CRITICAL REASONING 101

Transcription

1 CRITICAL REASONING 101 Two guys are looking at a glass filled to half its capacity. One guy reaches the conclusion that the glass is half full and the other guy reaches the conclusion that the glass is half empty. This story, in a nutshell, encapsulates what an interpretation of evidence is all about. In this instance, notice that the two so-called different interpretations have the SAME significance and the interpretations will qualify as logical interpretations. On the other hand, if the person looking at the glass filled to half its capacity were to reach the conclusion that someone forgot to fill the entire glass or that someone did not finish drinking all the liquid in the glass, the person will be guilty of making an ILLOGICAL CONCLUSION. An ILLOGICAL CONCLUSION is one that is derived on the basis of the stated EVIDENCE and on the basis of additional information TAKEN FOR GRANTED. The additional information taken for granted is the ASSUMPTION of the argument. In the first case, the persons reaching the conclusion that the glass is half full or half empty did not bring in additional information into the argument in order to reach a conclusion. Therefore, the persons reaching the conclusion were logical in their interpretation of the evidence. However, in the second case, the person looking at the same evidence assumed or took for granted that the liquid in the glass could not have evaporated or spilled out, or could not have been drunk by the drinking bird. (Therefore, the person forgot to fill it to the brim or forgot to drink all of it.) An ARGUMENT is essentially the conclusion of a line of reasoning using an evidentiary basis and additional information either taken for granted or not considered at all. The EVIDENCE provides the CONTEXT for the Conclusion, and is critical to the conclusion. The conclusion of an argument taken alone is without context and may not shed light on the WHY of the conclusion. All information needs to be processed in terms of two questions: WHAT is being said? And Why is it being said? The conclusion answers WHAT is being said whereas the evidence answers WHY the conclusion is being said. If the conclusion is that the use of marijuana can cause cancer, the basis or the context for this conclusion is that an ingredient called THC inactivates the herpes virus that can trigger the uncontrolled growth of cancer cells, we need to process both the WHAT and WHY of the argument. The test is about your ability to process information in context and to understand the question that relates to the argument in order that you pick an answer choice that is relevant to the specific scope of information that is presented to you and to the question posed to you. Do not process information in vague generalities. For example, the above argument about marijuana cannot be processed as something about marijuana being bad. Process the specifics and deal with the question on that basis. Page 1

2 LOGICAL REASONING 101 Deductive and Inductive Arguments Logical Reasoning involves two types are arguments: Deductive and Inductive. A deductive argument is an argument in if the premises (generally explicitly stated) are true, it would be impossible for the conclusion to be false. In order words, if the evidence is true, then the conclusion is necessarily true or the conclusion MUST BE TRUE. Deductive reasoning will be tested in verbal context (in the LSAT) and in the verbal and quantitative context in the other two graduate school tests GMAT and GRE. An inductive argument is an argument in which the evidence used is such that the conclusion that is reached on the basis of the premises (explicit and implied) is merely PROBABLE, not CERTAIN. All three tests LSAT, GRE, and GMAT will ask you to identify arguments in which the conclusion is merely one of several probable scenarios consistent with the evidence. The Argument essays tested on all three tests are about your ability to identify OTHER equally probable conclusions that are consistent with the evidence. GMAT and GRE will also test your ability to test more than ONE PROBABLE interpretation of the evidence and to see whether the conclusion that can reached on this basis is consistent across different scenarios consistent with the evidence. Because deductive arguments (also referred to as Logical Conclusions on the three tests) are those in which the truth of the conclusion is thought to be completely guaranteed and not just made probable by the truth of the premises (usually explicit or necessarily implied in the explicit information). In such arguments, the truth of the conclusion is "contained within" the truth of the premises; i.e., the conclusion does not go beyond what the truth of the premises implicitly requires. For this reason, Page 2

3 deductive arguments are usually limited to inferences that follow from literal interpretation of the evidence and from universal definitions relied upon in mathematics and other rules of formal logic. For example, the following are deductive arguments in which the conclusion is necessarily true if the premises used as evidence are true: There are 120 people in the class, taking either English or Spanish language courses, and no person takes both courses. 80 people take English language courses. Therefore, there are 40 students taking Spanish language courses. Each year, the official estimate of the available cod in the Atlantic is made on the basis of an AVERAGE of the two estimates: the official tonnage of cods caught by research vessels and the commercial tonnage of cods caught by other fishing vessels. In the past, the two tonnages agreed were within 1% of each other. However, in the past, the official tonnage went markedly down by the same amount as the commercial tonnage went up. Therefore, the official estimate remained practically unaffected. Notice that because the average is computed by adding up the two estimates and dividing the sum by 2, if one of the values goes up by about the SAME amount as the other went down, then the sum of the two tonnages should remain the same and the average will remain unaffected. The conclusion stated is a valid DEDUCTION and necessarily true. Inductive arguments or ILLOGICAL ARGUMENTS, on the other hand, can appeal to any consideration that might be thought relevant to the probability of the truth of the conclusion. Inductive arguments, therefore, can take very wide ranging forms, including arguments dealing with statistical data, generalizations from past experience, appeals to signs, evidence or authority, and causal relationships. Page 3

