Question Database: Critical Thinking
Validity and truth
True or false?
If all the premises of an argument are true, the conclusion must be true too.
A. True
B. False
Answer: B
Topic:
Validity and truth
Course Level:
First year, critical thinking.
Notes:
Example:
1. Australia has six states.
2. Each state has exactly one capital.
Therefore:
C. Australia has seven state capitals.
2006: All correct
True or false?
If the conclusion of an argument is true, then all the premises must be true too.
A. True
B. False
Answer: B
Topic:
Validity and truth
Course Level:
First year, critical thinking.
Notes:
2006: All but 1 correct.
True or false?
If the conclusion of a valid argument is true, it's premises must be true too.
A. True
B. False
Answer: B
Topic:
Validity and truth
Course Level:
First year, critical thinking.
Notes:
True or false?
A valid argument can have all false premises and a true conclusion.
A. True
B. False
Answer: A
Topic:
Validity and truth
Course Level:
First year, critical thinking.
Notes:
2006: Before discussion: 50-50. After discussion: 60-40.
True or false?
A valid argument with a false conclusion cannot have premises which are all true.
A. True
B. False
Answer: A
Topic:
Validity and truth
Course Level:
First year, critical thinking.
Notes:
2006: Initial: 10% A, 90% B. After explanation by lecturer: 100% A
If all the premises of an argument are true and the conclusion is false, then the argument is not valid.
A. True
B. False
Answer: A
Topic:
Validity and truth
Course Level:
First year, critical thinking.
Notes:
Labradors are dogs and all dogs have tails. Therefore, all animals with tails are dogs.
Which of the following evaluations of this argument are correct?
I. The premises of the argument are all true, but the conclusion is false, so the argument is invalid.
II. Labradors are not the only kind of dog, so one of the premises is false.
III. Some animals with tails are not dogs, so the conclusion of the argument is false.
IV. The conclusion does not follow from the premises because some animals have tails, but are not dogs.
A. II only
B. IV only
C. I and III only
D. III and IV only
Answer: C
Topic:
Validity and truth
Course Level:
First year, critical thinking.
Notes:
2006: Before discussion: 49% C , 49% D, 2% Bs. After discussion: 95% C, 5% D
1. All leopards are mammals.
2. All mammals are carnivores.
Therefore:
C. All leopards are carnivores.
Do the premises support the conclusion?
A. Yes
B. No
Answer: A
Topic:
validity and truth
Course Level:
First year, critical thinking.
Notes:
A: Yes. Although one of the premises is false, IF all the premises were true, THEN the conclusion would be. So an argument can satisfy the second condition (support) without satisfying the first (truth).
1. If it rains on Saturday, the party will be cancelled.
2. The party was cancelled.
Therefore:
C. It rained on Saturday.
Do the premises support the conclusion?
A. Yes
B. No
C. Can’t tell
Answer: B
Topic:
validity and truth
Course Level:
First year, critical thinking.
Notes:
B. No. Even IF all the premises were true, the conclusion need not be. The party might have been cancelled for some other reason. Notice that the premises still fail to support the conclusion, even if the conclusion is true or plausible.
Deductive validity and argument forms
A deductively valid argument can have all true premises and a false conclusion.
A. True
B. False
Answer: B
Topic:
Deductive validity
Course Level:
First year, critical thinking.
Notes:
If the argument is deductively valid it is impossible for all the premises to be true and the conclusion false: if all the premises are true, the conclusion MUST be true.
All Kangaroos are marsupials. Fish are not kangaroos. Therefore, fish are not marsupials.
Opinion poll: Is this argument deductively valid?
A. Yes
B. No
C. Not sure
Answer:
Topic:
Deductive validity
Course Level:
First year, critical thinking.
Notes:
Poll the students first, to see if they think this is a valid argument, before using the following sequence of questions to illustrate the 'method of counter-example'.
