Routledge

Student Material

Chapter 3: Logic – deductive validity

Students’ material

A
Indicate whether or not each of the following arguments is valid or invalid

  1. P1) All horses have tails.
    P2) Kevin is a horse.
    C) Kevin has a tail.
  2. P1) If it’s raining, we need umbrellas.
    P2) It’s raining.
    C) We need umbrellas.
  3. P1) If it’s raining, we need umbrellas.
    P2) It’s not raining.
    C) We don’t need umbrellas.
  4. P1)  If it’s raining, we need umbrellas.
    P2) We need umbrellas.
    C) It’s raining.
  5. P1) Either John Campbell is a journalist or he is a chef.
    P2) John Campbell is not a journalist.
    C) John Campbell is a chef.
  6. P1) Either he is listening to the radio or he is working.
    P2) He is playing chess.
    C) He is not working.
  7. P1) If he’s listening to the radio, he’s not at work.
    P2) He’s not at work.
    C) He’s listening to the radio.
  8. P1) If he’s listening to the radio, he’s not at work.
    P2) He’s not listening to the radio.
    C) He’s not at work.
  9. P1) If he’s listening to the radio, he’s not at work.
    P2) He’s at work.
    C) He’s not listening to the radio.
  10. P1) If he’s listening to the radio, he’s not at work.
    P2) He’s not listening to the radio.
    C) He’s at work.

B
Indicate whether the following cases represent valid or invalid arguments

  1. The premises are all true and the conclusion is true.
  2. Some of the premises are false and the conclusion is true.
  3. The premises are all true and the conclusion is false.
  4. The premises are all false the conclusion is true.
  5. Some of the premises are true and the conclusion is true.
  6. The premises are all false and the conclusion is false.

C
Imagine arguments the premises and conclusions of which have truth values as indicated. Indicate whether the arguments could be valid.

  1. P1) T
    P2)T
    C) T
  2. P1) F
    P2) F
    C) T
  3. P1) F
    P2) F
    C1) F
    P3) T
    C2) T
  4. P1) F
    P2) F
    C) T
  5. P1) T
    P2) F
    C) T
  6. P1) T
    P2) F
    C) F
  7. P1) T
    P2) T
    C) F
  8. P1) T
    P2) F
    C) F
  9. P1) T
    P2) T
    C1) T
    P3) T
    C) F
  10. P1) F
    P2) F
    C) T

D
Are these arguments deductively sound? We have provided premises whose truth values we think you will know. If you don’t, find the relevant information here.

  1. P1) All sheep are herbivores.
    P2) Shrek is a sheep.
    C) Shrek is a herbivore.
  2. P1) All sheep are herbivores.
    P2) Shrek is a herbivore.
    C) Shrek is a sheep.
  3. P1) If Barack Obama is US President, his wife, Michelle Obama, is first  lady of the USA.
    P2) Barack Obama is US President.
    C) Michelle Obama is first lady of the USA.
  4. P1) The team that scores the most goals in a soccer match is the winner.
    P2) In the 2008 FA Cup Final Portsmouth scored the most goals.
    C) Portsmouth won the 2008 FA Cup Final.
  5. P1) Either Hilary Clinton or Barack Obama won the Democratic nomination for the 2008 US Presidential election.
    P2) Hillary Clinton won the nomination.
    C) Barack Obama did not win the nomination.
  6. P1) If the English monarch has sons, the eldest son is first in line to the throne.
    P2) Prince Charles, Prince of Wales, is the eldest son of the present English queen.
    C) Prince Charles is first in line to the throne of the English monarchy.
  7. P1) London is west of Moscow.
    P2) Moscow is west of Mumbai.
    P3) Mumbai is west of Bangkok.
    C) London is west of Mumbai and Bangkok.
  8. P1) If Knut is a polar bear, Knut eats seals.
    P2) Knut is not a polar bear.
    C) Knut does not eat seals.
  9. P1) Bill Clinton was US President before George W. Bush.
    P2) George W. Bush was US President before Barack Obama.
    P3) Robert De Niro was US President before Bill Clinton.
    C) Robert De Niro was US President before Barack Obama.
  10. P1) All fish are mammals.
    P2) All mammals live in water.
    P3) All salmon are fish.
    C) Salmon live in water.

E
For each question, indicate whether the pair of sentences express the same relation between propositions.