4 To sum up, an INDUCTIVE ARGUMENT is one in which the conclusion that is drawn on the basis of a set of premises explicitly stated or implied in the line of reasoning is PROBABLE but NOT logically certain. The conclusion is but ONE of several PROBABLE interpretations of the evidence. X is an integer. Therefore, X is equal to 2. The above is an example of an INDUCTIVE argument in which the conclusion that X is equal to 2 is PROBABLE but not certain because X could also be 1, 3, 4, 5 or any other positive or negative value or zero. A DEDUCTIVE ARGUMENT is one in which the conclusion is NECESSARILY CERTAIN if the evidence is true. If X is an integer, then it is necessarily true that X is a whole number. If John Scored 160 on the LSAT, then it is necessarily true that John took the LSAT because unless the test is taken, a score may not be obtained. All three tests will require that you logically interpret evidence or any statement and draw deductions or necessarily valid conclusions. The Reading Comprehension section on the three tests will test your ability to make logical and literal interpretation of context-specific information relevant to the question. The Logical Reasoning Section on the LSAT and the Critical Reasoning Section on the GMAT and GRE will require that you draw conclusions that are logically certain for a set of stated or implied premises. Remember that questions asking you to identify that which could be true are about identifying probable answers consistent with the evidence. IF the evidence is that at most one person recognizes everybody in the room it is probable that one person recognizes everybody in the room. It is equally probably that nobody recognizes anybody in the room because at most implies equal to or less than. The questions asking you to identify that which MUST BE true for a set of premises asks you to pick an answer that is LOGICALLY CERTAIN for a set of evidence used. Page 4

5 HOW IS LOGICAL REASONING TESTED ON THE GRADUATE SCHOOL ADMISSION TESTS? LSAT LOGICAL REASONING SECTION LSAT test will include TWO scored sections of Logical Reasoning section, each section having questions to be answered in 35 minutes. WE will discuss the different types of questions that will be tested in this section on the LSAT. It is also probable that the test will include a third LR section that may not be scored, although it is more probable that the not-scored section will be Analytical Reasoning or Reading Comprehension. LSAT will measure your logical reasoning skills throughout the entire test and in the various sections. While the Logical Reasoning Section is specifically geared to measuring your ability to critique inductive or illogical arguments, to engage in deductive reasoning using the evidence presented, and to identify parallel forms and logical explanations for the described paradoxes, the Reading Comprehension and Analytical Reasoning sections will also measure your inductive and deductive reasoning skills. Reading Comprehension is about your ability to deductively interpret context-specific information relevant to the question and to identify the main point of the whole passage. The Analytical Reasoning Section on the LSAT will ask you to draw logically certain conclusions using a set of statements provided to you and then to use the deductions to make further decisions about the presented questions. For example, if the game in the Analytical Reasoning Section stated the following: A Storm passes through five towns and drops either rain or both rain and hail. It passes through each town exactly once. The storm passes through Oakville immediately AFTER it passes through Rockville. We would logically interpret the last statement to mean that Oakville cannot be the first town that the storm passes through and Rockville cannot be the last town that the storm passes through. We would then use this logically derived conclusion to check out valid and permissible scenarios for the storm s path. If the game stated that the five music stores in Ghost Town carried three genres of music: Rock, Pop, and Jazz. Each store must carry at least one genre of music. Store B carries more types of music than Store C does and Store D carries more types of music than Store B does, we would logically conclude that Store B must carry two types of music and Store D all three types of music. Store C must carry exactly one type of music in order to make the specified statements work and to be consistent with the requirement that each store carry at least one genre of music We would then use this deduction to make further decisions about the scenarios presented. Page 5

6 Analytical Reasoning Section on the LSAT will test your ability to come up with inductive reasoning and deductive reasoning. Questions asking you to identify that which COULD BE TRUE involve your ability to consider PROBABLE scenarios. Questions asking you to identify that which MUST BE TRUE test your ability to engage in DEDUCTIVE or LOGICALLY CERTAIN reasoning involving a probability of 100%. Therefore, your ability to engage in inductive and deductive reasoning will be put to the test throughout the LSAT. Get ready for the adventure. GMAT CRITICAL REASONING SECTION GMAT does not have a SEPARATE section for Critical Reasoning. The questions in this category will be mingled with other questions and tested throughout the test. Typically, GMAT test-takers will receive questions, 10 of which are typically scored. The other 3 or 4 questions will not be scored. Logical and Critical Reasoning will also be tested in Quantitative Assessment. Some of the problem solving questions will ask you to identify an answer that MUST BE TRUE for a set of evidentiary statements provided in the question stem. The Data Sufficiency section will test your ability to deductively interpret evidence, and to identify at least two different probable interpretations of evidentiary information if the evidence allows more than one interpretation. You will then be required to check whether the decision that you will reach will remain consistent across the two or three different, valid interpretations of the evidence. If the question in Data Sufficiency asks: IF 2X = 3Y, is X > Y?, we need to proceed as follows: 1. We need to logically and deductively interpret evidence 2X = 3Y to mean that X and Y MUST HAVE THE SAME SIGN (must lie on the same side of zero; one cannot be positive and the other negative) but we must also engage in inductive reasoning involving PROBABLE SCENARIOS or WHAT IF scenarios: X and Y could be both positive or both negative or both zero. X and Y could be whole numbers or fractions in order to make the evidence work. 2. In one PROBABLE interpretation of the evidence, X = 3 and Y = 2. In this scenario, X > Y. In another, equally probable scenario, X = -3 and Y = -2. In this scenario, X is less than Y. In a third and equally valid scenario, X = 0 and Y = 0. In this scenario, X and Y are equal. 3. You will then conclude that our LOGICAL REASONING using the stem evidence as it applies to the DECISION (whether X is definitely greater than Y or definitely NOT greater than Y) does not permit a unique decision. Page 6

