Instructor Manual
Chapter 3: Logic – deductive validity
Instructors’ material
The self-assessment exercises can be extended for use by instructors. Here are some suggestions:
Exercise A
Ask students to construct their own valid arguments following the structures of the arguments given here that are valid.
Exercise B
Students could be asked to construct arguments the premises of which have the truth-values indicated. This could be extended further by asking students whether or not the resulting arguments are deductively sound.
Exercise C
Ask students to construct their own arguments as per the suggestion (above) for Exercise B.
Exercise D
The aim of this exercise is to reinforce and extend students’ understanding of deductive soundness by requiring that the correct connection is made between validity and deductive soundness. Although some hints have been provided with the solutions, for some students it may pay to re-examine the exercise in a classroom setting.
Exercise E
The inferences in which the premises support
the conclusion or the intermediate conclusion independently of each other are,
strictly speaking, relying on implicit premises. Thus, this exercise lends
itself to extension by asking students to identify and supply the missing
premises where appropriate.
Here are more exercises for class/assessment purposes:
a) Identify premises and conclusions.
b) Put the propositions into the
standard form.
c) Say whether or not you think the argument is deductively
valid.
d) Explain your answer to C. Hint: 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.
e) If the argument isn’t deductively valid make it deductively
valid by adding or changing a premise and/or by changing the conclusion.
1.
Given enough time the Iranians will overthrow any oppressive regime.
The ruling religious establishment in Iran is an oppressive regime. Given enough
time the Iranians will overthrow the ruling religious establishment.
2.
In the past, opposition protesters always used important religious or
national days for their protests. Tomorrow is the most holy day of the year.
Tomorrow there will be a protest by the opposition.
3.
Kelly is 13 years old. She is an experienced and competent sailor. She
has been training as a solo sailor for several years. She has a yacht that is
ready to sail around the world. Kelly wants to be the youngest person to sail
around the world alone, and her parents support her decision to do so. That’s
why I believe that Kelly should be allowed to sail around the world alone.
4.
A policeman was shot in a gun battle in the south of the city today.
This area of the city is full of gangs, and when there is a gun battle there it
is always between the police and the gangs or between rival gangs. The policeman
must have been shot by a gang member.
5.
Soccer is a dangerous sport. Children should not play dangerous sports,
so they shouldn’t play soccer.
6.
People that overdose on heroine and are not taken to hospital
immediately will die from it. Sheena was addicted to heroin before she died at
home at age 24. She did not have any medical problems, so I think she overdosed
on heroine.
7.
A boat that carries passengers for pay should be certified to do so.
This boat is not certified so it doesn’t carry passengers for pay.
8.
The cost of a super-yacht can be more than enough to feed one hundred
thousand starving children in Africa for a whole year. The amount of enjoyment a
billionaire can get out of his super-yacht in a year pales in comparison to the
suffering of a hundred thousand starving children. There can not be moral
justification for owning super-yachts in a world that has starving children.
9. Whenever a policeman has unpaid sex with a prostitute he coerced her into it. John is a policeman and he had unpaid sex with Paula – a prostitute. So despite the fact that they seem to like each other, he coerced her into having sex with him.
10.
Every year toddlers die by being run over by reversing cars. Making it
compulsory that new cars have reversing sensors or cameras would prevent many
such incidents from occurring. This requirement will not add much to the price
of a new car and is technically and legally feasible. We should do anything that
will help save lives and is not too costly, so we should require all new cars to
have reversing sensors or cameras.
11.
When a Jewish memorial is vandalized it is always by anti-Semites. The
defendants are anti-Semites.
12.
A computer technician was caught stealing children’s pictures from
computers he was given to repair.
Provide a sentence expressing the if-then proposition equivalent to the proposition expressed by each of the following:
- She only eats oysters if she’s by the seaside.
- The Government will collapse unless the Prime Minister resigns.
