Arguments

Example:

Whether the world is Euclidean or non-Euclidean is still an open question. However, if a star's position is predicted based on non-Euclidean geometry, then when a telescope is pointed to where the star should be it will be there. Whereas, if the star's position is predicted based on Euclidean geometry, then when a telescope is pointed to where the star should be it won't be there. This strongly indicates that the world is non-Euclidean.

Which one of the following best expresses the main idea of the passage?

(A) The world may or may not be Euclidean.
(B) The world is probably non-Euclidean.
(C) The world is non-Euclidean.
(D) The world is Euclidean.
(E) The world is neither Euclidean nor non-Euclidean.

Choice (A) understates the main idea. Although the opening to the passage states that we don't know whether the world is non-Euclidean, the author goes on to give evidence that it is non-Euclidean. Choice (C) overstates the main idea. The author doesn't say that the world is non-Euclidean, just that evidence strongly indicates that it is. In choice (B), the word "probably" properly limits the scope of the main idea, namely, that the world is probably non-Euclidean, but we can't yet state so definitively. The answer is (B).

Premises

Once you've found the conclusion, most often everything else in the argument will be either premises or "noise." The premises provide evidence for the conclusion; they form the foundation or infrastructure upon which the conclusion depends. To determine whether a statement is a premise, ask yourself whether it supports the conclusion. If so, it's a premise. Earlier we saw that writers use certain words to flag conclusions; likewise writers use certain words to flag premises. Following is a partial list of the most common premise indicators:

Premise Indicators

Counter-Premise Indicators

As you may have anticipated, the LSAT writers sometimes use counter-premises to bait wrong answer-choices. Answer-choices that refer to counter-premises are very tempting because they refer directly to the passage and they are in part true. But you must ask yourself "Is this the main point that the author is trying to make?" It may merely be a minor concession.

Logic II (Diagramming)

We thoroughly covered diagramming in the game section. Diagramming is also useful with arguments. However, the diagrams won't be as elaborate as those used with games. In fact, in these cases, the term "diagramming " is somewhat of a misnomer. Rarely will we actually draw a diagram; instead we will symbolize the arguments, much as we did the conditions of the games.

Most arguments are based on some variation of an if-then statement. However, the if-then statement is often embedded in other equivalent structures. We already studied embedded if-then statements in the chapter on flow charts. Still, we need to further develop the ability to recognize these structures.

If-Then
A-->B

By now you should be well aware that if the premise of an if-then statement is true then the conclusion must be true as well. This is the defining characteristic of a conditional statement; it can be illustrated as follows:

A-->B
A
Therefore, B

This diagram displays the if-then statement "A-->B," the affirmed premise "A," and the necessary conclusion "B." Such a diagram can be very helpful in showing the logical structure of an argument.

Example: (If-then)

If Jane does not study for the LSAT, then she will not score well. Jane, in fact, did not study for the LSAT; therefore she scored poorly on the test.

When symbolizing games, we let a letter stand for an element. When symbolizing arguments, however, we may let a letter stand for an element, a phrase, a clause, or even an entire sentence. The clause "Jane does not study for the LSAT" can be symbolized as ~S, and the clause "she will not score well" can be symbolized as ~W. Substituting these symbols into the argument yields the following diagram:

~S-->~W
~S
Therefore, ~W

This diagram shows that the argument has a valid if-then structure. A conditional statement is presented, ~S-->~W; its premise affirmed, ~S; and then the conclusion that necessarily follows, ~W, is stated.

Embedded If-Then Statements

Usually, arguments involve an if-then statement. Unfortunately, the if-then thought is often embedded in other equivalent structures. In this section, we study how to spot these structures.

Example: (Embedded If-then)

John and Ken cannot both go to the party.

At first glance, this sentence does not appear to contain an if-then statement. But it essentially says: "if John goes to the party, then Ken does not."

Example: (Embedded If-then)

Danielle will be accepted to graduate school only if she does well on the GRE.