7 4. We will, therefore, conclude that no logical determination as to the question can be made using the available evidence. We will then go on to examine the next statement or the second item of evidence, and so on. 5. Remember that Logical Reasoning will be tested throughout the GMAT. Even GMAT Sentence Correction will test your logical reasoning skills. In deciding whether problems in counseling are responsible for students failing to graduate is better than the statement problems in counseling are responsible for the failure of students to graduate, you will decide that the latter is the more logically sound expression because the problems cannot be responsible for the students but could be responsible for the failure of students to do something. GRE CRITICAL REASONING SECTION GRE will test logical reasoning in Sentence Completion, which requires test-takers to logically interpret words and phrases used outside the underlined part of the sentence, and Reading Comprehension, which will test your ability to engage in DEDUCTIVE reasoning and to question INDUCTIVE arguments put forth in the passage. Logical and Critical Reasoning will also be tested in GRE Quantitative Assessment. Some of the problem solving questions will ask you to identify an answer that MUST BE TRUE for a set of evidentiary statements provided in the question stem. The QUANTITATIVE COMPATISON section will test your ability to deductively interpret evidence, and to identify at least two different probable interpretations of evidentiary information if the evidence allows more than one interpretation. You will then be required to check whether the decision that you will reach will remain consistent across the two or three different, valid interpretations of the evidence. Consider the GRE Quantitative comparison problem stated as follows: STEM EVIDENCE: (a, 3) is a point in Quadrant II of an X-Y plane. (-4, b) is a point in Quadrant III of the same X-Y plane. DECISION QUESTION: (compare the two values in the two columns and determine whether you can conclude which of the two values MUST BE greater of the two values. COLUMN A a COLUMN B b Page 7

8 PROCEDURE FOR LOGICAL REASONING IN THIS CONTEXT OF GRE QUANTITATIVE COMPARISON You are required to DEDUCTIVELY interpret the stem evidence and then to use the deduction to decide which of the two values, a and b, is greater of the two. Our understanding of coordinate geometry would lead us to conclude that a and b must be both negative because a, the x-value of the first point, is negative in QII and b, the second value of the point (-4, b) is negative in QIII. We are, therefore, comparing a negative value with another negative value, In one scenario a could be -1 and b could be -3. In this scenario, a is greater than b. In an equally plausible scenario, a could be -3 and b -1. In this alternative and equally probable scenario, a is less than b. You will, therefore, conclude that our DEDUCTIVE REASONING of the evidence does not permit a LOGICALLY CERTAIN conclusion about which of the two values is greater. We will pick option D as explained in Module II GRE file and in the Quantitative preprogram work file. LOGICAL INTERPRETATION OF QUANTITATIVE CONCEPTS All formulas and properties of geometric shapes tested on the GMAT and GRE are valid DEDUCTIONS. If ABC is an isosceles triangle, then ABC must have two equal sides and two equal angles. All three angles of ABC must add up to 180. If 5 is the median value of a set of values, then we MUST conclude that there is an equal number of values of either side of 5. If the average and the median of a set of values are the same, then we MUST conclude that the set comprises values that have the same spacing between any two successive values. We will learn in Quantitative Modules that any set of values such that the absolute different of any two successive values is the same as that of any other two successive values, then the median and the mean must be the same. If X,Y, and Z are integers such that XYZ is an odd, positive integer, then we MUST CONCLUDE that each of the three integer values must be odd. With respect to the positioning of these values on a number line, they could all be positive or any one positive and the other two negative. WE cannot be logically certain, under the second scenario, which two of the three values is negative and which is positive. X could be positive and Y and Z are negative, or X and Y are negative and Z is positive, or X and Z are negative and Y is positive. When you try to make decisions, you will be required to use these other, equally probable scenarios and see whether your decision is consistent across different valid scenarios. Page 8