  1. a) If you treat your cat kindly, it will reward you will affection.
    b) Your cat will not reward you with affection unless you treat it unkindly.
  2. a) Either Elizabeth I was beautiful or Mary Queen of Scots was beautiful.
    b) Elizabeth I was beautiful only if Mary Queen of Scots was not beautiful.
  3. a) The Whalers will only beat the Marlins if they play a zone defence.
    b) The Whalers will not beat the Marlins unless they play a zone defence.
  4. a) Your children will not drive you to drink if you keep them properly occupied.
    b) Unless you keep them properly occupied, your children will drive you to drink.
  5. a) Either Jonah ate all the biscuits or Jethro ate all the biscuits.
    b) Jethro ate all the biscuits only if Jonah did not eat all the biscuits.
  6. a) Unless it was Jonah who ate all the chocolate, Norman ate all the chocolate.
    b) Either Norman ate all the chocolate or Jonah ate all the chocolate.
  7. a) If it’s sunny tomorrow, we can play tennis.
    b) Unless it’s sunny tomorrow we can’t play tennis.
  8. a) You can only come if you bring some beer.
    b) You cannot come unless you bring some beer.
  9. a) He’s either on Facebook or he’s on MySpace.
    b) If he’s not on Facebook, then he’s on MySpace.
  10. a) He’s either sleeping or he’s working.
    b) He only works when he’s not sleeping.

F
Indicate which argument tree correctly represents each of the following arguments.


  1. P1) Jack is a bear.
    P2) All bears eat honey.
    C) Jack eats honey.
    a)

    b) 

  2. P1) Jerry is a mouse.
    P2) Jerry is a rodent.
    C) Jerry is a small, furry creature.
    a)

    b) 

  3. P1) Boeing 737s are smaller than Boeing 767s.
    P2) Boeing 767s are smaller than Boeing 747s.
    C) Boeing 737s are smaller than Boeing 747s.
    a)

    b) 

  4. P1) All small children are noisy.
    P2) Sheila is a small child.
    C) Sheila is noisy.
    a)

    b) 

  5. P1) The Philosophy Department’s papers are too difficult.
    P2) The Philosophy Department’s staff are incompetent.
    C) The Philosophy Department should be closed down.
    a)

    b) 

  6. P1) The Philosophy Department’s papers are too difficult.
    P2) The Philosophy Department’s staff are incompetent.
    P3) Any Department whose papers are too difficult and whose staff are incompetent should be closed down.                                                                                                                
    C) The Philosophy Department should be closed down.
    a)

    b) 

  7. P1) If the cookie jar is empty then either someone ate all the cookies or someone stole all the cookies or the cookies were teletransported to another planet.
    P2) Brian ate all the cookies.
    C) The cookies were not stolen and the cookies were not teletransported to another planet.
    a)

    b) 

  8. P1) Boeing 737s are smaller than Boeing 767s.
    P2) Boeing 767s are smaller than Boeing 747s.
    C1) Boeing 737s are smaller than Boeing 747s.
    P3) Any aircraft that is smaller than a Boeing 747 is smaller than an Airbus A380
    C2) Boeing 737s are smaller than Airbus A280s.
    a)

    b) 

  9. P1) If Pete is a penguin, Pete can swim.
    P2) Pete is a penguin.
    C1) Pete can swim.
    a)

    b) 

  10. P1) Our manager does not treat staff with respect.
    P2) Our manager is rude to clients.
    C1) Our manager is a bad manager.
    P3) If our manager is a bad manager he should be demoted.
    C2) Our manager should be demoted.
    a)

    b) 

G.

Are these arguments deductively valid? Why/why not? If the argument isn’t valid try to come up with a situation in which all the premises are true but the conclusion is false.

1.
P1)       My llama is having a bad hair day.
P2)       Almost always, when my llama is having a bad hair day, the air is humid.
C)        The air is humid.

2.
P1)       My llama is having a bad hair day.
P2)       When my llama is having a bad hair day the air is humid.
C)        The air is humid.

3.
P1)       An apple never falls far from the tree.
C)        When this apple falls from the tree, it will not fall far.

4.
P1)       People often resemble their parents.
P2)       J.R. is greedy.
C)        J.R.’s mother or father (or both) must have been greedy.

5.
P1)       Every saint with a divine message for humanity was ridiculed before being recognized as a messenger of God.
P2)       Now, the Reverend Moon is being ridiculed.
C)        The Reverend Moon is a messenger of God.

6.
P1)       Every saint with a divine message for humanity was ridiculed before being recognized as a messenger of God.
C)        Everyone who claims to be a messenger of God and is ridiculed is actually a messenger of God.

7.
P1)       Humans have gene ‘x’.
P2)       Humans who’s ‘x’ gene is faulty have problems speaking.
P3)       Neanderthals also had gene ‘x’.
C)        Neanderthals could speak.

8.
P1)       Wherever gene ‘x’ occurs language also occurs.
P2)       Neanderthals had gene ‘x’.
C)        Neanderthals had language.

9.
P1)       Two of my friends work for the Police.
P2)       The starting salary is high at the police.
P3)       Working for the police has lots of benefits like flexible hours, tuition funding, and large superannuation employer contribution.
P4)       Working for the police is a contribution to society.
C)        I should work for the police.

10.
P1)       Working for the police is a contribution to society.
P2)       I’m going to work for the police.
C)        I’m going to contribute to society.

