Critical Thinking |
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These sample quizzes model precisely the format of the quizzes that will be given in the course. Further, the general format that they follow mirrors the different sections of the Logic Exam that will conclude the course. In order to make the best use of these sample exams, you should try to "take" the quiz completely before viewing the solutions.
1. Reconstruction Quiz
This quiz is intended to test your ability to identify the parts of
an argument (premises and conclusions), to identify the argument type,
and to represent the argument in logical symbols.
2. Fallacy Quiz
This quiz is intended to test your ability to identify and diagnose
fallacious forms of reasoning in arguments.
3. Deductive Validity Quiz
This quiz is intended to test your ability to determine the logical
quality (validity) of complex deductive arguments.
To ensure character equivalences across the net, the following symbols will be used throughout the Deductive Validity Quiz samples:
~ = not
& = and
v = or
--> = if/then
For each of the following, (a) reconstruct the argument in standard form; (b) identify the the kind of reasoning (deductive or inductive) and argument pattern (modus ponens, dilemma, generalization, etc.); and (c) symbolize the argument.
1. Ethel's Ford was a real lemon. It seems like it was always in the shop, if it wasn't sitting by the side of the road, crippled and unable to move. Now that I think about it, Jose's Ford never seems to have run very well either. And the new Ford sports car that Elaine bought was recalled after only three months. That just shows that Fords are lousy cars.
(a)
(b)
(c)
2. I'm really in a bind. If I complain about my boss's treatment of me, he'll probably make my life miserable. But on the other hand, if I don't do anything, he'll continue to take advantage of me by giving me the worst work schedules of anyone in the company. What other alternative is left to me? Either I complain, or I refrain from complaining.
(a)
(b)
(c)
For each of the following, (a) reconstruct the argument in standard form; (b) identify the the kind of reasoning (deductive or inductive) and argument pattern (modus ponens, dilemma, generalization, etc.); and (c) symbolize the argument.
1. Rock bands that manage to produce music that is popular over a span of time in very different musical eras are truly great. So the Rolling Stones are a truly great rock band.
(a)
(b)
(c)
2. Computers are just like untrustworthy friends. In the case of untrustworthy friends, you need them, you get used to them, but then, without warning, they let you down.
(a)
(b)
(c)
For each of the following, (a) reconstruct the argument in standard form; (b) identify the the kind of reasoning (deductive or inductive) and argument pattern (modus ponens, dilemma, generalization, etc.); and (c) symbolize the argument.
1. Recent researchers have noticed links between academic success and parochial education. Parochial students demonstrate better grasp of basic academic subjects such as reading and mathematics, and tend to score much higher on standardized tests than public school students. A significantly higher percentage of parochial school students go on to pursue higher education. Even among poor inner-city students, performance is better in Catholic schools, so this relationship cannot be explained as the result of generally better students in parochial schools. Who can doubt that the real explanation is the quality of Catholic education?
(a)
(b)
(c)
2. The reason for allowing no handicapped or physically disabled people to sit in airline window seats-that is, in rows with emergency exits-is clear. Any airline passengers who sit in window seats must be physically able to respond quickly in a time of crisis in order to save themselves and contribute to the safety of other passengers.
(a)
(b)
(c)
Sample Quiz 2.1
For each passage, (a) write the conclusion of the argument, and (b)
identify the fallacy that most clearly diagnoses the problem with the argument,
and briefly explain your identification
1. There is no reasonable way for a person to doubt that the miracles described in the Bible actually took place. We are constantly seeing miracles in our own dayónew developments in airplane technology, amazing feats of medical science, advances in computers, and almost unbelievable inventiveness with plastics and synthetic fibers. With all of these miracles of science before us, we simply have no grounds to question those older miracles.
(a) Conclusion:
(b) Fallacy:
2. Representative Rogers, I really think that a yes vote on the foreign aid bill is your wisest course of action. Elections are in several months, you know, and my lobbying organization can guarantee some hefty contributions if I know that I can depend on you. I shouldn't have to mention it, but that money could go to your challenger.
(a) Conclusion:
(b) Fallacy:
3. Of course we should increase government funding for artists. Only lowbrow uncultured types--philistines, as they used to say--would object to spending a few pennies a day of tax money to support the soul-stirring work of artists.