- If there is no rain tonight, there won’t be enough water for the plants.
- Either Melissa or Anya will win America’s Next Top Model.
- Unless you eat your broccoli, you won’t grow big and stong.
- Murray will only win if Federer makes too many unforced errors.
- The aircraft can’t take off unless all passengers are seated and have their seatbelts fastened.
- Either she’ll wear the Jimmy Choo sandals or the Lanvin ballet flats.
- West Ham will be relegated unless Stoke lose at Tottenham.
- She’ll either hit a birdie at the eleventh hole or she’ll put the ball in the rough.
Many of the arguments provided already offer examples for practice drawing argument trees. Here are some more. Since they are repeated from self-assessment exercise E in Chapter 1, they could also be used to demonstrate how to write extended arguments in standard form (omitting indicator words, etc.). Strictly speaking, some of these arguments are incomplete. To extend the exercise, students could be asked to provide the missing premises and draw new tree-diagrams to represent the complete argument. Question 2 offers a good launching point for the ensuing discussion of inductive arguments in Chapter 4. Since the exercise does not require the assessment of the arguments, the conclusion is not preceded by ‘Probably’, as discussion of why we do this does not appear until Chapter 4.
- P1) Geoff is a goldfish.
P2) No goldfish are mammals.
C1) Geoff is not a mammal.
P3) All mammals are warm-blooded
C2) Geoff is not warm-blooded. - P1)If we take my car to class we’ll be on time.
P2) If we take the bus we’ll be late for class.
P3) If we’re late for class, we’ll miss the test
C1) We should take my car to class.
P3) My car is very low on gas.
C2) If we take my car we will probably run out of gas.
P4) If we run out of gas we will be late for class.
P5) If we take your car, we will get to class on time.
P6) If we get to class on time, we won’t miss the test.
C3) We should take your car. - P1) On the night of Professor Peacock’s death Mrs White observed
Lady Scarlet in the library pulling a rope tight around Professor Peacock’s
neck.
P2) The rope and Professor Peacock’s jacket were later found to bear traces of DNA that are a 99.9% match with Lady Scarlet’s DNA.
C1) Lady Scarlet killed Professor Peacock in the library with the rope.
P3) If Lady Scarlet is the killer, then Colonel Mustard is innocent of Lady Scarlet’s murder.
P4) If he is innocent, he should be released immediately.
C2) Colonel Mustard must be released without delay. - P1) All those who caused the latest financial crash should bear
responsibility.
P2) Bankers who made bad loans caused the crash.
C1) They should be held responsible.
P3) Bankers were able to make those loans because Governments failed to regulate banking systems properly.
C2) Governments must take responsibility as well.
P4) We elected those Governments.
C3) We should accept some responsibility for the mess we are in. - P1) Consumer confidence is declining
P2) Whenever consumer confidence declines the dollar loses value.
C1) We can expect the dollar to become weaker against international currencies.
P3) When the dollar is weaker, inflation rises.
C2) It’s reasonable to expect that prices will rise.
P4) When inflation increases central banks increase interest rates.
C3) Interest rates will go up.
Exercise H
The common focus on informal logic in critical thinking courses may unintentionally lead students to think that subject-specific knowledge is not as important for critical thinking. This exercise can be used to show that important arguments often rely on facts which are not so easy to ascertain, and which need to be studied in depth.
Exercise J
Argument 1 presents another opportunity to deal with controversial facts. Some students who believe deeply in the truth of the propositions of argument 2 may not notice that to be valid, another premise needs to be added. Argument 2 can also be used to highlight questions of truth and plausibility.
Exercise K
This exercise highlights some of the common obstacles which students need to surpass before they could use the concept of deductive validity appropriately.
Multiple Choice Questions for chapter 3
This should be a relatively easy exercise. It is as much an exercise in reading comprehension as it is in deductive validity. In argument 6 “has two healthy children” does not preclude the possibility that they are adopted.