only person who hasn't tried it.
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C3) He should let me have a go.

 

10.
P1) If we concentrate on climate change, the world economy will collapse.
P2) If the world economy collapses, then much of the world's population will face hardship and suffering.
--------------------------------------------------------------------
C1) If we concentrate on climate change, then much of the world's population will face hardship and suffering.
P3) If we concentrate on the world economy, climate change will continue apace.
P4) If climate change continues apace, then there will be hardship and suffering for many millions of people.
--------------------------------------------------------------------
C2) If we concentrate on the world economy, then there will be hardship and suffering for many millions of people.
P5) We can only concentrate on climate change, or on the world economy, but not on both.
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C3) Whatever we do many, many people will face hardship in the years ahead.