(a) Conclusion:
(b) Fallacy:
Sample Quiz 2.2
For each passage, (a) write the conclusion of the argument, and (b)
identify the fallacy that most clearly diagnoses the problem with the argument,
and briefly explain your identification
1. You bet my modified Kia is a high-performance sports vehicle! It has bucket seats and leather trim, so it's just like a Porsche or Ferrari, eh?
(a) Conclusion:
(b) Fallacy:
2. Well, I guess we can head out to climb Mount Everest now! Rob said that if we didn't have low-temperature sleeping bags, we couldn't go mountain climbing. But I found some low-temp bags at a garage sale yesterday. Let's roll!
(a) Conclusion:
(b) Fallacy:
3. I know that it is my fault that the party went so badly. I feel terrible. And I'll feel even worse if you don't let me plan the next party. OK?
(a) Conclusion:
(b) Fallacy:
Determine the validity of each of the following arguments by the appropriate
method. Show your work.
| 1. | ~r. | |
| ~(r v s) --> ~(p v ~q). | ||
| ~r --> (p v ~q) | ||
| --------------------- | ||
| s. |
| 2. | No P1s are P2s. | |
| No P2s are P3s. | ||
| --------------------- | ||
| No P3s are P1s. |
Determine the validity of each of the following arguments by the appropriate
method. Show your work.
| 1. | No P1s are P2s. | |
| All P1s are P3s. | ||
| m is a P2. | ||
| --------------------- | ||
| m is not a P3. |
| 2. | (p v ~q) --> (s & t). | |
| p. | ||
| t --> r. | ||
| --------------------- | ||
| s & r. |
1. Ethel's Ford was a real lemon. It seems like it was always in the shop, if it wasn't sitting by the side of the road, crippled and unable to move. Now that I think about it, Jose's Ford never seems to have run very well either. And the new Ford sports car that Elaine bought was recalled after only three months. That just shows that Fords are lousy cars.
(a)
P1. Ethel's Ford was a real lemon.
P2. Jose's Ford was a real lemon.
P3. Elaine's Ford sports car was a real lemon.
-----------------------------------------------
L: Fords are lemons.
(b) inductive; generalization
(c)
Ford Example 1 has characteristic L.
Ford Example 2 has characteristic L.
Ford Example 3 has characteristic L.
----------------------------------------
Fords are L.
2. I'm really in a bind. If I complain about my boss's treatment of me, he'll probably make my life miserable. But on the other hand, if I don't do anything, he'll continue to take advantage of me by giving me the worst work schedules of anyone in the company. What other alternative is left to me? Either I complain, or I refrain from complaining.
(a)
P1. Either I complain or refrain from complaining.
P2. If I complain, my boss will make my life miserable.
P3. If I don't complain, my boss will take advantage of me.
------------------------------------------------------------
C: Either my boss will make my life miserable or take advantage of
me.
(b) deductive; dilemma
(c)
C v ~C.
C -> M.
~C -> A.
------
M v A.
1. Rock bands that manage to produce music that is popular over a span of time in very different musical eras are truly great. So the Rolling Stones are a truly great rock band.
(a)
P1: Rock bands that persistently produce popular music are truly great.
[P2: The Rolling Stones persistently produce popular music.]
---------------------------------------------------------------
C: The Rolling Stones are a truly great rock band.
(b) deductive; applied categorical syllogism
(c)
All Bs are Gs.
r are a B.
--------
r are a G.
2. Computers are just like untrustworthy friends. In the case of untrustworthy friends, you need them, you get used to them, but then, without warning, they let you down.
(a)
P1: Computers are like untrustworthy friends.
P2: Untrustworthy friends grow familiar and then let you down.
--------------------------------------------------------------
[L: Computers grow familiar and then let you down.]
(b) inductive; analogy
(c)
Cs are like Fs.
Fs have characteristic L.
---------------------------
Cs have characteristic L.
1. Recent researchers have noticed links between academic success and parochial education. Parochial students demonstrate better grasp of basic academic subjects such as reading and mathematics, and tend to score much higher on standardized tests than public school students. A significantly higher percentage of parochial school students go on to pursue higher education. Even among poor inner-city students, performance is better in Catholic schools, so this relationship cannot be explained as the result of generally better students in parochial schools. Who can doubt that the real explanation is the quality of Catholic education?
