Logical Reasoning Flashcards
Necessary vs. Sufficient Conditions
Definition: A necessary condition for some state of affairs S is a condition that must be satisfied in order for S to obtain.
For example, a necessary condition for getting an A in 341 is that a student hand in a term paper. This means that if a student does not hand in a term paper, then a student will not get an A, or, equivalently, if a student gets an A, then a student hands in a term paper.
Definition: A sufficient condition for some state of affairs S is a condition that, if satisfied, guarantees that S obtains.
For example, a sufficient condition for getting an A in 341 is getting an A on every piece of graded work in the course. This means that if a student gets an A on every piece of graded work in the course, then the student gets an A.
Handing in a term paper is not a sufficient condition for getting an A in the course. It is possible to hand in a term paper and not to get an A in the course.
Getting an A on every piece of graded work is not a necessary condition for getting an A in the course. It is possible to get an A in the course even though one fails to get an A on some piece of graded work.
Example #2
In her essay, Mary Anne Warren does not maintain that each of her five conditions is individually sufficient for being a person, though she thinks that some of them may be, and she thinks that the conjunction of the first three (consciousness, reasoning, and self-motivated activity) is probably sufficient for personhood. This means that she thinks it is probably true that if anything is conscious, able to reason, and engages in self-motivated activity, then that thing is a person. She maintains that satisfying all three of these conditions is sufficient for being a person.
Warren does not argue that any of her five conditions is individually necessary. But she does maintain that the disjunction of the five conditions is necessary. That is, she maintains that a necessary condition for personhood is that something satisfy at least one of these five conditions. In other words, she maintains that if none of these five conditions is true of something, then that thing is not a person.
Necessary versus Sufficient Conditions: Self-Test Answers
- Being a mammal is a sufficient condition for being human. False. Being a mammal does not guarantee that one is a human. There are mammals that are not human.
- Being human is a sufficient condition for being a mammal. True. Being a human guarantees that one is a mammal. As soon as we find out that something is not a mammal, we know that it cannot be a human.
- Being alive is a necessary condition for having a right to life. True. Nothing that is not alive can have a right to life.
- Being alive is a sufficient condition for having a right to life. False. There are lots of things that are alive that do not have a right to life. What about, for example, grass? This answer could be questioned by those who think that it is seriously wrong to kill anything that is alive.
- If it is true that if P then Q, then P is a sufficient condition for Q. True. The truth of P is sufficient for, guarantees the truth of Q.
- If it is true that if P then Q, then Q is a necessary condition for P. True. If Q is not true, then P is not true. The falsity of Q rules out the truth of P. It is necessary for Q to be true in order for P to be true.
- If it is true that if P is not the case, then Q is not the case, then P is a necessary condition for Q. True. The truth of P is necessary in order for Q to be true. When P is not true, Q is not true.
- If it is true that if P is not the case, then Q is not the case, then P is a sufficient condition for Q. False. The truth of P does not guarantee the truth of Q. All we know is that the falsity of P guarantees the falsity of Q. For example, let P be “A student hands in his/her term paper” and Q be “This student gets an A in 341.”
- Something is a brother if and only if it is a male sibling. This means that being a male sibling is both necessary and sufficient for something to be a brother. True. In general if it is the case that P is true if and only if Q is true, then Q is necessary and sufficient for P and P is necessary and sufficient for Q. If anything fails to be male or fails to be a sibling, then it is not a brother. So being a male sibling is a necessary condition for being a brother. Furthermore, it is impossible for anything to be a male sibling and not to be a brother. So being a male sibling is a sufficient condition for being a brother.
Diagramming Conditionals
Try and diagram every conditional relationship you encounter and infer any supported conclusions.
- This year Santa has been forced to make some changes. Because of the poor economy and the rising cost of fuel, now only children on his nice list will be given stockings filled with coal. Kids on his naughty list will now receive stockings stuffed solely with socks.
- Answer: If Coal -> Nice. If Naughty -> Socks
- Those who make the mistake of imbibing too much “holiday cheer” at their company’s holiday party usually find themselves without a job the next day, and certainly avoid asking your boss if they’d like to sit on your lap unless you’re bearded and in a bright red suit.
- Answer: If Drunk at Company Party –m–> Get Fired. If Not Bearded or Not in Bright Red Suit -> Don’t Ask Boss
- Besides choir groups and drunks, only families with children should go caroling.
- Answer: If Should go Caroling -> Choir Group or Drunks or Children
- No drink with Scotch counts as a holiday drink unless it includes a cinnamon stick. Nor should Egg Nog be served at holiday parties without plenty of Nog and fresh eggs, and certainly no holiday party is complete without an excellent Egg Nog. This party will eventually run out of Nog and always was without cinnamon sticks, but we did all drink delicious holiday drinks and only delicious holiday drinks.
- Answer: If Scotch -> (Holiday Drink -> Cinnamon Stick). If Egg Nog Served -> Plenty Nog + Fresh Eggs. If Holiday Party Complete -> Egg Nog. This Party: Not Cinnamon Sticks + Holiday Drinks. MBT: No one at the part is drinking Scotch
- Breaking into peoples’ homes to eat their cookies and drink their milk is illegal in every country. And consistently asking children to sit on your lap will definitely get you arrested.
- Answer: If Break in + Eat -> Illegal. If Ask Kids -> Arrested
- Any drinking game that involves a dreidel should not be played until after the eighth day of Hanukkah. No Hanukkah is Happy without loads of Gelt. And you will invariably feel ill if you consume too many Latkes.
- Answer: If Drinking Game + Dreidel -> Not Play Before 8th Day. If Happy Hanukkah -> Loads of Gelt. If Too Many Latkes -> Feel Ill.
- Although no one who celebrates Hanukkah also celebrates Christmas, many of those who celebrate Kwanzaa do celebrate Christmas. Those who greet others with “Joyous Kwanzaa” always celebrate Kwanzaa, but those who wish others a “Merry Christmas” may or may not celebrate Christmas.