9 WHY IS LOGICAL REASONING SUCH A BIG DEAL FOR GRADUATE SCHOOL ADMISSION TEST-TAKERS? No matter what career you choose to pursue be it a nurse, a biochemist, a cytologist, an engineer, a lawyer, a consultant, or a business manager -- you will be required to maintain a healthy dose of skepticism about theories that involve single explanation that excludes alternative ones. Scientists are loath to accept one explanation for the evidence unless they have ruled out other possible explanations for the evidence. Trial lawyers are skeptical about the prosecution s self-serving single explanation for the evidence and usually present alternative explanations for the evidence in the course of creating a reasonable doubt about the explanation proffered by the prosecution. Business Consultants make a living by questioning the single explanation arguments advanced by their clients. If the client wants to improve employee retention by offering more benefits, the consultant will want to explore other explanations for why the company has issues retaining people. The management style or prospects for growth within the organization could be the issues that the client may have overlooked. In short, logical reasoning involves searching for alternative explanations for the evidence or identifying alternative factors that could have led to the same outcome. Take a look at the following argument: In a recent citywide poll, fifteen percent more residents said that they watch television programs about the visual arts than was the case in a poll conducted five years ago. During these past five years, the number of people visiting our city s art museums has increased by a similar percentage. Since the corporate funding that supports public television, where most of the visual arts programs appear, is now being threatened with severe cuts, we can expect that attendance at our city s art museums will also start to decrease. Thus some of the city s funds for supporting the arts should be reallocated to public television. You should bear in mind that the explanation that is offered in the argument may not always be explicit; it could be implied as in this argument. The argument offers ONE explanation for why the number of people visiting the city s museums increased by the same 15%: the public television show on visual arts. What could be other explanations for the same increase observed in attendance at museums? The museums advertised or lowered the admission price or had a tie-up with the local schools. It may very well be that the 15% increase in viewership may represent an increase of, say, 1000 viewers whereas the 15% increase in the visitors to the museums may represent, say, 20,000 people, Maybe, the locals watch the television program whereas the tourists from out of town go to museums. Critical thinking is about considering alternative explanations for the same information presented as evidence. Page 9

10 FACTORS, CRITICAL FACTORS, ENABLING FACTORS Factors are events or things that are causally linked to the evidence as presented in a chain of reasoning. Some of the factors that could be causally linked to admission to a law school are LSAT test scores, undergraduate GPA, motivation as demonstrated through application essays and campus visits, recommendations, and on-time applications. If the evidence is that John was denied admission to Yale Law school and the factor attributed to the evidence was his low LSAT Score of 145, the argument implies that some of the other, equally relevant factors could not have resulted in the denial of admission to John. All the factors identified are PLAUSIBLE in equal measure and the very act of suggesting the existence of other factors that could have led to the same outcome as used in the evidence decreases the PROBABILITY of the original factor identified in the argument. CONCEPT OF PROBABILITY AS IT IS USED IN CRITIQUING THE ARGUMENTS We all know that in probability, the larger the set of values the smaller the probability that any one of those values will be randomly selected. Likewise, the more explanations and factors we can think of for the evidence, the less the probability that the explanation or factor identified in the argument will have played out. The argument seems to imply that, in the absence of other factors addressed in the argument, the probability of the one factor to which the evidence is attributed appears to be 1 or certainty. But if you can identify 4 other factors, deficiency in any of which could have led to the same denial of admission, then the original explanation becomes one out of 5 equally plausible explanations. Therefore, the probability of the original explanation drops from 1 to 1/5. Weakening of an argument is done by decreasing the probability of the original explanation or of the original factor identified in the argument. Weakening of an argument is done by identifying other factors and explanations that increase the set of factors and explanations that could have played out in producing the evidence and, in doing so, by decreasing the probability of the original explanation or of the factor. Strengthening of an argument is done by asserting that the factor or explanation identified in the argument is more probable than other factors. This is usually done by providing additional evidence or information in support of the conclusion for a stated evidence. The Assumption underlying an illogical argument attempts to make the conclusion logically certain (probability of 1) by DENYING the existence or probability of other factors. Page 10

11 CONTEXT FOR INFORMATION Context is defined as the parts of a discourse that surround a word or passage and can shed light on its meaning. It is also a set of interrelated conditions in which something exists or occurs. The conclusion of an argument has to be viewed in the CONTEXT of the evidence used in the argument. In Reading Comprehension passages, the main idea has to be viewed in the context of the rest of the information presented in the passage. Context is the setting or the environment in which the conclusion exists and must be processed as such. To use an algebra analogy, context for information and the information that is provided exist as TERMS or chained values that cannot be separated. (We know that in algebra X + Y is a binomial expression in which X and Y are chained as terms and cannot be separated). The test will be about your ability to process information in context. This is done by asking two questions: What is being said? Why is it being said? If we consider a simple argument, John scored 580 on the GMAT. Therefore, he will not be admitted to Harvard Business School, the conclusion he will not be admitted to HBS must be viewed in the CONTEXT of John s GMAT Score of 580. Context for information is referred to as SCOPE of information in the following pages. No matter what the nomenclature, you need to process information in context and not deal with the two chained values (evidence and conclusion) as if they exist in isolation. If the conclusion of an argument is that the use of marijuana will cause cancer, we need to know why the use of marijuana would or could cause cancer. The evidence will provide the context or the setting for the conclusion and the answer choice for any question has to be consistent with the context or the setting for the conclusion. Page 11

12 LOGICAL REASONING FUNDAMENTALS You need to be conversant with the ground rules in logical reasoning. 1. IF ALL OF X IS Y, THEN ALL OF Y IS NOT NECESSARILY X BUT AT LEAST SOME OF Y IS X. An example of this logic is as follows: IF all Americans speak English, all those who speak English are not necessarily Americans. But at least some of those who speak English are Americans. 2. If ALL OF X IS Y, THEN, NOT X COULD BE Y. An example of this logic is as follows: If all Mexicans are Catholics, then a person who is NOT MEXICAN could be catholic. 3. IF ALL OF X IS Y, THEN NOT Y IS NOT X. An example of this logic is as follows: If all Business Schools require GMAT Scores for admission, then any school that does NOT REQUIRE GMAT Scores for admission cannot be a Business School. 4. IF Y WILL NOT HAPPEN UNLESS X IS PRESENT, THEN Y MAY OR MAY NOT HAPPEN IF X IS PRESENT. (If the absence of a factor precludes an outcome, the presence of the factor may not guarantee the outcome) An example of this logic is as follows: You cannot get into a Graduate School unless you take the standardized admission test. If you have taken the standardized admission test, you may or may not be admitted to a Graduate School if the score is not good enough or if other factors are not in order. If it is true that unless one saves money, one cannot buy a house, then the fact that someone saves money may not guarantee that the person can purchase a house. If the person does not save enough or if other emergencies crop up requiring the using the savings (such as a medical emergency), then the person may still not be able to purchase a house. Page 12