(a) There are two obvioius reconstructions of this argument: a simple one and a more complex one. The simple one is:
P1. Parochial education is correlated (in several ways) with academic
success.
--------------------------------------------------------
L: Parochial education causes (or is a significant cause of)
academic success.
A more complex one would spell out all of the correlative links that are mentioned in the argument:
P1. Parochial education is significantly correlated with grasp
of basic subjects.
P2. Parochial education is significantly correlated with high
standardized test scores.
P3. Parochial education is significantly correlated with student
participation in higher ed.
P4. Parochial education is significantly correlated with better
academic performance in low-income environments.
-------------------------------------------------
L: Parochial education causes (or is a significant cause of)
academic success.
(b) inductive; causal argument (The second formulation makes the argument look like a generalization, but remember that all causal arguments rest on correlations that are justified by appeal to a body of information.)
(c)
P is significantly correlated with A.
----------------------------------------
P causes A.
2. The reason for allowing no handicapped or physically disabled people to sit in airline window seats-that is, in rows with emergency exits-is clear. Any airline passengers who sit in window seats must be physically able to respond quickly in a time of crisis in order to save themselves and contribute to the safety of other passengers.
(a) There are several possible reconstructions of this argument; I've offered two of the most obvious here:
P1. Any airline passengers who sit in window seats must be physically
able to respond quickly in emergencies.
P2. Handicapped or disabled people are not physically able to
respond quickly in emergencies.
---------------------------------------------
C: Handicapped or disabled people should not sit in airline window
seats.
OR you could change the first premise around to eliminate the negation:
P1. (All) handicapped or disabled people are not physically able
to respond quickly in emergencies.
P2. Persons unable to respond quickly in emergencies should not
be allowed to sit in airline window seats.
------------------------------
C: Handicapped or disabled people should not be allowed to sit
in airline window seats.
(b) deductive; Universal Syllogism (the second version above handles the negations in a way that makes this clearest)
(c) Here's a symbolization of the second version above:
H=handicapped or disabled people
P=people physically able to respond quickly in emergencies
W=people allowed to sit in airline window seats
All Hs are ~Rs.
All ~Rs are ~W.
------------------
All Hs are ~Ws.
Quiz 2.1 Solutions
For each passage, (a) write the conclusion of the argument, and (b)
identify the fallacy that most clearly diagnoses the problem with the argument,
and briefly explain your identification
1. There is no reasonable way for a person to doubt that the miracles described in the Bible actually took place. We are constantly seeing miracles in our own dayónew developments in airplane technology, amazing feats of medical science, advances in computers, and almost unbelievable inventiveness with plastics and synthetic fibers. With all of these miracles of science before us, we simply have no grounds to question those older miracles.
(a) Conclusion: We should believe that the miracles described in the Bible really took place.
(b) Fallacy: Equivocation
The word "miracle" is used in two senses in this passage.
The first, which is used in reference to the Bible, means "an event caused
by supernatural or divine intervention in the normal course of things."
But that is not at all what we mean when we speak of "miracles of science."
These are amazing events that suprise us with their innovation or complexity,
but are nonetheless fully explainable in natural or scientific terms.
2. Representative Rogers, I really think that a yes vote on the foreign aid bill is your wisest course of action. Elections are in several months, you know, and my lobbying organization can guarantee some hefty contributions if I know that I can depend on you. I shouldn't have to mention it, but that money could go to your challenger.
(a) Conclusion: You should vote yes on the foreign aid bill.
(b) Fallacy: Appeal to force
The speaker clearly means to influence the representative's vote not
on the basis of whether or not the foreign aid bill is good policy, but
on the potential "carrot" of campaign donations. The fallaciousness
of this approach becomes even more clear when the lobbyist points out that
the funds he has to offer could very well go to someone else. This
is nothing more than a threat.
3. Of course we should increase government funding for artists. Only lowbrow uncultured types--philistines, as they used to say--would object to spending a few pennies a day of tax money to support the soul-stirring work of artists.
(a) Conclusion: Government funding for artists should be increased.
(b) Fallacy: Straw man
The argument gives no hint that there are reasonable grounds
for objecting to increasing government funding of arts (such as limited
resources, more pressing social needs such as hunger and poverty, and so
on). This is an intentional strategy of making the views of potential
opponents look silly. Therefore, it is a "straw man," an attack on
a weak scarecrow rather than a strong argument.