- Answer: If Celebrate Hanukkah -> Not Celebrate Christmas. If Celebrate Kwanzaa –s– Celebrate Christmas. If Greet with “Joyous Kwanzaa” -> Celebrate Kwanzaa. MBT: Some people who celebrate Kwanzaa don’t celebrate Hanukkah.
Contrapositives
A contrapositive just describes the same statement written differently. It is just the reversed and negated version of whatever statement you originally start with.
So if your original statement is “if A, then B,” the contrapositive of that is “if not B, then Not A.”
And if your original statement is “if not B, then not A” the contrapositive of that is “if A, then B.”
Because both a statement and it’s contrapositive represent the same exact logical relationship, just expressed differently, you really have to understand both to understand a conditional statement.
Sufficient Assumption
The definition of “sufficient assumption” is “something that would prove the argument’s conclusion to be correct.”
Premise: Anything times zero equals zero.
Conclusion: Therefore A times B equals zero.
Question: “Which one of the following, if true, would allow the conclusion to be properly inferred?” Or, stated another way, “Which one of the following, if assumed, would justify the argument’s conclusion?” Both of these are asking for sufficient assumptions. (You might want to memorize the wording of those questions so that you can differentiate a sufficient assumption question from a necessary assumption question.)
This question is asking you to prove the argument’s conclusion. In order to prove a conclusion on the LSAT, the conclusion of the argument must be connected, with no gaps, to the evidence offered. So we need an answer that connects the evidence “anything times zero is zero” to the conclusion “A times B is zero.”
It’s pretty simple. The answer must contain one of the following:
“A equals zero.” If it’s true that A is zero, and if it’s true that anything times zero equals zero, then no matter what B is, the conclusion “A times B equals zero” would be proven correct. And a proof is what we’re looking for on a sufficient assumption question.
“B equals 0” would be just as good, because no matter what A is, the conclusion “A times B equals zero” would be proven correct.
Here’s the really interesting part (if you’re a nerd like me, which I hope you are). While “A equals zero” and “B equals zero” are each sufficient to prove the conclusion correct, neither of these statements, independently, are necessary in order for the argument to possibly make sense. A could be 1,000,000, and the conclusion “A times B equals zero” could still be conceivable (if B equals zero). Likewise, B could be 1,000,000 and the conclusion could still be possible (as long as A equals zero.) So if the question had said “which one of the following is an assumption required by the argument,” (that’s asking for a necessary component of the argument) then “A equals zero” would not be a good answer. Nor would “B equals zero.”
“Conclusion” Key Words
CONCLUSION:
- Hence
- Therefore
- So
- Accordingly
- Thus
- Consequently
- Clearly/Obviously
- For this reason
- In light of this
- In view of this
- As a result
- Clear that/Obvious that
- Implies that
- Seems that
- Can infer that
- Follows that
- Shows that
- Conclude that
- Means that
- Must be that
- Can be concluded that
- Should be noted that
- Strongly supports that
- (Premise keyword) … , __________
- __________ (Premise keyword) …
Sequential Parallels Explained
How will they ask this?
Which of the following best illustrates the principle illustrated by the argument above?
Which of the following is most similar in its reasoning to the argument above?
Which of the following exhibits the same pattern of reasoning as the argument above?
Which of the following exhibits the same pattern of flawed reasoning as the argument above?
What do they want me to do?
Describe the argument, then identify another argument that fits that same description.
Weaken/Strengthen Questions
Since the LSAT is set up to test your understanding of the structure of arguments, the correct answer choices for weakening and strengthening questions will more often undermine or support their respective conclusions structurally rather than by directly attacking stated evidence, or by providing new evidence. You can undermine conclusions by finding a key assumption in the argument and then finding the answer choice that will make that assumption more likely to be true or less likely to be true, as the case may be.
Remember that weakening an argument does not mean disproving it completely and strengthening an argument does not mean proving it beyond all doubt. To strengthen an argument is to make the conclusion more likely to be true, and to weaken an argument is to make the conclusion at least somewhat less likely to be true.
Weaken - How will they ask this?
- Which one of the following, if true, would most weaken the above argument?
- The prediction that ends the paragraph would be most seriously called into question if it were true that
- Which one of the following, if true, most weakens the researcher’s argument?
- Which one of the following, if true, most calls into question the argument that…?
- Which one of the following, if true, most undermines the conclusion?
- Which one of the following, if true, would be the strongest challenge to the author’s conclusion?
What do they want me to do?
- Make the conclusion less likely to be true.
Strengthen - How will they ask this?
- Which one of the following, if established, does most to justify the position advanced by the passage?
- Which one of the following, if true, provides the best reason in favor of the proposal?
- Which one of the following, if true, most strengthens the argument?
- Which of the following principles, if valid, most helps to justify the scientist’s reasoning?
- Which one of the following, if true, most helps to support the claim that…?
- Which one of the following, if true, most supports the proposal?
What do they want me to do?
- Make the conclusion more likely to be true.
Strategies for solving
To answer either a weaken or strengthen question, you must first identify the key assumptions in the argument. In some cases of weaken questions, the correct answer actually contradicts a statement made in the stimulus argument.
Sample Weaken/Strengthen Questions
Consider the following example:
More and more computer software that is capable of correcting not just spelling, but also grammar and punctuation is being developed. Therefore, it is increasingly unnecessary for working reporters and writers to have a complete knowledge of the principles of English grammar and punctuation. Consequently, in training journalists, less emphasis should be placed on the principles of grammar so that students and professors can concentrate on other important subjects.
Which one of the following, if true, most seriously weakens the argument given for the recommendation above?
- The effective use of software that corrects grammar and punctuation requires an understanding of grammatical principles.
- Much of the software that corrects grammar and punctuation is already in use.
- Development of more complex ethical guidelines for reporters and writers has meant that professors and students in journalism schools must allow time for teaching such issues.