13 CRITICAL FACTORS AND ENABLING FACTORS Factors, absence of which will preclude an outcome from actualizing, are called critical factors. The absence of an LSAT score will preclude admission to a Law School. But the mere presence of an LSAT score will not necessarily lead to the desired outcome if other factors that come into play once the critical threshold is met are not in order. For example, if one scored 150 on the LSAT, the mere existence of a test score will not guarantee the outcome (admission). If the score is below the school average or if other factors are not in order. Consider the following argument: Autopsies performed on the bodies of those who had Alzheimer s disease reveal abnormal deposits of protein in the brain and extensive brain lesions. However, autopsies performed on the bodies of those who died without Alzheimer s disease also reveal abnormal deposits of protein in the brain but not lesions. Therefore, we can conclude that any person lives long enough will eventually suffer from Alzheimer s disease. The context for the conclusion that anyone who lives long enough will eventually suffer from Alzheimer s disease is the observation of abnormal deposits of protein in the brain area of both Alzheimer and non-alzheimer patients. Will the mere presence of protein in the brain lead to Alzheimer s disease or do the abnormal deposits of protein require a trigger or enabler to result in Alzheimer s disease? If the question requires that you weaken the argument, you would be looking for a reason why the deposits of protein alone cannot produce Alzheimer s disease in the absence of an enabling factor or a trigger. If the question required that you strengthen the argument, you would look for a reason why the mere presence of abnormal deposits of protein in the brain area alone is sufficient to produce Alzheimer s disease. Consider another real-world example. Unless you buy/obtain an airline ticket, you cannot travel to your destination by plane. If you bought or obtained an airline ticket, you may still get to the destination if the flight were to be canceled, or if you arrived late and missed the flight, or if you were prevented from boarding the aircraft because your name was inadvertently put on the watch list. Understand that there are several kinds of factors: factors, critical factors, and enabling factors. Some factors require the presence of other enablers to be able to produce the required outcome. Page 13

14 PAY ATTENTION TO AUXILIARIES USED IN THE STATEMENTS Auxiliary verbs such as COULD, WOULD, WILL, CAN, MAY, MIGHT need to be processed. In fact, when you work on Reading Comprehension passages, you will be required to pay attention to and process these auxiliary verbs. COULD means likely can and denotes a PROBABILITY of occurrence of an event. WOULD means likely will and connotes a probability of occurrence of an event. Would also may suggest an assumption that the author is making in advancing the argument. WILL implies speculation that is based on a good degree of confidence. IF the statement is that if Perry s faction wins the elections, the nation WILL suffer militarily and if Terry s faction wins the elections, the nation WILL suffer economically. The use of WILL suggests speculation that is based on reasonable certainty. But the statement also implies that the nation COULD suffer economically if Perry s faction wins, and the nation could suffer militarily if Terry s faction wins the elections. CAN implies a potential or confidence. Replenishment of the gene pool of the cultivated wheat CAN be accomplished through tapping into the resources of the wild wheat -- The statement connotes a degree of confidence in potentially enriching the gene pool of cultivated wheat through using the model of wild wheat. MAY implies an uncertainty and a smaller probability. MIGHT is a weaker may. QUALIFIERS AND THEIR CONNOTATIONS The QUALIFIER at most means equal to or less than The QUALIFIER at least means equal to or greater than SOME means a small proportion of the total population. MOST means a significant proportion of the total population. SOME, SOME, SOME does not cover the entire population. For example, if the statement goes: some are good cooks, some are gourmet cooks, and some are fast-food cooks, you should know that you have not covered the entire population of cooks. SOME, OTHERS, THE REST cover the whole population. If the statement goes: some are good cooks, others are gourmet cooks, and still others or the rest are fast-food cooks, then you have covered 100% of the group of cooks. Page 14