In addition, the argument uses several instances of prejudicial language.
For example, "lowbrow" and "philistine" are meant to make opponents of
increased arts funding seem stupid, and calling art "soul-stirring" is
intended to evoke positive feelings for art and hence for arts funding.
Quiz 2.2 Solutions
For each passage, (a) write the conclusion of the argument, and (b)
identify the fallacy that most clearly diagnoses the problem with the argument,
and briefly explain your identification
1. You bet my modified Kia is a high-performance sports vehicle! It has bucket seats and leather trim, so it's just like a Porsche or Ferrari, eh?
(a) Conclusion: My modified Kia is a high-performance sports vehicle.
(b) Fallacy: False Analogy
Bucket seats and leather trim don't make a car a high-performance sports
vehicle. Using these features to compare a modified compact car to
a precision-engineered sports car sets up a very poor analogy.
2. Well, I guess we can head out to climb Mount Everest now! Rob said that if we didn't have low-temperature sleeping bags, we couldn't go mountain climbing. But I found some low-temp bags at a garage sale yesterday. Let's roll!
(a) Conclusion: We can go mountain climbing now (on Mount Everest).
(b) Fallacy: Denying the Antecedent
Look at the structure of the argument that is offered:
P1: If we don't have low-temperature sleeping bags, we can't go mountain climbing.If you symbolize it out, you will see that it is an instance of denying the antecedent. Further, you can tell just by common sense that even though sleeping bags are a necessary condition for mountain climbing, possessing sleeping bags is hardly full preparation for climbing mountains.
P2: We have low-temperature sleeping bags.
---------------------------------------------------------
C: We can go mountain climbing.
3. I know that it is my fault that the party went so badly. I feel terrible. And I'll feel even worse if you don't let me plan the next party. OK?
(a) Conclusion: You should let me plan the next party.
(b) Fallacy: Appeal to Pity
The arguer simply tries to get the listener to feel sorry so that the
arguer will get to plan the party. This is clear manipulation of
emotions.
1. This is a sentence-based deductive argument; hence
a proof must be constructed.
| 1. | ~r. | |
| 2. | ~(r v s) --> ~(p v ~q). | |
| 3. | ~r --> (p v ~q). | /s. |
| 4. | p v ~q. | 1, 3, MP |
| 5. | r v s. | 2, 4, MT (with DN) |
| 6. | s. | 1, 5, DS |
| QED (valid) |
Note especially the importance of the Double Negation (DN) rule when
using MT on the complex conditional in Step 5. Since the disjunction
in Step 4 is the negation of the consequent of the conditional in Premise
2, that allows the use of Modus Tollens (MT). The result is the negation
of the antecedent of the conditional in Step 2; the negations then
cancel out. The conclusion can be successfully inferred from the
premises; the argument is valid.
2. This is a predicate-based/categorical deductive argument;
hence a Venn diagram must be constructed.
|
No P1s are P2s. |
 |
No P2s are P3s.  |
|
| --------------------- | |
| No P3s are P1s. | |
The conclusion of the argument asserts that No P3s
are P1s. But as the Venn diagram
shows, the common area between P1 and P3
is unshaded, and hence is open. Therefore, it is possible for the
conclusion to be false even if the premises are true. The argument
is invalid.
1. This is a predicate-based/categorical deductive argument;
hence a Venn diagram must be constructed.
|
No P1s are P2s. |
 |
| All P1s are P3s. |
|
| m is a P2. | |
| --------------------- | |
| m is not a P3.
|
According to Premise 3, m can fall anywhere in the P2
circle, including the area in common with P3.
The conclusion asserts that m is not a P3,
which can therefore be false. The argument is invalid.
2. This is a sentence-based deductive argument; hence
a proof must be constructed.
| 1. | (p v ~q) --> (s & t). | |
| 2. | p. | |
| 3. | t --> r. | /s & r. |
| 4. | p v ~q. | 2, Add |
| 5. | s & t. | 1, 4, MP |
| 6. | s. | 5, Sim |
| 7. | t. | 5, Sim |
| 8. | r. | 3, 7, MP |
| 9. | s & r. | 6, 8, Con |
| QED (valid) |
The conclusion can be successfully inferred from the premises;
the argument is valid.
 |
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David H. Calhoun
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