- Most of the software that is capable of correcting grammar and punctuation can be run on the types of computers available to most media outlets.
- The journalism curriculum already requires that journalism students be familiar with, and able to use, a variety of software packages.
The best answer is A. If journalists must be able to understand the principles of grammar in order to effectively use the software described, the conclusion of the argument—that less emphasis should be placed on such principles in journalism school—is less likely to be true. Answer choices B, D, and E are irrelevant to the argument. Answer choice C actually strengthens the argument by making the conclusion just slightly more likely to be true.
Assumption Questions
Assumption questions ask you to identify the missing link in the logic of the stimulus argument.
Some example question stems are:
- Which one of the following, if assumed, allows the argument’s conclusion to be properly drawn?
- Which one of the following is an assumption on which the argument depends?
- The final conclusion above follows logically if which one of the following is assumed?
- The claim made by the official in the argument above depends on the presupposition that
- Which one of the following is an assumption on which the argument relies?
Because an assumption is an unstated piece of evidence, this technique “knocks out” each answer choice that you test, one by one. When you test the correct answer, you are knocking out a piece of evidence, and the argument should suffer accordingly.
Sample Assumption Question
The birth rate in Country X is down this year by 12% compared to last year. The death rate in Country X has remained stable for several years. Therefore, the population of Country X is decreasing measurably.
Which of the following is assumed by the author of the argument above?
- The causes of the declining birthrate in Country X can be discovered through physician surveys.
- Statisticians are able to predict future changes in the size of the population of Country X.
- Country Y, which has a nearly identical population to Country X, is experiencing the same population shift as Country X.
- There was no significant migration into Country X during the time under discussion.
- The causes of the declining birthrate in Country X are primarily economic in nature.
The best answer is D. You might be able to answer the question directly by simply recognizing the missing piece of evidence and selecting it. However, if you aren’t able to do so, you can still determine the correct answer by negating whichever answer choices you view as potentially correct. It is not likely that you will have time to carefully negate each choice presented. So, you will need to “filter out” choices that you find clearly irrelevant.
Let’s say that you could easily recognize that answer choice C is irrelevant since it discusses Country Y and, therefore, it can’t possibly be the missing link between the stated evidence and the stated conclusion, which both involve Country X. Likewise, let’s say that you could eliminate answer choice B, which is about predicting the future, whereas the stimulus argument is about the recent past.
That leaves answer choices A, D, and E still in contention. Try to negate answer choice A. You should come up with something like: “The causes of the declining birthrate in Country X cannot be discovered through physician surveys.” Since physicians play no part in the stimulus argument, you should recognize that neither the original phrasing of answer choice A, nor its negation, has any bearing on the relationship between the evidence and the conclusion stated in the argument. Similarly, negating E with “The causes of the declining birthrate in Country X are not primarily economic in nature,” has no impact on the likelihood that the conclusion is valid. However, if you negate answer choice D, you get “There was significant migration into Country X during the time under discussion.” This would dramatically call into question the stated conclusion that the population of Country X is declining measurably. Therefore, answer choice D must be correct.
Necessary Assumption Questions
- Which one of the following is an assumption on which the argument depends [or relies]?
- Which one of the following is an assumption required by the argument?
- Which of the following is a necessary assumption of the argument?
- The argument assumes which one of the following?
- Name a piece of evidence the argument needs but does not have.
Sufficient Assumption Questions
- Which one of the following principles, if valid, most helps to justify the reasoning above?
- Which one of the following, if assumed, allows the conclusion to be properly drawn?
- The conclusion above follows logically if which of the following is assumed?
- Choose a response that will prove the conclusion is true.
Inference Questions
How will they ask this?
- Which one of the following judgments most closely conforms to the principle stated above?
- Which of the following is most strongly supported by the information above?
- If the statements above are true, which one of the following must also be true on the basis of them?
- Which of the following can be properly concluded [or properly inferred] from the statements above?
- Which of the following follows logically from the information above?
What do they want me to do?
- Identify any claim that is proved by the passage.
Logical Reasoning - Skills
- Recognizing the parts of an argument and their relationships.
- Recognizing similarities and differences between patterns of reasoning.
- Drawing well-supported conclusions.
- Reasoning by analogy
- Recognizing misunderstandings or points of disagreement.
- Determining how additional evidence affects an argument.
- Detecting assumptions made by particular arguments
- Identifying and applying principles or rules
- Identifying flaws in arguments Identifying explanations
Logical Reasoning - Types of Questions
- Flaw in the Reasoning - 57 questions; 16%
- Must be True - 51 questions (tie); 14.3%
- Strengthen - 51 questions (tie); 14.3%
- Assumption - 34 questions; 9.6%
- Parallel Reasoning - 29 questions; 8.1%
- Weaken - 26 questions; 7.3%
- Method of Reasoning - 24 questions (tie); 6.7%
- Main Point - 24 questions (tie); 6.7%
- Resolve the Paradox - 22 questions; 6.2%
- Justify the Conclusion - 20 questions; 5.6%
- Point at Issue (or Point of Agreement) - 7 questions; 2%
- Evaluate the Argument - 5 questions; 1.4%
- Cannot be True - 3 questions; 0.8%
“Justify the Conclusion” Questions
These questions ask you to draw a conclusion from evidence presented within the stimulus. In some cases, the conclusion that you are asked to draw is based on only part of the stimulus and will not necessarily be the main idea of the stimulus paragraph. Some conclusion questions use the terms “infer” and “imply.”
Remember that “imply” and “infer” are just two sides of the same coin; the speaker, or author, implies and the listener, or reader, infers.
Some example question stems are:
- If the statements above are true, which one of the following must also be true on the basis of them?
- If the environmentalist’s statements are true, they provide the most support forwhich one of the following?
- Which one of the following statements is most strongly supported by the information above?
- Amy’s reply is structured to lead to which one of the following conclusions?
- Which one of the following inferences is most strongly supported by the information above?
- Which one of the following can be properly inferred from the argument above?