15 LOOK FOR DELIBERATE VAGUENESS OR AMBIGUITY IN THE ITEMS OF INFORMATION PROVIDED TO YOU The test is about your ability to look for and identify words and phrases that are interchangeably used but are not synonymous. Deliberate attempts at creating ambiguities may involve dropping of a qualifier or introduction of a qualifier, or use of words that mean different things in different context. Consider the following argument: In a recent study, 40 handwriting analysts could not predict the occupations of 100 persons whose handwriting were analyzed Therefore, handwriting analysis is a poor way to predict the personality-types of job applicants. Notice that the argument implies that personality types and occupations are correlated in some fashion. Consider another example: Studies have shown that sugars, if consumed immediately after 45 minutes of continuous exercise may actually promote burning of fact and lead to weight loss. Therefore, people who drink aspartame drinks rather than soft-drinks containing sugar may be acting against their self-interest in pursuing dietary goals. Notice that the argument refers to a study about SUGARS (which are normally fructose found in fruits and juices) and then switches to a reference about SUGAR (notice the singular case noun here). The sugar found in soft-drinks may be processed sugar (sucrose) made from sugarcane, and may not be interchangeably used with SUGARS that occur naturally in fruits and 100% orange juice. Another ambiguity that you should pay attention to is that the argument implies that dietary goals involve weight loss. A dietary goal may not necessarily involve weight loss or, in some instances, may actually involve weight gain. You need to look for, identify, and process these elements of deliberate vagueness that are found in the information provided to you. Consider the following argument in which the word EXPLOITATION is used in two different connotations but interchangeably referred to: Your argument that unions protect workers against exploitation misses the point that exploitation of workers is just as natural as exploitation of natural resources. Notice that exploitation of workers does not carry the same connotation as exploitation of resources. When workers are exploited, they are not paid well or provided benefits or good working conditions. Exploitation of resources could mean complete utilization of resources. Logical and critical reasoning is about paying attention to and processing these subtleties. As well, When you deal with the Argument essay in Analytical Writing Section, look for intended vagueness and interchangeable use of words and phrases, and question their use. Page 15

16 TYPES OF QUESTIONS TESTED ON THE LSAT, GRE, and GMAT 1. ANALYSIS OF AN ILLOGICAL ARGUMENT WEAKEN AN ILLOGICAL ARGUMENT STRENGTHEN AN ILLOGICAL ARGUMENT FIND THE ASSUMPTION UNDERLYING AN ILLOGICAL ARGUMENT 2. FIND THE FLAW IN THE ARGUMENT 3. IDENTIFY THE STRUCTURE OF AN ARGUMENT AND IDENTIFY AN ARGUMENT HAVING PARALLEL STRUCTURE 4. IDENTIFY THE PRINCIPLE THAT WILL SUPPORT THE ARGUMENT (tested more frequently on the LSAT and less frequently on the GMAT; the principle supporting the argument has the same connotation as stare decisis or case law or precedent in legal jurisprudence. Lawyers make arguments using precedents set by prior rulings on matters similar to the argument they are making). 5. IDENTIFY A LOGICAL CONCLUSION THAT IS NECESSARILY SUPPORTED BY THE EVIDENCE PRESENTED. 6. IDENTIFY a LOGICAL EXPLANATION for the discrepancy or paradox described in the passage. AN ILLOGICAL Argument is a conclusion that requires at least TWO statements in support of it. The EVIDENCE constitutes one statement and the assumption the other. An illogical argument may require several assumptions in support of the conclusion. We will discuss the anatomy of an illogical argument a bit later in this file. An ILLOGICAL argument can be recognized by noticing the disconnect between the evidence and the conclusion. As Johnny Cochran, the attorney for O.J. Simpson, would say, the illogical argument involves a rush to judgment and does not clearly lay out the reasoning leading to the conclusion. In other words, an illogical argument IMPLIES at least one statement before the conclusion, and the implied statement is referred to as the argument s assumption. In addition to IMPLYING something between the evidence and the conclusion, the illogical argument may also IMPLY something in the conclusion. If the conclusion of an argument is that John will not be admitted to Yale law school, the conclusion implies that John will apply or has applied for admission to Yale law school because one cannot be considered for admission unless one applies. Application is a NECESSARY precondition for admission consideration, and in order for the conclusion about the admission to be valid, the statement must imply that the person named will APPLY for admission. We will get into a more serious discussion of assumptions later on in this file. Page 16

17 ANATOMY OF AN INDUCTIVE OR ILLOGICAL ARGUMENT EVIDENCE PRESENTED ADDITIONAL INFORMATION TAKEN FOR GRANTED OR ASSUMED CONCLUSION All ILLOGICAL ARGUMENTS are non sequiturs (Latin for it does not follow ), in which a statement (conclusion) does not NECESSARILY follow from the preceding statement or statements. An example of a simple nonsequitur is: I live in New York City. Therefore, I do not drive a car to work. Notice that the conclusion Therefore, I do not drive to work is NOT necessarily true UNLESS it is true that all those who live in New York City do not drive to work. Politicians make use of non sequiturs all the time. Consider the argument: Democrats are bad. Therefore, Republicans are good. Notice that the conclusion Republicans are good is not NECESSARILY TRUE UNLESS it is true that either Republicans or Democrats are good. The UNLESS STATEMENT that the argument relies on is the ASSUMPTION of the argument. The purpose of the UNLESS STATEMENT or the ASSUMPTION is to make the otherwise non sequitur conclusion a necessarily true. REMEMBER: IN A NON SEQUITUR, THE CONCLUSION IS NOT NECESSARILY TRUE UNLESS THE ASSUMPTION IS VALID, or the IMPLIED ASSUMPTIONS ARE TRUE OR VALID. A non sequitur may rely on more than one UNLESS STATEMENT in order to become necessarily true. Consider the following argument: Herbal Magic is a cough mixture that is promoted by the manufacturer as an instant cough relief. Yet, this mixture has only 60% of the market share. If it were as effective as claimed, the mixture should command a market-share close to 100%. Because it does not, (therefore) it is not effective. Page 17