Given this statement, we know that if Danielle is accepted to graduate school, then she must have done well on the GRE. Note: Students often wrongly interpret this statement to mean:

"If Danielle does well on the GRE, then she will be accepted to graduate school."

There is no such guarantee. The only guarantee is that if she does not do well on the GRE, then she will not be accepted to graduate school.

"A only if B" is logically equivalent to "if A, then B."

Affirming the Conclusion Fallacy

A-->B
B
Therefore, A

Remember that an if-then statement, A-->B, tells us only two things: (1) If A is true, then B is true as well. (2) If B is false, then A is false as well (contrapositive). If, however, we know the conclusion is true, the if-then statement tells us nothing about the premise. And if we know that the premise is false (we will consider this next), then the if-then statement tells us nothing about the conclusion.

Example: (Affirming the Conclusion Fallacy)

If he is innocent, then when we hold him under water for sixty seconds he will not drown. Since he did not die when we dunked him in the water, he must be innocent.

The logical structure of the argument above is most similar to which one of the following?

(A) To insure that the remaining wetlands survive, they must be protected by the government. This particular wetland is being neglected. Therefore, it will soon perish.
(B) There were nuts in that pie I just ate. There had to be, because when I eat nuts I break out in hives, and I just noticed a blemish on my hand.
(C) The president will be reelected unless a third candidate enters the race. A third candidate has entered the race, so the president will not be reelected.
(D) Every time Melinda has submitted her book for publication it has been rejected. So she should not bother with another rewrite.
(E) When the government loses the power to tax one area of the economy, it just taxes another. The Supreme Court just overturned the sales tax, so we can expect an increase in the income tax.

To symbolize this argument, let the clause "he is innocent" be denoted by I, and let the clause "when we hold him under water for sixty seconds he will not drown" be denoted by ~D. Then the argument can be symbolized as

I-->~D
~D
Therefore, I

Notice that this argument is fallacious: the conclusion "he is innocent" is also a premise of the argument. Hence the argument is circular--it proves what was already assumed. The argument affirms the conclusion then invalidly uses it to deduce the premise. The answer will likewise be fallacious.

We start with answer-choice (A). The sentence

"To insure that the remaining wetlands survive, they must be protected by the government"

contains an embedded if-then statement:

"If the remaining wetlands are to survive, then they must be protected by the government."

This can be symbolized as S-->P. Next, the sentence "This particular wetland is being neglected" can be symbolized as ~P. Finally, the sentence "It will soon perish" can be symbolized as ~S. Using these symbols to translate the argument gives the following diagram:

S-->P
~P
Therefore, ~S

The diagram clearly shows that this argument does not have the same structure as the given argument. In fact, it is a valid argument by contraposition.

Turning to (B), we reword the statement "when I eat nuts, I break out in hives" as

"If I eat nuts, then I break out in hives." This in turn can be symbolized as N-->H.

Next, we interpret the clause "there is a blemish on my hand" to mean "hives," which we symbolize as H. Substituting these symbols into the argument yields the following diagram:

N-->H
H
Therefore, N

The diagram clearly shows that this argument has the same structure as the given argument. The answer, therefore, is (B).

Denying the Premise Fallacy

A-->B
~A
Therefore, ~B

The fallacy of denying the premise occurs when an if-then statement is presented, its premise denied, and then its conclusion wrongly negated.

Example: (Denying the Premise Fallacy)

The senator will be reelected only if he opposes the new tax bill. But he was defeated. So he must have supported the new tax bill.

The sentence "The senator will be reelected only if he opposes the new tax bill" contains an embedded if-then statement: "If the senator is reelected, then he opposes the new tax bill." (Remember: "A only if B" is equivalent to "If A, then B.") This in turn can be symbolized as R-->~T. The sentence "But the senator was defeated" can be reworded as "He was not reelected," which in turn can be symbolized as ~R. Finally, the sentence "He must have supported the new tax bill" can be symbolized as T. Using these symbols the argument can be diagrammed as follows:

R-->~T
~R
Therefore, T

[Note: Two negatives make a positive, so the conclusion ~(~T) was reduced to T.] This diagram clearly shows that the argument is committing the fallacy of denying the premise. An if-then statement is made; its premise is negated; then its conclusion is negated.

