Practice Proficiency Exam - Answers
(All citations are from Moore/McCann/McCann, Creative and Critical Thinking. Page numbers are inserted in parentheses.)
I. Language and Logic
1. (a) An argument is "a set of propositions related in such a way that one of them is claimed to follow from the other or others" (20).
(b) An inductive argument is one in which the conclusion may be false and yet the premises are true. This is because the conclusion "intentionally goes beyond the information cited in the premises" (25). Thus the conclusion follows only as a matter of probability, not absolute certainty.
(c) A deductive argument is on in which "the premises are intended to make the conclusion inevitable, in the sense that if they turn out to be true, it will not be possible for the conclusion to be false" (25).
(d) A frame of reference is a way of looking at the world and oneself. It includes a stock of beliefs about nature, the social world, other people, and oneself, and also the complex processes, open and hidden, of social conditioning through which those beliefs are formed.
(e) Ambiguity means that a word or phrase has at least two different meanings. The opposite of ambiguity is clarity.
(f) Vagueness means that a word or phrase has an indefinite extension of meaning. The opposite of vagueness is precision.
2. (a) informative (b) expressive, emotive (c) performative (d) persuasive (e) directive
3. (a) "drops" is ambiguous because it can mean the substance or "to drop off."
(b) "visits" is ambiguous: it could mean the noun or the verb. "Hurt" is also ambiguous: it can be a verb or adjective.
(c) "awake" is ambiguous: it could mean "alert" or "wake up." In turn, "wake up" could mean that the police woke up, or that they woke up, and then arrested, the suspect.
(d) "filling . . . with" is ambiguous: it could mean "alongside" or the contents of the bags.
(e) "giving" (milk) is ambiguous: it could mean donating it or providing their own breast milk.
4. (a) false implication, half-truth, because the ad could be true and yet the candy bar could have always been that size.
(b) ambiguous comparison (see 325) because the ad does not specify harder than whom or what.
(c) "up to" is vague and also a weasel phrase because the relief could last anywhere from one second to 8 hours. "half-truth" could also be a right answer.
(d) exaggeration, misuse of evaluative words (misuse of labels) (327).
(e) puffery-vacuous, meaningless language-misuse of evaluative words.
II. Propositional Reasoning
1. If the car skidded on the ice, then the driver was drunk.
The car did skid on the ice.
The driver was drunk. VALID; modus ponens
2. If cigarette smoking is hazardous to your health, then cigarettes would not be marketed.
Cigarettes are marketed
Cigarette smoking is not hazardous to your health. VALID; modus tollens
3. If the Supreme Court's decision about homosexuals is not reversed, policemen will soon be under every bed.
The Supreme Court's decision will be reversed.
Policemen will not soon be under every bed. INVALID; fallacy of denying the antecedent.
4. If more radar traps were installed, highway speeding would be reduced greatly.
No more radar traps will be installed.
Highway speeding will not be reduced. INVALID; fallacy of denying the antecedent
5. If earthquake preparedness in our area is not improved drastically, the "big one" will kill many people.
The "big one" will kill many people.
Earthquake preparedness in our is not being improved drastically. INVALID; fallacy of affirming the consequent.
6. Either this beer tastes great or it's less filling.
This beer tastes great.
This beer is not less filling. INVALID; fallacy of affirming an alternate.
7. Either the exam was too hard or I didn't understand the material.
I understood the material.
The exam was too hard. VALID
8. Either this pain is indigestion or a heart attack.
This pain is indigestion.
This pain is not a heart attack. INVALID; fallacy of affirming an alternate.
9. Not both can Reaganomics be a good thing and that we have buried our children under a cesspool of debt.
We have buried our children under a cesspool of debt.
Reaganomics was not a good thing. VALID
10. Not both can Monica Lewinsky be telling the whole truth and President Clinton be telling the whole truth.
President Clinton is not telling the whole truth.
Monica Lewinsky is telling the whole truth. INVALID; fallacy of denying a disjunct.
III. Categorical Reasoning
1. (a) Some weird people are rock musicians.
(b) No creatures that give at the office are vampires.
(c) Some stout drinkers are elves.
(d) Some of those especially prone to psychosis are critical thinking students.
(e) N/A; an O-form proposition has no converse.
2. (a) Some young children are not non-barbarians.
(b) All dentists are non-compassionate people.
(c) No Bach organ concertos are non-sublime pieces of music.
(d) All vampires are non-silver mine stock owners.
(e) Some snakes were non-recaptured creatures.
3. (A) Some S are TSOP
(B) Some TSOP are not non-S
obvert (B): Some TSOP are S convert: Some S are TSOP EQUIVALENT
4. (A) Some CT are not SP
(B) Some non-SP are not non-CT
obvert (B): Some non-SP are CT convert: Some CT are non-SP obvert: Some CT are not SP
5. (A) Some P are DP
(B) Some non-DP are not non-P
obvert (B): Some non-DP are P convert: Some P are non-DP obvert: Some P are not DP NOT
6. (A) Some PO are not IQ3D
(B) Some non-IQ3D are non-PO
obvert (B): Some non-IQ3D are not PO NOT EQUIVALENT
7. Some BST are I
Some I are not S
Some S are BST INVALID; fallacy of undistributed middle term
8. No non-S are PECC convert & then obvert: All PECC are S
No SIUES are S
No SIUES are PECC VALID
9. No P are OPS obvert: All P are non-OPS
Some CG are not P
Some CG are non-OPS INVALID; fallacy of drawing an affirmative conclusion from a negative premise.