18 Notice that the conclusion that the HERBAL MAGIC is not effective because it does not have a market share of close to 100% is a non sequitur and is NOT NECESSARILY TRUE UNLESS each of the following is true: Herbal Magic is widely distributed and carried by distributors throughout the country. Herbal Magic is widely KNOWN to all cold-sufferers. Herbal Magic does not have adverse side effects that may preclude use by some cold-sufferers. Herbal Magic does not have a competing alternative which is equally effective. The UNLESS STATEMENTS that must be true in order for the conclusion to be not a non sequitur are the ASSUMPTIONS of the argument. Therefore, the non sequitur must be understood as a statement that is NOT NECESSARILY TRUE UNLESS AT LEAST ONE OTHER STATEMENT IMPLIED IS TRUE. The IMPLIED unless statement is the ASSUMPTION. The assumption is IMPLIED and never openly stated. COUNTER-SCENARIO is a MAYBE scenario that questions the ASSUMPTION. Consider the relationship between the assumption and the counter-scenario as presented in the table below. ASSUMPTION COUNTER-SCENARIO 1. HERBAL MAGIC IS WIDELY KNOWN TO ALL COLD- SUFFERS. 2. HERBAL MAGIC does not have any adverse side effects that could preclude use by some cold-sufferers. 3. Herbal Magic does NOT have a competing alternative that is equally effective. 1. MAYBE, HERBAL MAGIC IS NOT WIDELY ADVERTISED AND NOT KNOWN TO ALL COLD-SUFFERERS. 1. Maybe, Herbal Magic DOES HAVE side effects that could preclude use by some cold-sufferers. 3. Maybe, Herbal Magic DOES HAVE a competing alternative that is equally effective so that at least some coldsufferers need not use HERBAL MAGIC. Page 18

19 THE FLAW IN AN ARGUMENT IS any DEFECT in the structure of the argument that detracts from the persuasiveness of the argument. The FLAW in an argument could be that It uses terms interchangeably when the terms are not interchangeable; It ignores an alternative and equally plausible explanation; It draws a conclusion about the larger population on the basis of a sample, without establishing that the sample is representative; It considers just one factor as sufficient for success or failure; FLAW arising from interchangeable use of terms Consider the following argument: The common procedure for determining whether a food additive should be banned from use is to compare its health-related benefits with its potential risks. Yellow Dye No.5, an additive used to color lemon soda, might cause allergic reactions in a few consumers. For most consumers of lemon soda, however, the coloring enhances their enjoyment of the beverage. Therefore, this particular additive should not be banned, because the benefits greatly outweigh its risks. As you can see, the argument interchangeably uses health-related benefits and enjoyment of beverage, and treats the terms synonymously. The Flaw is, therefore, that the argument treats enjoyment of beverage as a health-specific benefit. FLAW arising from ignoring an alternative and equally plausible explanation for the evidence Consider the following argument; Premiums for automobile accident insurance are often higher for red cars than for cars of other colors. To justify these higher charges, insurance companies claim that, overall, a greater percentage of red cars are involved in accidents than are cars of any other color. If this claim is true, then lives could undoubtedly be saved by banning red cars from the roads altogether. The argument advocates banning red cars from the roads altogether as a solution for the greater percentage of red cars that are involved in accidents. The alternative explanation for why a greater percent of red cars are involved in accidents is that aggressive drivers prefer to drive red cars that match their type-a or aggressive personalities. The argument ignores this alternative explanation and is, therefore, FLAWED. Page 19

20 FLAW arising from consideration of a single factor as sufficient reason for the outcome as predicted The arguments having this flaw will attribute a single factor as sufficient cause for the predicted outcome and ignore the possibility that other factors may offset the benefits or the drawbacks of the factor mentioned in the argument. (We will discuss SINGLE FACTOR arguments later on in this file these arguments assume that the effects of any single factor, good or bad, may not be offset by other factors). Consider the following argument: If the play were successful, it would be adopted as a movie or revived at the Decade Festival. But it is not successful. We must, regrettably, conclude that neither become a movie nor revived at the Decade Festival The argument assumes that in order for the play to be made into a movie or revived at the Decade Festival, it must satisfy the ONLY CRITERION of being successful. Maybe, there are other considerations besides success as a play for the play to be made into a movie or revived at the Decade Festival. The argument fails to recognize that the fact that the play does not satisfy one sufficient condition may not preclude the play satisfying a different but sufficient condition for adaptation as a movie or revival at the Decade Festival. Arguments having this flaw are classic single factor arguments that ignore the possibility that an outcome may depend on one or another factor. Admission to law school may be predicated on LSAT Scores or, equally, on Legacy as a factor. FLAW in an argument can also arise from a reasoning that is predicated on a single, usually valid, criticism leading to the conclusion that the criticism justifies invalidating the whole thing under consideration (Missing the forest for trees flaw). For example, an argument that LSAT or GMAT test is unfair to those whose native language is not English is a valid criticism but the criticism itself does not invalidate the purpose of the standardized testing for Graduate School Admission. Interestingly, voters in an election are able to intuitively identify this flaw during elections: the fact that George Bush had a DUI arrest on his record did not invalidate his viable candidacy. (A counter-argument we hear is that this mantra was not repeated with Goebbelsian obsession during the 2000 election. In support of this counter-argument, people may cite the swift-boating on Kerry that worked because the technique of argumentum ad nauseam was followed to the letter so that the electors were focused on the single criticism rather than on the bigger picture). Page 20