Transitive Property

A-->B
B-->C
Therefore, A-->C

These arguments are rarely difficult, provided you step back and take a bird's-eye view. It may be helpful to view this structure as an inequality in mathematics. For example, 5 > 4 and 4 > 3, so 5 > 3.

Notice that the conclusion in the transitive property is also an if-then statement. So we don't know that C is true unless we know that A is true. However, if we add the premise "A is true" to the diagram, then we can conclude that C is true:

A-->B
B-->C
A
Therefore, C

As you may have anticipated, the contrapositive can be generalized to the transitive property:

A-->B
B-->C
~C
Therefore, ~A

Example: (Transitive Property)

If you work hard, you will be successful in America. If you are successful in America, you can lead a life of leisure. So if you work hard in America, you can live a life of leisure.

Let W stand for "you work hard," S stand for "you will be successful in America," and L stand for "you can lead a life of leisure." Now the first sentence translates as W-->S, the second sentence as S-->L, and the conclusion as W-->L. Combining these symbol statements yields the following diagram:

W-->S
S-->L
Therefore, W-->L

The diagram clearly displays the transitive property.

DeMorgan's Laws

~(A & B) = ~A or ~B
~(A or B) = ~A & ~B

If you have taken a course in logic, you are probably familiar with these formulas. Their validity is intuitively clear: The conjunction A&B is false when either, or both, of its parts are false. This is precisely what ~A or ~B says. And the disjunction A or B is false only when both A and B are false, which is precisely what ~A and ~B says.

You will rarely get an argument whose main structure is based on these rules--they are too mechanical. Nevertheless, DeMorgan's laws often help simplify, clarify, or transform parts of an argument. They are also useful with games.

Example: (DeMorgan's Law)

It is not the case that either Bill or Jane is going to the party.

This argument can be diagrammed as ~(B or J), which by the second of DeMorgan's laws simplifies to (~B and ~J). This diagram tells us that neither of them is going to the party.

A unless B
~B-->A

"A unless B" is a rather complex structure. Though surprisingly we use it with little thought or confusion in our day-to-day speech.

To see that "A unless B" is equivalent to "~B-->A," consider the following situation:

Biff is at the beach unless it is raining.

Given this statement, we know that if it is not raining, then Biff is at the beach. Now if we symbolize "Biff is at the beach" as B, and "it is raining" as R, then the statement can be diagrammed as ~R-->B.

CLASSIFICATION

In Logic II, we studied deductive arguments. However, the bulk of arguments on the LSAT are inductive. In this section we will classify and study the major types of inductive arguments.

An argument is deductive if its conclusion necessarily follows from its premises--otherwise it is inductive. In an inductive argument, the author presents the premises as evidence or reasons for the conclusion. The validity of the conclusion depends on how compelling the premises are. Unlike deductive arguments, the conclusion of an inductive argument is never certain. The truth of the conclusion can range from highly likely to highly unlikely. In reasonable arguments, the conclusion is likely. In fallacious arguments, it is improbable. We will study both reasonable and fallacious arguments.

We will classify the three major types of inductive reasoning--generalization, analogy, and causal--and their associated fallacies.

Generalization

Generalization and analogy, which we consider in the next section, are the main tools by which we accumulate knowledge and analyze our world. Many people define generalization as "inductive reasoning." In colloquial speech, the phrase "to generalize" carries a negative connotation. To argue by generalization, however, is neither inherently good nor bad. The relative validity of a generalization depends on both the context of the argument and the likelihood that its conclusion is true. Polling organizations make predictions by generalizing information from a small sample of the population, which hopefully represents the general population. The soundness of their predictions (arguments) depends on how representative the sample is and on its size. Clearly, the less comprehensive a conclusion is the more likely it is to be true.

