E)*Depression has in turn been linked to desperation and suicide.
See solution Tip #34: If A is thought to be causing B, the idea that B is causing A is called reverse causation and casts serious doubt on the notion that A is really causing B.
Problem 23: TV Viewing An investigator divided 128 adults into two distinct groups (high TV viewers and low TV viewers) based on the number of hours of violent TV programming they watched per day. A significantly larger percentage of the high-viewing group than of the low-viewing group demonstrated a high level of aggression. The investigator concluded that greater TV viewing, particularly of violent programming, caused higher aggression levels.
Which of the following, if true, most seriously weakens the conclusion above?
A)*Some subjects in the high-viewing group experienced lower levels of aggression than did other subjects in the high-viewing group.
B)*Some subjects in the low-viewing group did not experience any aggression.
C)*Fear of aggressive tendencies as a result of watching large amounts of TV was the reason some subjects restricted their viewing of TV.
D)*Some subjects watched live programming whereas other viewers watched pre-recorded TV programs.
E)*Some subjectsa already-high levels of aggression caused them to increase their viewing, particularly of violent TV programs.
See solution Tip #35: Test the opposite scenario a" if you hear that a full moon causes the crime rate to rise, always ask what the crime rate is like when the moon is not full.
Problem 24: Shark In a marine reserve off the south coast of Australia, people sometimes are attacked by sharks. Here, it is believed that the sharks will only attack people who are mistaken for seals, which occurs when surfers wear entirely black body suits. So for the past few years, surfers have started wearing bright metallic body suits. While many area residents remain skeptical, no surfer wearing a metallic body suit has yet been attacked by a shark.
Which of the statements below, if true, would best support the argument of those who advocate the use of metallic body suits?
A)*Surfers at other surf areas who wear metallic body suits have not been attacked recently by sharks.
B)*A number of surfers in this marine area wearing black body suits have been attacked recently by sharks.
C)*No sharks have been spotted in this marine reserve off the south coast of Australia in recent months.
D)*Some of the surfers who wear metallic suits also wear wristbands that contain metal bells in order to frighten away any sharks.
E)*Underwater divers have observed sharks attacking tuna and other ocean fish, some of them black in color.
See solution Tip #36: Theory may be divorced from practice. Plans may not equal completed action. Do not a.s.sume that plans will be implemented without a hitch.
Problem 25: Solar Energy Energy from the sun suffers none of the major problems of more traditional energy sources, such as oil, coal, and nuclear energy. It requires no imports from foreign countries, it creates no air and water pollution, it threatens no one with death from radiation, and it cannot be withheld by powerful utility monopolies. Therefore, we should encourage families to use solar energy.
Which of the following statements, if true, most seriously weakens the argument in the pa.s.sage above?
A)*There have been very few studies on the use of solar energy in the average household.
B)*Most of the studies critical of solar energy have been conducted by powerful utility monopolies.
C)*Research has not yet developed an effective way to capture and store solar energy in a way that most individual families can employ.
D)*Federal price controls on domestically produced crude oil and natural gas could reduce the cost of fuel to the average family.
E)*The cost of building and installing the apparatus needed to collect enough solar energy for a family of four is equal to the amount a family of four would pay for oil, coal, or nuclear-based energy in one year.
See solution Tip #37: aCana does not equal awill.a The ability to do something should not imply application of that ability, whether due to choice or neglect.
Problem 26: Cla.s.sics Any literate person who is not lazy can read the cla.s.sics. Since few literate persons have read the cla.s.sics, it is clear that most literate persons are lazy.
Which of the following is an a.s.sumption on which the argument above is based?
A)*Only literate persons can understand the cla.s.sics.
B)*Any literate person should read the cla.s.sics.
C)*Any literate person who is lazy has no chance of reading the cla.s.sics.
D)*Any literate person who will not read the cla.s.sics is lazy.
E)*Any literate person who can read the cla.s.sics will choose to do so.
See solution Tip #38: One way to uncover implementation a.s.sumptions is to antic.i.p.ate bottlenecks.
Problem 27: Public Transportation People should switch from driving their cars to work on weekdays to taking public transportation, such as buses and subways. In major cities such as New York, London, or Tokyo, for example, cars are an expensive and inefficient means of transportation, and fossil fuel emissions are the major source of the cityas pollution.
The argument above makes all of the following a.s.sumptions EXCEPT A)*There may be easier ways to combat pollution in large cities than by having people switch to taking public transportation.
B)*There are enough people who actually own cars, which are currently being used to drive to work, to make this plan realistically feasible.
C)*Public transportation is both available and accessible should someone wish to switch.
D)*Current public transportation systems can accommodate all the people who decide to switch.
E)*The city can afford to pay public transport drivers and related personnel who may otherwise remain idle once the morning and evening rush hour periods are over.
See solution Tip #39: An argument may depend on the a.s.sumption that a person or organization is aware of a pre-existing fact, situation, or condition.
Problem 28: Rainbow Corporation aTina obviously cares little about the environment. She continues to use Purple Rider Felt Pens even though the company that makes these pens, Rainbow Corp., has been the focus of several recent newspaper articles as a result of its indictment for several violations involving dumping toxic wastes in the harbor.a Which of the following would most weaken the claim that Tina cares little about the environment?