Strategies for Solving
To correctly answer these questions you must consider the validity of the argument. Look for the logical end of the chain of reasoning started in the stimulus argument. Answer choices that go beyond the scope of the argument are incorrect, even if they include factual statements.
Sample Conclusion Question
Physician: The continued use of this drug to treat patients with a certain disease cannot be adequately supported by the proposition that any drug that treats the disease is more effective than no treatment at all. What must also be taken into account is that this drug is very expensive and has notable side effects.
Which one of the following most accurately expresses the main point of the physician’s argument?
- The drug is more effective than no treatment at all.
- The drug is more effective than other forms of treatment for the disease.
- The drug is more expensive than other forms of treatment for the disease.
- The drug should not be used to treat the disease unless it is either effective or inexpensive.
- The drug’s possible effectiveness in treating the disease is not sufficient justification for using it.
The best answer is E. According to the physician, the fact that the drug might be somewhat effective is not enough reason to continue to use it. The physician suggests that other factors beyond mere effectiveness, such as cost and side effects, be considered when deciding whether to use the drug.
Answer choice A is incorrect because, although it might be inferred from evidence presented in the stimulus, the question stem calls for the main point of the argument.
Answer choices B and C are incorrect because no comparison is made between the drug and any other form of treatment for the disease.
Answer choice D is incorrect because the physician also contends that the side effects of the drug should be considered when deciding whether to use the drug.
“Method of Reasoning” Questions
Method of reasoning (or argument) questions ask you to recognize the way that the argument is put together. You must choose the answer that properly describes the structure of the stimulus argument. Some, but certainly not all, method of argument questions are based on dialogues.
Some examples of question stems are:
- The scientist’s argument proceeds by
- Trillian’s response to Douglas proceeds by
- Karen uses which one of the following argumentative techniques in countering Rob’s argument?
- The argument criticizing the essay employs which one of the following strategies?
- The relationship of Svetlana’s statement to Katalya’s argument is that Svetlana’s statement
Strategies for Solving
To answer these questions correctly, you must pay attention to the structure of the argument rather than to the content or subject matter. Describe the argument in your own words (paraphrase) and try to match up the analogous parts of your paraphrased argument to the answer choices. The LSAT purposely uses difficult language to disguise relatively simple arguments. Practice sufficiently so that you can recognize the argument amidst the tricky language.
Sample Method of Argument Question
It is widely accepted that eating sugar can cause weight gain. Indeed, many people who are susceptible to weight gain report that, in their own experience, eating large amounts of sugar is invariably followed by a measurable weight gain within a few days. However, it is likely that common wisdom has confused cause and effect.
Recent studies suggest that hormonal changes associated with stress can cause weight gain, and there is ample evidence that people who are fond of sugar tend to eat more of it when they are under stress.
The argument employs which one of the following argumentative strategies?
- It cites evidence that questions the accuracy of the evidence advanced in support of the position that is being called into question.
- It gives additional evidence that suggests an alternative interpretation of the evidence offered in support of the position being challenged.
- It relies upon the superiority of science versus common opinion as a means of dismissing the relevance of evidence based upon common experience.
- It shows that the position being challenged is not consistent with cited, proven factual evidence.
- It calls into question the intelligence of those who subscribe to a certain popularly held belief.
The best answer is B. The additional evidence provided is regarding hormonal changes causing weight gain; the alternative interpretation of the correlation between sugar consumption and weight gain is the possibility that both the weight gain and sugar consumption are, in fact, caused by stress.
“Parallel Reasoning” Questions
These questions ask you to match up two arguments that share structural characteristics. There are usually two parallel structure questions in each Logical Reasoning section. They are usually in the second half of the section, and they can usually be recognized by their length since each answer choice is a complete argument. Sometimes the stimulus argument is flawed. In such a case, you must identify the answer choice argument that shares the same flaw.
Some sample question stems are:
- Which one of the following arguments is most similar in its reasoning to the argument above?
- The flawed reasoning in which one of the following arguments most closely resembles the flawed reasoning in the professor’s argument?
- The reasoning in the argument above most closely parallels that in which one of the following?
- The flawed pattern of reasoning in the argument above is most similar to that in which one of the following?
- Which one of the following contains questionable reasoning most similar to that in the argument above?
- The pattern of reasoning in which of the following is most similar to that in the mayor’s argument?
Strategies for Solving
One way to approach the parallel structure questions is to reason by analogy. In other words, if you match up the analogous parts, the structure becomes clearer. The structure of the argument is more important than the content or subject matter of the argument.
Do not be fooled by answer choices that refer to the same subject matter as that presented in the stimulus argument. You are expected to see past the facts presented and look at the relationship between the evidence and conclusion in the argument.
Sample Parallel Structure Question
Murcheson’s drawing of the Lincoln Monument contains several inaccuracies. Therefore, your attempt to reproduce the drawing of the monument will not be a very accurate reproduction of the drawing.
Which one of the following is most similar in its flawed reasoning to the flawed reasoning in the argument above?
- Katrina’s presentation was made up primarily of fabrications and distortions. So the video recording made of it cannot be of good quality.
- An architect who creates a model of an ugly building must necessarily create an ugly model, unless the sculpture is a distorted representation of the building.
- If a puppy’s coloring resembles its mother’s, then if the mother’s fur is curly, the puppy’s fur must also be curly.
- Kelly imitated Rory. But, Kelly is different from Rory, so Kelly could not have imitated Rory very well.
- Quentin’s second movie is similar to his first. Therefore, his second movie must be entertaining since his first movie won many awards.
The best answer is A. The flaw in the stimulus argument is that it concludes that a reproduction of a flawed reproduction cannot, itself, be an accurate reproduction.
Answer choice A makes the same mistake. In this instance, Murcheson’s drawing and Katrina’s presentation fill the same role as one another in their respective arguments. And, video recording of Katrina’s presentation is analogous to the attempted reproduction in the stimulus argument. Some of the other answer choices are also flawed arguments; however, they do not share the same structure.