Example:

During the late seventies when Japan was rapidly expanding its share of the American auto market, GM surveyed owners of GM cars and asked them whether they would be more willing to buy a large, powerful car or a small, economical car. Seventy percent of those who responded said that they would prefer a large car. On the basis of this survey, GM decided to continue building large cars. Yet during the '80s, GM lost even more of the market to the Japanese.

Which one of the following, if it were determined to be true, would best explain this discrepancy.

(A) Only 10 percent of those who were polled replied.
(B) Ford which conducted a similar survey with similar results continued to build large cars and also lost more of their market to the Japanese.
(C) The surveyed owners who preferred big cars also preferred big homes.
(D) GM determined that it would be more profitable to make big cars.
(E) Eighty percent of the owners who wanted big cars and only 40 percent of the owners who wanted small cars replied to the survey.

The argument generalizes from the survey to the general car-buying population, so the reliability of the projection depends on how representative the sample is. At first glance, choice (A) seems rather good, because 10 percent does not seem large enough. However, political opinion polls are typically based on only .001 percent of the population. More importantly, we don't know what percentage of GM car owners received the survey. Choice (B) simply states that Ford made the same mistake that GM did. Choice (C) is irrelevant. Choice (D), rather than explaining the discrepancy, gives even more reason for GM to continue making large cars. Finally, choice (E) points out that part of the survey did not represent the entire public, so (E) is the answer.

Analogy

To argue by analogy is to claim that because two things are similar in some respects, they will be similar in others. Medical experimentation on animals is predicated on such reasoning. The argument goes like this: the metabolism of pigs, for example, is similar to that of humans, and high doses of saccharine cause cancer in pigs. Therefore, high doses of saccharine probably cause cancer in humans.

Clearly, the greater the similarity between the two things being compared the stronger the argument will be. Also the less ambitious the conclusion the stronger the argument will be. The argument above would be strengthened by changing "probably" to "may." It can be weakened by pointing out the dissimilarities between pigs and people.

Example:

Just as the fishing line becomes too taut, so too the trials and tribulations of life in the city can become so stressful that one's mind can snap.

Which one of the following most closely parallels the reasoning used in the argument above?

(A) Just as the bow may be drawn too taut, so too may one's life be wasted pursuing self-gratification.
(B) Just as a gambler's fortunes change unpredictably, so too do one's career opportunities come unexpectedly.
(C) Just as a plant can be killed by over watering it, so too can drinking too much water lead to lethargy.
(D) Just as the engine may race too quickly, so too may life in the fast lane lead to an early death.
(E) Just as an actor may become stressed before a performance, so too may dwelling on the negative cause depression.

The argument compares the tautness in a fishing line to the stress of city life; it then concludes that the mind can snap just as the fishing line can. So we are looking for an answer-choice that compares two things and draws a conclusion based on their similarity. Notice that we are looking for an argument that uses similar reasoning, but not necessarily similar concepts. In fact, an answer-choice that mentions either tautness or stress will probably be a same-language trap.

Choice (A) uses the same-language trap--notice "too taut." The analogy between a taut bow and self-gratification is weak, if existent. Choice (B) offers a good analogy but no conclusion. Choice (C) offers both a good analogy and a conclusion; however, the conclusion, "leads to lethargy," understates the scope of what the analogy implies. Choice (D) offers a strong analogy and a conclusion with the same scope found in the original: "the engine blows, the person dies"; "the line snaps, the mind snaps." This is probably the best answer, but still we should check every choice. The last choice, (E), uses language from the original, "stressful," to make its weak analogy more tempting. The best answer, therefore, is (D).

Causal Reasoning

Of the three types of inductive reasoning we will discuss, causal reasoning is both the weakest and the most prone to fallacy. Nevertheless, it is a useful and common method of thought.

To argue by causation is to claim that one thing causes another. A causal argument can be either weak or strong depending on the context. For example, to claim that you won the lottery because you saw a shooting star the night before is clearly fallacious. However, most people believe that smoking causes cancer because cancer often strikes those with a history of cigarette use. Although the connection between smoking and cancer is virtually certain, as with all inductive arguments it can never be 100 percent certain. Cigarette companies have claimed that there may be a genetic predisposition in some people to both develop cancer and crave nicotine. Although this claim is highly improbable, it is conceivable.