All Kangaroos are marsupials. Fish are not kangaroos. Therefore, fish are not marsupials.
This argument is an instance of which one of the following forms:
A.
1. All As are Bs
2. All Cs are As
Therefore:
C. Cs are not Bs
B.
1. All As are Bs
2. As are not Cs
Therefore:
C. Cs are not Bs
C.
1. All As are Bs
2. Cs are not As
Therefore:
C. Bs are not Cs
D.
1. All As are Bs
2. Cs are not As
Therefore:
C. Cs are not Bs
Answer: D
Topic:
Deductive validity
Course Level:
First year, critical thinking.
Notes:
1. All As are Bs
2. Cs are not As
Therefore:
C. Cs are not Bs
Which one of the following substitutions shows this form to be invalid?
A. A = dogs, B = mammals, C = cats
B. A = Labradors, B = dogs, C = cats
C. A = mammals, B = dogs, C = cats
D. A = Labradors, B = mammals, C = fish
Answer: A
Topic:
Course Level:
First year, critical thinking.
Notes:
1. All As are Bs
2. Cs are not As
Therefore:
C. Cs are not Bs
A = dogs
B = mammals
C = cats
1. All dogs are mammals (T)
2. Cats are not dogs (T)
Therefore:
C. Cats are not mammals (F)
This instance has true premises and a false conclusion, showing the form to be invalid (not every argument of this form with true premises has a true conclusion).
All Kangaroos are marsupials. Fish are not kangaroos. Therefore, fish are not marsupials.
Is this argument deductively valid?
A. Yes
B. No
C. Not sure
Answer: B
Topic:
Deductive validity
Course Level:
First year, critical thinking.
Notes:
(Ask the opinion poll question again, to see if more students have the right answer).
Although the conclusion is true, it does not follow (deductively) from the premises (which also happen to be true). The argument does not have a valid FORM. So it is not deductively valid.
Belief bias in assessing validity
For each of these arguments, say whether:
A. The argument is valid.
B. The argument is invalid.
1. All things with four legs are dangerous. Poodles are not dangerous. Therefore, poodles do not have four legs.
2. All mammals walk. Whales are mammals. Therefore, whales walk.
3. All African countries are hot. Canada is not an African country. Therefore, Canada is not hot.
4. All things that are alive drink water. Televisions do not drink water. Therefore, televisions are not alive.
5. All nuts can be eaten. Rocks cannot be eaten. Therefore, rocks are not nuts.
6. All things made of wood can be used as fuel. Petrol is not made of wood. Therefore, Petrol cannot be used as fuel.
Answer: 1, 2, 4 and 5 are valid
Topic:
Validity. Myside bias.
Course Level:
First year, critical thinking.
Notes:
This question was used to illustrate the myside bias effect in argument evaluation.
These six arguments were taken from those used in a study of confirmation bias in syllogistic reasoning (Markovits, H., & Nantel, G. (1989). "The belief-bias effect in the production and evaluation of logical conclusions".Memory and Cognition, 17, 11-17. See also: Sá, W. C., West, R. F., & Stanovich, K. E. (1999). "The domain specificity and generality of belief bias: Searching for a generalizable critical thinking skill." Journal of Educational Psychology , 91 (3), 497-510).
In Q4-6, the truth-value of the conclusion conforms to the validity of the argument: these are either valid arguments to true conclusions (4,5) or invalid arguments to false conclusions (6).
In Q1-3, the truth-value of the conclusion does not conform to the validity of the argument: these are either valid arguments to false conclusions (1-2) or invalid arguments to true conclusions (3).
Myside bias is the tendency for people tend to judge arguments in terms of the acceptability of the conclusion; if they accept the conclusion, they will be more likely to think the argument is valid than if they don't. So if there is a myside bias effect, people will tend to find Q1-3 harder and Q4-6 easier.
In the 2006 lecture, this was borne out by students' responses: 85% of students got Q1-3 correct, 90% fot Q4-6 correct.