“Main Point” Questions
“Role of Fact”
Some of the questions ask about the role, or function, of a specific fact that is included in the stimulus argument.
Some sample question stems are:
- The claim that taxes should increase in proportion to a person’s income plays which one of the following roles in the argument?
- The claim in the first sentence of the passage plays which one of the following roles in the argument?
- Joshua’s statement that “this claim simply cannot be proved” plays which one of the following roles in his argument?
- Which one of the following most accurately describes the role played in the passage by the claim that fish have gills?
Strategies for Solving
To answer these questions correctly, you must determine the reason why the author included this particular fact or detail. Most of the incorrect answer choices will either be too narrow or too broad, or beyond the scope of the stimulus argument.
Sample Role of Fact Question
Some environmentalists have argued that there are two independently sufficient justifications for recycling waste materials: one based on economics and the other based on the aversion to the continued consumption of pristine global resources. But suppose that recycling were not economically efficient. Then it would be less clear that an aversion to consuming pristine global resources is enough of a reason to recycle.
Which one of the following most accurately describes the role played in the argument by the supposition that recycling is not economically efficient?
- It is used to disprove the environmentalist position that we should recycle.
- It is used to show that the two reasons given by environmentalists are each individually sufficient.
- It is used to disprove the claim that recycling is beneficial.
- It is used to weaken the claim that consumption of pristine resources is sufficient reason to recycle.
- It is used to show that there is no sufficient reason for recycling.
The best answer is D. The author of the argument asks the reader to go along with the supposition that recycling is not economically efficient in order to show that a mere aversion to consuming pristine resources might not be a sufficient, independent justification for recycling after all. Answer choices A, C, and E are incorrect because the argument does not actually show that there is no support for recycling. Answer choice B is incorrect because the argument is meant to question the reasons given for recycling, not to shore up the reasons given by environmentalists.
“Resolve the Paradox” Questions
“Resolution Questions”
A paradox arises when you are presented with two statements that are both true, yet they appear to be mutually contradictory. The key words to help you spot paradox question stems are “explain” and “reconcile.”
Some sample questions stems are:
- Which one of the following, if true, most helps to explain why the people mentioned continued to grow beans?
- Which one of the following, if true, most helps to explain the finding of the caffeine study?
- Which one of the following, if true, helps to reconcile the statements above?
- Which one of the following, if true, does the most to reconcile the apparent conflict in the system described above?
Strategies for Solving
The stimulus argument in paradox questions usually includes a term that either must be redefined in order to resolve the paradox, or contains a misinterpretation of a term upon which the author relies. You must recognize the contradiction that exists and look for an answer choice that more clearly defines a critical term.
We often refer to the “bumblebee paradox” with our tutoring students. Current research suggests that a bumblebee’s wings are aerodynamically unsound; as a result, a bumblebee should not be able to fly. However, bumblebees do fly, so clearly the term “aerodynamically unsound” is poorly defined.
Sample Paradox Question
Researchers concur with one another on the issue of the harm that can result when children are exposed to microscopic asbestos fibers. The resulting disease, asbestosis, is almost always debilitating and even sometimes fatal. Many older school buildings contain asbestos insulation around hot water pipes and heating ducts because, until recently, the dangers of asbestos were unknown. Yet, these same researchers also agree that laws requiring the removal of asbestos from schools could actually lead to an increased likelihood of exposure to asbestos fibers to the students who attend those schools.
Which one of the following, if true, most helps to resolve the apparent discrepancy in the researchers’ positions?
- New insulation materials used instead of asbestos are as potentially harmful to children as asbestos is.
- The money that would be spent on the removal of asbestos from schools could be spent in other ways that would be more likely to increase the overall health of school children.
- Other sources of asbestos, such as automobile and household uses, are responsible for more cases of asbestosis than school-based sources are.
- Removing the asbestos from older schools disperses a large quantity of asbestos fibers into the air, where they are more easily inhaled than when they are left in place around the pipes and ducts.
- Lead-based paint poses more of a health hazard to children than asbestos does.
The best answer is D. Answer choice D provides an explanation for the suggestion not to remove the asbestos. Essentially, this answer boils down to pointing out that the act of removal itself is more dangerous than simply leaving the hazard in place.
Answer choices A, C, and E are all incorrect because they focus on other potential sources of harm rather than the apparent conflict between the two positions that the researchers hold simultaneously: 1) that asbestos can cause serious harm, and 2) that it should not be removed from schools.
Answer choice B is incorrect because it focuses on financial issues rather than the seemingly logical inconsistency inherent in the researchers’ positions.
“Point at Issue” Questions
“Principle Question”
These questions ask you to identify a rule, or principle, that supports the stimulus argument presented. In some cases, you are required to choose an argument that conforms to the stimulus principle.
Some example question stems are:
- The reasoning above most closely conforms to which one of the following principles?
- Which one of the following conforms most closely to the principle illustrated above?
- Which one of the following employee behaviors most clearly violates the company policy outlined above?
- Which one of the following illustrates a principle most similar to that illustrated by the passage?
Sample Principle Question
The best way to create a successful party is to visualize the guests discussing it with friends the next day. The hostess should first decide what aspects of the party will lead to favorable comments from guests during those conversations and then come up with refreshments and activities that will actually cause such post-party talk to occur.
Which one of the following illustrates a principle most similar to that illustrated by the passage?
- When planning a vacation, some travelers decide first where they want to go, and then plan their route. But, for most people, financial issues must also be taken into account.
- When landscaping the grounds of a new home, you should start with the topsoil and then choose your shrubbery and other foliage.
- Good moviemakers do not extemporaneously film their movies in one or two days with no script; a movie cannot be separated from the story upon which it is based.
- In negotiating an employment contract, the best method is to make as many outlandish demands as possible and then agree to forgo the most outrageous of them.
- To make a great golf shot, you should picture the ball landing where you want it to land, and then you will be able to line up your body and your club accordingly.