21 Consider an argument having the flaw of focusing on the trees and missing out on the forest that was tested on the LSAT. Extensive research shows that television advertisements affect the buying behavior of consumers. Some people conclude from this that violent television imagery sometimes causes violent behavior. But the effectiveness of television advertisements could be a result of those televised images being specifically designed to alter buying habits, whereas television violence is not designed to cause violent behavior in the audience. Therefore, we can safely conclude that violent television imagery does not cause violence. The flaw in the argument is that it concludes that the entire first claim is invalid because the evidence on which the first conclusion is drawn does not necessarily support the first conclusion. Another flaw is that the argument assumes that if violent images are not MEANT or DESIGNED to cause violence behavior in the audience, they will not. This flaw, referred to as Columbine flaw, ignores the possibility that Some children may find violence portrayed on television or in the movies enticing and may want to ape the behavior portrayed on the screen, even though the producer did not intend for the images to have that effect. FLAW in the argument could also arise from a reasoning that because a sample shows a certain behavior, the larger population will likewise show the same characteristics. The arguments having the flaw will fail to establish that the sample under review is representative. Identifying the flaw in the argument is a matter of extreme critical reasoning. Flaw in the argument could also arise from attacking the character of the person making the argument to discredit his or her argument. Politicians resort to arguments having this flaw. If Richard Clark, a former National Security Advisor, argued that the 500 warheads discovered in Iraq during 2003 date back to pre-1990 Gulf war and could not be weaponized, his critics may counter-argue that Mr. Clark contributed to Kerry s political campaign and lacks the credibility to make logical arguments. The fact that a person may have a character flaw does not make the person s argument defective. That Clinton was a womanizer did not possibly detract from his ability be a good administrator or leader (at least, that is what you would think if you are a Clintonista). Put on your critical reasoning cap and understand the manner in which the argument is structured in order to be able to identify the flaw in the argument. Page 21

22 LET US RECAP OUR UNDERSTANDING OF THE ANATOMY OF AN ILLOGICAL ARGUMENT. The CONCLUSION of an ILLOGICAL argument is derived on the basis of the presented EVIDENCE and on the basis of the ADDITIONAL INFORMATION ASSUMED or taken for granted. Typically, the Conclusion that we reach is an INTERPRETATION of the evidence. If the interpretation involves using experience or expectation on top of the presented evidence, the conclusion thus reached will be ILLOGICAL. An ILLOGICAL conclusion is NOT a BAD CONCLUSION. It simply means that the conclusion cannot be accepted at face value, and must be verified. When the corporate managers make decisions or when the prosecution attorneys present a case in a court of law, they always use experience or stereotypical expectations in order to interpret the evidence, and arrive at ILLOGICAL decisions or conclusions. A CONSULTANT or a DEFENSE ATTORNEY must question the ASSUMPTIONS that were brought to bear on the decision or the conclusion. Experience and expectations lead one to take additional information for granted in the context of the evidence. An ILLOGICAL ARGUMENT has the following rationale for its conclusion: Given the evidence, the conclusion is valid BECAUSE the ADDITIONAL INFORMATION ASSUMED OR TAKEN FOR GRANTED is valid. The GMAT, LSAT, and GRE test takers will have some experience in dealing with the assumptions in the context of the Argument Essays in Analytical Writing Assessment. The requirement was for the test takers to question the unexplained and unexamined assumptions underlying the presented argument. You can look at an illogical argument as one in which the conclusion is one of several possible scenarios that might have played out, and one in which another person looking at the same evidentiary information will go to a different conclusion by bringing his or her own perspectives to bear on the evidence. Page 22

23 For example, if the evidence is: Tom received a GMAT score of 400 out of 800 on the GMAT, and if 5 people are looking at this evidence, each one might make a different conclusion along the following lines: Tom will not be admitted to a leading Business School. Tom did not take a prep class. Tom is not a good test taker. Tom must have been partying all night the night before. Tom is not smart. Notice how each person s conclusion is driven by his or her unique set of experience and expectations. Neither one of these conclusions is necessarily valid, and each one is illogical or non sequitur for that reason alone. The upshot of this analysis is that anytime we use our experience or expectations to reach a conclusion, we are guilty of making an illogical conclusion. LOGICAL CONCLUSION OR INFERENCE A logical conclusion is a necessarily true statement that is supported by a literal interpretation of the specifics of the evidence. EVIDENCE USED CONCLUSION REACHED BY LITERAL INTERPRETATION OF THE EVIDENCE USED A LOGICAL argument is one in which the Conclusion is essentially a restatement of the argument s evidentiary piece of information, or a statement of that which is implied but not openly stated. When you make a logical conclusion or an inference, you do not TAKE ANYTHING FOR GRANTED or use information that goes beyond that which is stated in the evidence presented to you. A LOGICAL interpretation of the evidence presented to you may also be about interpreting the qualifiers used in the evidence or the verbs and nouns used in the evidence. A logical conclusion can also be made by interpreting information presented in a mutually exclusive context. Page 23