OR: obvert the conclusion to Some CG are not OPS. The argument is still invalid, and the fallacy would be that of exclusive (two negative) premises.
10. All DW are SH
Some TVC are DW
Some TVC are SH VALID
11. Some MI are P
All SOV are MI
Some SOV are P INVALID; fallacy of undistributed middle term
12. No tortures are fun
All enthymemes are tortures
No enthymemes are fun
13. All pleasant experiences are welcome things.
No root canals are welcome things (or vice-versa)
No root canals are pleasant experiences
14. No logic exams are erotic experiences
Some erotic experiences are dangerous experiences
Some dangerous experiences are not logic exams
15. All relaxed times are easy times
No job interview is an easy time
No job interview is a relaxed time
16. All politicians are mentally defective people
All windbags are politicians
All windbags are mentally defective people.
IV. Inductive Reasoning
1. (a) Make the hypothesis relevant for solving the problem. E.g., if your problem is to determine why you and your roommate can't get along, don't form hypotheses about solar flares and global warming.
(b) Form as many hypotheses as possible. This will maximize your chances of getting the right answer.
(c) Form disagreeable hypotheses first. Form first especially those that threaten your self-image so that you are not likely to avoid looking at them.
2. (a). The number and significance of converging propositions
(b) The number and significance of diverging propositions.
(c) The reliability of the evidence
(d) Completeness of the evidence
(e) Unexplained evidence
(f) Thoroughness of the investigation
(g) Possibility of unformed rival hypotheses
(h) Reliability of rival hypotheses
(2 hypotheses are rivals when both can't be true.)
3. Hypotheses are tested by constructing hypothetical syllogisms. (a) Make the hypothesis the antecedent of the major premise. E.g., "If the crash of TWA 800 was caused by a bomb, then ..."
(b) Then ask yourself, if the hypothesis is true, what else will be true? Write this part as the consequent of the major premise. E.g., "... then chemical residues from the bomb will be found in the wreckage."
(c) Check to see if the result predicted did in fact follow. The results of the test will be expressed as the minor premise. E.g., "Chemical residues from the bomb will be found in the wreckage." If the result predicted does follow, we call it a "converging proposition." This is one that makes it more likely that the hypothesis is true. It increases the reliability of the hypothesis. If the result predicted does not follow, it becomes a "diverging proposition." This means that it makes the hypothesis less probable. It decreases the reliability of the hypothesis and can sometimes falsify it completely.
4. A generalization is "an inference to a conclusion about a group of instances without observing all instances in the group" (115). An enumeration requires testing all instances in the group.
5. The fallacy of hasty generalization is "generalizing from insufficient or biased evidence" (116).
6. Loaded samples can be avoided by using only samples that are random, stratified, and, when appropriate, time-lapse (118ff.)
7. The questionable cause fallacy is arguing that just because event B follows event A, event A is the cause of event B.
8. Correlations are connections between different events. They can be positive or negative. Causal relationships exist when one event produces another. All causes are correlations, but not all correlations are causes.
9. A sufficient cause is one that, all by itself, is enough to produce a certain result. It is expressed as an "If … then …" relationship. Example: A rattlesnake bite is a sufficient cause of getting seriously ill. A necessary cause is one that is required to produce a given effect, even if it's not sufficient by itself to bring it about. It is expressed as an "Only if … then …" relationship. Example: Only if you are exposed to the AIDS virus can you get AIDS. If you're not exposed to the AIDS virus, there is no way you can get AIDS. A contributory cause is one that makes a certain result more likely to happen. Example: Icy roads are a contributory cause of traffic accidents. They are not a sufficient cause because sometimes the roads are icy and there are no traffic accidents. They are not a necessary cause because there can be traffic accidents when the roads are not icy.
10. Given proposition B, homocysteine could not be a sufficient or necessary cause of heart attacks and strokes. At most, it would be a contributory cause. It's not a sufficient cause because some people have high levels and do not get heart attacks or strokes, and it's not necessary because some people do not have high levels and still get heart attacks or strokes.
11. Questionable cause. So far, the evidence shows only a correlation.
12. Agreement: "If two or more instances of the phenomenon under investigation have only one circumstance in common, the circumstance in which alone all the instances agree is the cause (or effect) of the given phenomenon" (171; citing Mill's A System of Logic). In practical terms, it means "the existence of a common factor in at least two instances of a phenomenon" (173). Difference: "If an instance in which the phenomenon under investigation occurs, and an instance in which it does not occur, have every circumstances in common save one, that one occurring only in the former; the circumstance in which alone the two instances differ is the effect, or the cause, or an indispensable part of the cause, of the phenomenon" (173, citing Mill ut supra). In practical terms, the method of difference means "a factor that tends to be present in instances where a phenomenon has occurred and absent where the phenomenon has not occurred" (174). Concomitant variations: "Whatever phenomenon varies in any manner whenever another phenomenon varies in some particular manner is either a cause or an effect of that phenomenon, or it is connected with it through some fact of causation" (174, citing Mill, ut supra). At best, this method demonstrates perfect positive correlations, and so is the weakest of the three in terms of diminishing doubts that a given correlation is a causal relationship.
13. (A) Mill's method of agreement.(B) Mill's method of difference.