The best answer is E. The underlying principle in the stimulus argument is that it is best to work backward from a desired result in order to achieve that result. In the stimulus, the desired result is a successful party. In the correct answer, the desired result is a great golf shot.
Answer choices B, C, and D are incorrect because they work forward rather than backward. This particular format, choosing an argument that illustrates the same principle as the stimulus argument, is similar to parallel reasoning questions.
“Evaluate the Argument” Questions
These questions always involve a dialogue between two people who disagree about something. You are expected to choose the answer that best describes the crux of the disagreement.
Some sample question stems are:
- Todd’s and Andy’s positions indicate that they disagree about the truth of which one of the following?
- A point on which Randy and Salvatore’s views differ is whether
- William and Max disagree over whether
- The dialogue most supports the claim that Heather and Mike disagree about whether
Strategies for Solving
Your first step is to understand, then succinctly summarize the first party’s argument. Next, determine where the first and second parties differ in their statements. Paraphrasing will help you get to the root of the argument and quickly locate the correct answer.
Sample Point of Contention Question
Jason: The Internet is making more information available to more people than ever before in history. So, people can simply learn all they need to know without seeking the advice of experts.
Mark: In the past, the need for experts actually increased as the volume of knowledge increased. Therefore, the Internet will surely increase our dependence on experts.
The dialogue most strongly supports the claim that Jason and Mark disagree with each other about whether
- the Internet will contribute significantly to the increase in the spread of information throughout society
- the Internet will increase the likelihood that people will seek the advice of experts when searching for knowledge
- the Internet makes more information available to more people
- experts will increase their reliance on the Internet in the future
- explaining knowledge to specialists can only be accomplished by Internet experts
The best answer is B. Jason thinks that experts will become irrelevant because of direct public access to information. Mark thinks that the opposite will occur.
“Flaw in the Reasoning” Questions
These questions ask you to identify an error of reasoning in the stimulus argument.
Some sample question stems are:
- Which one of the following, if true, identifies a flaw in the plan for the program?
- The argument is vulnerable to criticism on the grounds that the argument
- The reasoning above is questionable because it fails to exclude the possibility that
- The reasoning in the politician’s argument is flawed because this argument
- Ralph’s reasoning in his response to Jessica is most vulnerable to criticism on the grounds that it
- Which one of the following is a questionable argumentative strategy employed in the above argument?
Strategies for Solving
The question stem tells you that a problem exists with the logic of the argument. You just have to choose the answer that describes the flaw. Most flawed arguments include an unwarranted assumption; in other words, the argument is weakened by a missing link between the stated evidence and the stated conclusion. The author of the argument is taking something for granted that is not necessarily true.
Sample Flaw Question
Giant Motors is attempting to dominate the automobile market by promoting its products with an expensive television advertising campaign. But, the results of recent surveys reveal that, in the opinion of 85 percent of all consumers, Giant Motors already dominates the market. Since any product with more than half of all sales in any given market is already dominant, Giant Motors dominates the market now and must only preserve its market share in order to continue to dominate its market.
The argument commits which one of the following errors in reasoning?
- Failing to eliminate the possibility that what seems to be the outcome of a specific market condition might actually be the cause of the condition
- Confusing a condition necessary for certain outcome to obtain for a condition that, alone, is sufficient to assure that result
- Treating the failure to establish the falsity of a specific claim as tantamount to showing that such a claim is certainly accurate
- Accepting evidence that a claim is believed to be true as evidence that the claim, itself, is actually true
- Describing the results of a survey that was done in the past as acceptably predicting future conditions
The best answer is D. The survey results only show the opinions of consumers. The stimulus argument relies upon those beliefs as fact in concluding that Giant Motors dominates the automobile market. There is no reason to accept the opinion of consumers as an accurate measure of Giant Motors’s actual share of the automobile market. Each of the other answer choices describes an error in reasoning that is irrelevant to the stimulus argument.
Example #1
Laird: Pure research provides us with new technologies that contribute to saving lives. Even more worthwhile than this, however, is its role in expanding our knowledge and providing new, unexplored ideas. Kim: Your priorities are mistaken. Saving lives is what counts most of all. Without pure research, medicine would not be as advanced as it is. Laird and Kim disagree on whether pure research derives its significance in part from its providing new technologies expands the boundaries of our knowledge of medicine should have the saving of human lives as an important goal has its most valuable achievements in medical applications has any value apart from its role in providing new technologies to save lives
Explanation #1
This question asks you to identify the point on which Laird and Kim disagree with respect to pure research. Laird identifies two contributions of pure research: its medical applications (“technologies that contribute to saving lives”) and its role in expanding knowledge and providing new ideas. Of these, Laird considers the second contribution to be more worthwhile. Kim, on the other hand, maintains that “Saving lives is what counts most of all.” Since pure research saves lives through medical applications, Kim disagrees with Laird about whether pure research has its most valuable achievements in medical applications. The correct response, therefore, is (D). Response (A) is incorrect since we can determine, based on their statements, that Laird and Kim agree that pure research “derives its significance in part from its providing new technologies.” Laird explicitly cites the value of pure research with respect to providing new technologies. Kim indicates agreement with (A), at least in the case of medical technologies, by asserting that “Without pure research, medicine would not be as advanced as it is.” Response (B) is incorrect since we can determine, based on their statements, that Laird and Kim would likely agree that pure research “expands the boundaries of our knowledge of medicine.” Laird notes that pure research provides us with new technologies that have medical applications. Kim points out that “Without pure research, medicine would not be as advanced as it is.” Response (C) is incorrect. Kim indicates agreement that pure research “should have the saving of human lives as an important goal” since Kim’s position is that “Saving lives is what counts most of all.” Since Laird cites the saving of lives as one way in which pure research is worthwhile or valuable, Laird also indicates agreement that pure research “should have the saving of human lives as an important goal,” although Laird indicates that expanding knowledge and providing new ideas should be an even more important goal of pure research. The same activity can of course have more than one goal. Response (E) is incorrect. Laird clearly agrees that pure research has value “apart from its role in providing new technologies to save lives,” given that Laird explicitly cites a second way in which pure research is valuable. However, nothing in what Kim says suggests disagreement with (E). Kim’s position is that the greatest value of pure research is its role in providing new technologies to save lives. We cannot infer from this that Kim believes this role to be the only value of pure research. This question was of medium difficulty, based on the number of test takers who answered it correctly when it appeared on the LSAT.