A)*Although the Rainbow Corp. has been the subject of several newspaper articles, it has been praised by consumers for its high-quality products.
B)*Tina is not aware of the recent newspaper articles which feature Rainbow Corp. and its indictment for several violations involving dumping toxic wastes in the harbor.
C)*The newspaper which ran the articles of Rainbowas indictments also owns a agossip magazinea called the Tipsy Tattler.
D)*The public relations department of Rainbow Corp. never issued a statement denying that the company violated the law.
E)*Tina was a member of an environmental protection organization during her freshman and soph.o.m.ore years in college.
See solution Tip #40: Searching for something does not guarantee that weall recognize it once weave found it. The ability to accurately ident.i.ty that which we are seeking to find may be a key a.s.sumption.
Problem 29: Personality The interview is becoming an integral part of the admissions process at most graduate business programs. Since personality is deemed important to success not only in business school but also on the job, feedback from interviews will help the admissions office select candidates whose personalities are suited for business school and the workplace.
Which of the following is a fundamental a.s.sumption in the argument above?
A)*Admission efforts will be successful if they include interviews.
B)*The interview is becoming the most important element in the business school admissions process.
C)*Interviewers can accurately identify those applicants whose personalities are suited and unsuited to success in business school.
D)*The sole purpose of the interview from the eyes of the admissions office is to evaluate whether business school applicantsa personalities are suited to the business school environment.
E)*Interviews will be held at similar times of the day and will be conducted in venues that are reasonably comparable.
See solution PUTTING IT ALL TOGETHER.
Tip #41: Always look for potentially vague terms in an argument and ask for or seek clarification.
Problem 30: Yuppie Caf For the purposes of reinforcing techniques used to a.n.a.lyze arguments, write or sketch a response to the following argument question.
The following appeared as part of a campaign to sell advertising to local businesses through various Internet service providers.
aThe Yuppie Caf began advertising on the Internet this year and was delighted to see its business increase by 15% over last yearas total. Their success shows that you too can use the Internet to make your business more profitable.a a.n.a.lyze the above argument according to cla.s.sic argument structure, identifying the conclusion, evidence, and at least three a.s.sumptions. How persuasive do you find this argument? What would make this argument more persuasive?
Chapter 5.
Mastering Logic.
When you have eliminated the impossible, whatever remains, however improbable, must be the truth.
a" Sherlock Holmes.
OVERVIEW.
This chapters focuses on four interrelated topics: 1. aIf a thena statements 2. aNo-some-most-alla statements 3. Mutual inclusivity and exclusivity 4. Logical equivalency statements To introduce formal logic, consider the following statements: Original: If you work hard, youall be successful.
Now ponder these related statements.
Statement 1: If youare successful, then youave worked hard.
Statement 2: If you donat work hard, you wonat be successful.
Statement 3: If youare not successful, then you didnat work hard.
The question becomes: Which of the above statements are logical deductions based on the original statement above?
Upon closer examination, statement 1 isnat necessarily correct. The fact that youare successful (whatever this means!) doesnat mean that you have necessarily worked hard. There could be several other ways to become successful. For example, perhaps youare skillful, intelligent, or downright lucky.
Likewise, statement 2 is not necessarily correct. Just because you donat work hard doesnat mean that you wonat be successful. As already mentioned, you might be skillful, intelligent, or lucky as opposed to hardworking. However, statement 3 is a perfectly logical deduction based on the original. If youare not successful, then you must not have worked hard. This doesnat mean, however, that there are not other explanations for why you might not have been successful. For example, perhaps you were neither intelligent in your approach nor skillful or lucky in your application.
aIF a THENa STATEMENTS aIf a thena statements are another way to represent causal relationships. Take the following generic statement: aIf A, then B.a This is sometimes written in a more formulaic manner: i.e., aIf A a" B.a Consider the statement aIf it is U.S. money (dollar bills), then it is green (colored).a This can also be written: If $US a" Green. Another way to ill.u.s.trate an aif a thena relationship is to draw circles. The aIfa item always represents the innermost circle while the athena item always represents the outermost circle. See Exhibit 5.1.
Exhibit 5.1 a" Diagramming aIf a thena Statements If it is U.S. money, then it is green (if US$, then Green) The above diagram ill.u.s.trates in picture form the relationship between U.S. money and all green things. We can read from the inside circle to the outside circle, but we cannot read from the outside circle to the inside circle. aIf U.S. money then greena does not equal aIf green then U.S. money.a What can we logically infer from this type of statement? Exhibit 5.2 contains four statements that may seem to the casual observer all to be inferable. However, only the fourth version is correctly inferable. In aif a thena statements, it is important that you read in one direction only, as the reverse is not necessarily true. Based on the original statement aIf it is U.S. money, then it is green,a the only thing we can infer logically from this statement is that it is true that aIf it is not green, then it is not U.S. money.a Exhibit 5.2 a" American Money To master aif a thena statements it is essential to memorize the information contained in Exhibit 5.3. According to formal logic, the contrapositive is always correct. That is to say, the only thing we can infer from an aIf A, then B statementa is the following: aIf not B, then not A.a Exhibit 5.3 a" The Logic of aIf a thena Statements Another way of understanding aIf a thena statements is through an understanding of necessary versus sufficient conditions. A necessary condition must be present for an event to occur but will not, by itself, cause the given event to occur. A sufficient condition is enough, by itself, to ensure that the event will occur. In more technical parlance, a necessary condition is a condition which, if absent, will not allow the event to occur. A sufficient condition is a condition which, if present, will cause the event to occur.