11.
P1)       Large numbers of people are dying from starvation in the third world because grain supplies are too low.
P2)       Producing bio-fuels takes land away from grain production.
P3)       The only way to grow sufficient grain is to stop bio-fuels production.
P4)       We should do anything we can to stop world hunger.
C)        We should stop producing bio-fuels.

12.
P1)       This news program is advertised as giving both sides, and of being in-depth and impartial.
P2)       I don’t think that the people involved with this reputable channel are going to lie to me.
C)        This news program is going to give both sides and will be in-depth and impartial.

13.
P1)       This news program is advertised as giving both sides, and of being in-depth and impartial.
P2)       Advertising on TV isn’t always accurate and truthful.
C)        This news program is not going to give both sides and will not be in-depth and impartial.

14.
P1)       This news program is advertised as giving both sides, and of being in-depth and impartial.
P2)       Advertising isn’t always accurate and truthful.
C)        This news program may not give both sides and may not be in-depth and impartial.

15.
P1)       The meat industry inflicts terrible suffering.
P2)       The meat industry is unnecessary for human survival.
C)        The meat industry should be eliminated.

16.
P1)       The meat industry inflicts terrible suffering.
P2)       The meat industry is unnecessary for human survival.
P3)       We should stop doing anything that inflicts terrible suffering and is unnecessary for human survival.
C)        We should eliminate the meat industry.

17.
P1)       A person who is a true believer of religion ‘x’ will not do evil deeds.
P2)       Religions are not responsible for deeds carried out by those who are not true believers.
C)        Religion ‘x’ is not responsible for the evil deeds it is accused of causing.

18.
P1)       The argument above commits the “No True Scotsman” fallacy.
P2)       Conclusions of fallacious arguments are not sufficiently supported by those arguments.
C)        The conclusion of the argument above is false.

19.
P1)       The argument above commits the “No True Scotsman” fallacy.
P2)       Whenever a fallacy is committed, the conclusion of the argument is false.
C)        The conclusion of the argument above is false.

20.
P1)       The argument above commits the “No True Scotsman” fallacy.
P2)       Conclusions of fallacious arguments are not sufficiently supported by those arguments.
C)        The conclusion of the argument above isn’t sufficiently supported by that argument.

21.
P1)       The Bible says that all species of animals were created by God.
C)        All species of animals were created by God.

 

H.

Arguments 16, 17, and 20 above are important arguments to settle. Argument 17 is also a popular one. Try evaluating these arguments for soundness. After you have done so, find a classmate that reached a judgment that is opposite to yours to discuss your results. Is the necessary evidence easily available, clear and uncontroversial? As a whole class, you can try to formulate a “research plan” detailing the information which is needed to settle the issues, and where and how to get it.


I.

Add a missing premise to these arguments so that they will be valid.

1.         P1) The premises of John Campbell’s argument are true.
P2)                                                                              
C) John Campbell’s argument is bad.

2.         P1) The premises of John Campbell’s argument are true.
P2)                                                                              
C) John Campbell’s argument is good.

3.         P1) Most people believe that the invasion of Iraq was morally wrong.
P2)                                                                              
C) The invasion of Iraq was morally wrong.

4.         P1) Almost everyone eats meat.
P2)                                                                              
C) Eating meat is not morally wrong.

5.         P1) You smoke.
P2)                                                                              
C) It’s okay for me to smoke.

6.         P1) Mrs Brown says it’s acceptable for parents to smack their kids.
P2) Mrs Brown raised eight kids successfully.
P3)                                                                                
C) It’s acceptable for parents to smack their kids.

7.         P1) Either John Smith or Peter Jones won the recent election for Mayor of Stone City.
P2)                                                                                 
C) Peter Jones is now the Mayor of Stone City.

8.         P1)
P2) Manchester Utd are top of the table.
C) Liverpool lost against Arsenal.


 

J.

Are the following deductive arguments sound? Why/why not? If you can’t be sure, explain why.

1.         P1) If many Unidentified Flying Objects (UFOs) are alien visitations, then the governments may be conspiring to hide this fact from the public.
P2) Many UFOs are alien visitations.                                 
C) The governments may be conspiring to hide the fact that many UFOs are alien visitations from the public.

2.         P1) The Bible says that we should not murder.
P2) The Bible is the word of God.                
C) We should not murder.


K.

Choose from the options below what you think are important lessons from chapter three.

1.

  1. If an argument is not deductively valid its conclusion is false.
  2. If an argument is not deductively valid it is not a good argument.
  3. If an argument is not deductively valid its conclusion is not well supported.
  4. If a deductive argument is not valid its conclusion is false.
  5. If a deductive argument is not valid its conclusion is not well supported.

2.

  1. If I can imagine situations in which the conclusion is false the argument is invalid.
  2. If at least one of the premises is false or controversial, then the argument is invalid.
  3. If the conclusion is actually false, then the argument is invalid.
  4. If I can imagine a situation in which the conclusion is false but the premises are true then the argument is invalid.
  5. If all the premises are false the argument can’t be valid.
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