Example #2
Executive: We recently ran a set of advertisements in the print version of a travel magazine and on that magazine’s website. We were unable to get any direct information about consumer response to the print ads. However, we found that consumer response to the ads on the website was much more limited than is typical for website ads. We concluded that consumer response to the print ads was probably below par as well. The executive’s reasoning does which one of the following? bases a prediction of the intensity of a phenomenon on information about the intensity of that phenomenon’s cause uses information about the typical frequency of events of a general kind to draw a conclusion about the probability of a particular event of that kind infers a statistical generalization from claims about a large number of specific instances uses a case in which direct evidence is available to draw a conclusion about an analogous case in which direct evidence is unavailable bases a prediction about future events on facts about recent comparable events
Explanation #2
This question asks you to identify how the executive’s reasoning proceeds. The ads discussed by the executive appeared in two places—in a magazine and on the magazine’s website. Some information is available concerning the effect of the website ads on consumers, but no consumer response information is available about the print ads. The executive’s remarks suggest that the ads that appeared in print and on the website were basically the same, or very similar. The executive reasoned that information about the effect of the website ads could be used as evidence for an inference about how the print ads likely performed. The executive thus used the analogy between the print ads and the website ads to infer something about the print ads. (D), therefore, is the correct response. Response (A) is incorrect. The executive’s conclusion about the likely consumer response to the print ads does not constitute a prediction, but rather a judgment about events that have already transpired. Moreover, the executive’s conclusion is not based on any reasoning about the cause of the consumer response to the print ads. Response (B) is incorrect. The executive does conclude that certain events are likely to have transpired on the basis of what was known to have transpired in a similar case, but no distinction can be made in the executive’s argument between events of a general kind and a particular event of that kind. There are two types of event in play in the executive’s argument and they are of the same level of generality—the response to the website ads and the response to the print ads. Response (C) is incorrect. The executive does not infer a statistical generalization, which would involve generalizing about a population on the basis of a statistical sample. The executive merely draws a conclusion about the likely occurrence of specific events. Response (E) is also incorrect. The executive does use the comparability of the print and website ads as the basis for the conclusion drawn; however, as noted above, the executive’s conclusion about the likely consumer response to the print ads does not constitute a prediction about future events, but rather a judgment about events that have already transpired. This was an easy question, based on the number of test takers who answered it correctly when it appeared on the LSAT.
Example #3
During the construction of the Quebec Bridge in 1907, the bridge’s designer, Theodore Cooper, received word that the suspended span being built out from the bridge’s cantilever was deflecting downward by a fraction of an inch (2.54 centimeters). Before he could telegraph to freeze the project, the whole cantilever arm broke off and plunged, along with seven dozen workers, into the St. Lawrence River. It was the worst bridge construction disaster in history. As a direct result of the inquiry that followed, the engineering “rules of thumb” by which thousands of bridges had been built around the world went down with the Quebec Bridge. Twentieth-century bridge engineers would thereafter depend on far more rigorous applications of mathematical analysis. Which one of the following statements can be properly inferred from the passage? Bridges built before about 1907 were built without thorough mathematical analysis and, therefore, were unsafe for the public to use. Cooper’s absence from the Quebec Bridge construction site resulted in the breaking off of the cantilever. Nineteenth-century bridge engineers relied on their rules of thumb because analytical methods were inadequate to solve their design problems. Only a more rigorous application of mathematical analysis to the design of the Quebec Bridge could have prevented its collapse. Prior to 1907 the mathematical analysis incorporated in engineering rules of thumb was insufficient to completely assure the safety of bridges under construction.
Explanation #3
The question asks you to identify the response that can be properly inferred from the passage. The passage indicates that the Quebec Bridge disaster in 1907 and the inquiry that followed caused the engineering “rules of thumb” used in construction of thousands of bridges to be abandoned. Since the Quebec Bridge disaster in 1907 prompted this abandonment, it can be inferred that these were the rules of thumb under which the Quebec Bridge was being built when it collapsed and that these were the rules of thumb used in bridge building before 1907. Further, since the Quebec Bridge collapsed while under construction and the rules of thumb being used were abandoned as a result, it can be inferred that the rules of thumb used in building the Quebec Bridge and bridges prior to 1907 were insufficient to completely assure the safety of bridges under construction. Finally, since the alternative that was adopted in place of the old engineering rules of thumb was to “depend on far more rigorous applications of mathematical analysis,” it can be inferred that the mathematical analysis incorporated in the engineering rules of thumb used prior to 1907 made them insufficient to completely assure the safety of bridges under construction. Thus, (E) is the correct response. Response (A) is incorrect. (A) asserts that bridges built before about 1907 were unsafe for the public to use because they were built without thorough mathematical analysis. But this conclusion goes far beyond what is established by the passage. The passage gives evidence only about the safety of bridges built before 1907 while they were under construction. It is silent on whether bridges built before about 1907 were safe when open for use by the public. Moreover, the passage indicates that the rules of thumb used in bridge construction before 1907 were abandoned because the use of those rules did not provide adequate assurance of safety for bridges under construction. It does not follow that bridges built using those rules of thumb (those built before about 1907) actually were unsafe, either while under construction or when open for public use. Response (B) is incorrect in claiming that Cooper’s absence from the construction site caused the breaking off of the cantilever. The passage does not establish that, had Cooper been at the site, he could have successfully intervened to prevent the cantilever from breaking off. By freezing the project, he might have spared lives by stopping work, but there is nothing in the passage to indicate that he necessarily would have prevented the collapse. Response (C) is incorrect; there is no evidence in the passage about why nineteenth-century bridge engineers relied on their rules of thumb. Response (D) is also incorrect. While the passage suggests that a more rigorous application of mathematical analysis would have prevented the collapse of the bridge, it offers no evidence that it is the only way the collapse could have been prevented. For example, it might have been prevented had corrective measures been taken in time. This question was of medium difficulty, based on the number of test takers who answered it correctly when it appeared on the LSAT.