When a person argues aIf A, then Ba and then argues aIf B, then A,a he or she erroneously reverses the conditional statement. The reason that a conditional statement cannot be reversed is that the original aIf a thena statement functions as a necessary condition. When it is reversed, an aIf a thena statement erroneously turns into a sufficient condition. In the example above, being agreena is a necessary but not a sufficient condition in order for something to be considered U.S. money. Obviously, other factors besides agreen coloringa need be present, including special watermarked paper, unique insignia, and precise size. By reversing the aIf a thena statement we erroneously suggest that being green-colored is enough of a criterion for something to be considered U.S. money.
Try one more example: aI gave my pet hamster water every day and he still died.a Giving your pet hamster water each day is a necessary condition for keeping him alive, but it is not a sufficient condition. Obviously, a hamster needs many other things besides water, one of which is food.
aNO-SOME-MOST-ALLa STATEMENTS Many errors are committed in drawing inferences because ordinary speech is inherently ambiguous. For example, take the four statements below: I.**No As are Bs II.*All As are Bs III.*Some As are Bs IV.*Most As are Bs To study the meaning of these four statements, refer to Exhibit 5.4. We can see that statement I corresponds to either diagram (1) or (2), but usually to diagram (1). Statement II could represent either diagram (3) or (4), although usually diagram (4). Statement III could typify any one of diagrams (5), (6), or (7), although usually (6). Statement IV could refer to either diagram (8) or (9), but typically (9). This is evidence that ordinary speech can hamper clear thinking, and that it is often necessary to use non-verbal symbols to reinforce clear thinking.
There are two major differences between amosta and asomea statements. First, it is a.s.sumed that amosta implies majority (greater than half), while asomea implies minority (less than half). Second, whereas asome statementsa automatically imply reciprocality, amost statementsa do not necessarily imply reciprocality. For example, the statement asome doctors are wealthy peoplea implies that some wealthy people are also doctors. But the statement amost doctors are wealthy peoplea does not necessarily mean that most wealthy people are doctors.
The diagrams in Exhibit 5.4 summarize the concepts of mutual inclusivity, mutual exclusivity, and overlap. Either circles are embedded inside one another, or circles are completely separated, or circles overlap with one another. Basically, there are eight possibilities.
Exhibit 5.5 provides a summary of logical equivalency statements. With a better understanding of the visual representations of these relationships, the next step is to be able to combine these visuals with verbal logic statements expressed in English. This is a translation exercise. For example, within the area of inclusion, we must be able to see that all of the following are equivalent forms: aAll cats are mammalsa; aEvery cat is a mammala; aIf it is a cat, then it is a mammala; aOnly mammals are catsa; and aNo cat is not a mammal.a MUTUAL INCLUSIVITY AND EXCLUSIVITY.
Exhibit 5.4 a" Overlap and Non-Overlap Scenarios Statement I a" No As are Bs a" refers to either diagram (1) or (2).
Statement II a" All As are Bs a" could refer to either diagram (3) or (4).
Statement III a" Some As are Bs a" could refer to any of diagrams (5), (6), or (7).
Statement IV a" Most As are Bs a" could refer to either diagram (8) or (9).
STATEMENTS OF LOGICAL EQUIVALENCY.
Exhibit 5.5 a" Logical Equivalency Statements TESTING LOGIC-BASED REASONING.
Tip #42: Be careful not to reverse the flow of aIf a thena statements. aIf A, then Ba is not the same as aIf B, then A.a This is known in logic as the fallacy of affirming the consequent.
Problem 31: Chemist aIf someone is a chemist, he or she is a scientist. Ms. Zubrinski is a scientist. Therefore, she is a chemist.a Which of the following best explains why the argument above is invalid?
A)*Someone cannot be a chemist without being a scientist, so someone cannot be a scientist without being a chemist.
B)*Someone cannot be a chemist without being a scientist, but someone can be a scientist without being a chemist.
C)*Someone cannot be a scientist without being a chemist, but someone can be a chemist without being a scientist.
D)*Someone can be a scientist without being a chemist, and a chemist without being a scientist.
E)*Someone can be either a scientist or a chemist, but not one without being the other.
See solution Tip #43: The statement aIf A, then Ba leads to the logical inference aIf not B, then not A.a This is known in logic as the contrapositive.
Problem 32: Intricate Plots The ability to create intricate plots is one of the essential gifts of the scriptwriter. Strong plot development ensures that eventual moviegoers will be intellectually and emotionally satisfied by the story. If scriptwriting is to remain a significant art form, its pract.i.tioners must continue to craft intricate plots.