Example #4
The supernova event of 1987 is interesting in that there is still no evidence of the neutron star that current theory says should have remained after a supernova of that size. This is in spite of the fact that many of the most sensitive instruments ever developed have searched for the tell-tale pulse of radiation that neutron stars emit. Thus, current theory is wrong in claiming that supernovas of a certain size always produce neutron stars. Which one of the following, if true, most strengthens the argument? Most supernova remnants that astronomers have detected have a neutron star nearby. Sensitive astronomical instruments have detected neutron stars much farther away than the location of the 1987 supernova. The supernova of 1987 was the first that scientists were able to observe in progress. Several important features of the 1987 supernova are correctly predicted by the current theory. Some neutron stars are known to have come into existence by a cause other than a supernova explosion.
Explanation #4
This question asks you to identify the response that most strengthens the argument. The argument concludes that “current theory is wrong in claiming that supernovas of a certain size always produce neutron stars” based on the observation that no evidence has been found of a neutron star left behind by the supernova event of 1987. However, the failure to find evidence of the predicted neutron star does not necessarily indicate that such evidence does not exist. It may instead indicate that the instruments used to search for the evidence are not powerful enough to detect a neutron star in the area where the 1987 supernova event occurred. The argument would thus be strengthened if there was evidence that the search instruments used would in fact be capable of finding the predicted neutron star if that star existed. Response (B) provides such evidence. If “sensitive astronomical instruments have detected neutron stars much farther away than the location of the 1987 supernova,” then it is less likely that the predicted neutron star is outside the detection range of “the most sensitive instruments ever developed.” Thus, (B) is the correct response. Response (A) reports that most supernova remnants that astronomers have detected have a neutron star nearby. Since (A) gives no information about the size of the supernovas that produced these remnants, it is possible that all of the remnants detected to date are consistent with the current theory’s claim that supernovas of a certain size always produce neutron stars. (A), therefore, lends no support to the argument that the current theory is wrong in this claim. Response (C) reports that the supernova of 1987 was the first supernova that scientists were able to observe in progress. This information has no direct bearing on the question of whether this event produced a neutron star and thus cannot be used to strengthen the argument that the current theory is wrong. Response (D) asserts that several important features of the 1987 supernova are correctly predicted by the current theory. This bolsters the support for the current theory and would thus, if anything, weaken the argument that the current theory is wrong. Response (E) reports that not all neutron stars are the products of supernova events. Since this information pertains to neutron stars that were not produced by supernovas, it is irrelevant to the question of whether all supernovas of a certain size produce neutron stars, as the current theory claims. Hence, (E) lends no support to the argument. This was a difficult question, based on the number of test takers who answered it correctly when it appeared on the LSAT.
Example #5
Political scientist: As a political system, democracy does not promote political freedom. There are historical examples of democracies that ultimately resulted in some of the most oppressive societies. Likewise, there have been enlightened despotisms and oligarchies that have provided a remarkable level of political freedom to their subjects. The reasoning in the political scientist’s argument is flawed because it confuses the conditions necessary for political freedom with the conditions sufficient to bring it about fails to consider that a substantial increase in the level of political freedom might cause a society to become more democratic appeals to historical examples that are irrelevant to the causal claim being made overlooks the possibility that democracy promotes political freedom without being necessary or sufficient by itself to produce it bases its historical case on a personal point of view
Explanation #5
This question asks you to identify how the reasoning in the political scientist’s argument is flawed. The argument bases its conclusion—that democracy does not promote political freedom—on two sets of historical examples. The first set of examples demonstrates that democracy is not sufficient for political freedom, and the second set demonstrates that democracy is not necessary for political freedom. But it does not follow from these examples that democracy does not promote political freedom. Even if democracy is not, by itself, sufficient for political freedom, it can still promote political freedom by contributing to it in most instances. Even if democracy is not necessary for political freedom, it can still be true that democracy is something that promotes political freedom wherever it is found. Thus, (D) is the correct response. Response (A) is incorrect. The political scientist’s argument does not indicate that any particular conditions are necessary for political freedom, nor does it indicate that any particular conditions are sufficient to bring about political freedom. Thus the argument could not be said to confuse these two sorts of conditions. Rather, the political scientist’s argument attempts to demonstrate that democracy does not promote political freedom on the grounds that democracy is neither necessary nor sufficient for bringing about political freedom. Response (B) is incorrect. The argument does fail to consider whether a substantial increase in the level of political freedom would cause a society to become more democratic, but this does not constitute a flaw in its reasoning. The truth of the claim that increased political freedom causes greater democratization would not by itself undermine the political scientist’s conclusion that democracies do not promote political freedom. Nor does that claim engage with the argument’s premises, which are concerned with the effect of democracy on political freedom, not the effect of political freedom on democracy. Response (C) is incorrect. The “causal claim being made” could only be the argument’s conclusion that democracy does not promote political freedom, which denies that there is a causal connection between democracy and political freedom. The historical examples in the argument are relevant to this claim, however. These examples are an important part of the larger body of historical evidence that one would look to when investigating the issue of whether democracy promotes political freedom. Response (E) is also incorrect. The political scientist does not express a personal point of view or base the historical examples on such a view. On the contrary, the historical examples themselves are an impersonal, though flawed, basis for the argument’s conclusion. This was a difficult question, based on the number of test takers who answered it correctly when it appeared on the LSAT.