There are two common fallacies associated with causal reasoning:

1. Confusing Correlation with Causation.

To claim that A caused B merely because A occurred immediately before B is clearly questionable. It may be only coincidental that they occurred together, or something else may have caused them to occur together. For example, the fact that insomnia and lack of appetite often occur together does not mean that one necessarily causes the other. They may both be symptoms of an underlying condition.

2. Confusing Necessary Conditions with Sufficient Conditions.

A is necessary for B means "B cannot occur without A." A is sufficient for B means "A causes B to occur, but B can still occur without A." For example, a small tax base is sufficient to cause a budget deficit, but excessive spending can cause a deficit even with a large tax base. A common fallacy is to assume that a necessary condition is sufficient to cause a situation. For example, to win a modern war it is necessary to have modern, high-tech equipment, but it is not sufficient, as Iraq discovered in the Persian Gulf War.

SEVEN COMMON FALLACIES

Contradiction

A Contradiction is committed when two opposing statements are simultaneously asserted. For example, saying "it is raining and it is not raining" is a contradiction. Typically, however, the arguer obscures the contradiction to the point that the argument can be quite compelling. Take, for instance, the following argument:

"We cannot know anything, because we intuitively realize that our thoughts are unreliable."

This argument has an air of reasonableness to it. But "intuitively realize" means "to know." Thus the arguer is in essence saying that we know that we don't know anything. This is self-contradictory.

Equivocation

Equivocation is the use of a word in more than one sense during an argument. This technique is often used by politicians to leave themselves an "out." If someone objects to a particular statement, the politician can simply claim the other meaning.

Example:

Individual rights must be championed by the government. It is right for one to believe in God. So government should promote the belief in God.

In this argument, right is used ambiguously. In the phrase "individual rights" it is used in the sense of a privilege, whereas in the second sentence right is used to mean proper or moral. The questionable conclusion is possible only if the arguer is allowed to play with the meaning of the critical word right.

Circular Reasoning

Circular reasoning involves assuming as a premise that which you are trying to prove. Intuitively, it may seem that no one would fall for such an argument. However, the conclusion may appear to state something additional, or the argument may be so long that the reader may forget that the conclusion was stated as a premise.

Example:

The death penalty is appropriate for traitors because it is right to execute those who betray their own country and thereby risk the lives of millions.

This argument is circular because "right" means essentially the same thing as "appropriate." In effect, the writer is saying that the death penalty is appropriate because it is appropriate.

Shifting The Burden Of Proof

It is incumbent on the writer to provide evidence or support for her position. To imply that a position is true merely because no one has disproved it is to shift the burden of proof to others.

Example:

Since no one has been able to prove God's existence, there must not be a God.

There are two major weaknesses in this argument. First, the fact that God's existence has yet to be proven does not preclude any future proof of existence. Second, if there is a God, one would expect that his existence is independent of any proof by man.

Unwarranted Assumptions

The fallacy of unwarranted assumption is committed when the conclusion of an argument is based on a premise (implicit or explicit) that is false or unwarranted. An assumption is unwarranted when it is false--these premises are usually suppressed or vaguely written. An assumption is also unwarranted when it is true but does not apply in the given context--these premises are usually explicit.

Example: (False Dichotomy)

Either restrictions must be placed on freedom of speech or certain subversive elements in society will use it to destroy this country. Since to allow the latter to occur is unconscionable, we must restrict freedom of speech.

The conclusion above is unsound because

(A) subversives do not in fact want to destroy the country
(B) the author places too much importance on the freedom of speech
(C) the author fails to consider an accommodation between the two alternatives
(D) the meaning of "freedom of speech" has not been defined
(E) subversives are a true threat to our way of life

The arguer offers two options: either restrict freedom of speech, or lose the country. He hopes the reader will assume that these are the only options available. This is unwarranted. He does not state how the so-called "subversive elements" would destroy the country, nor for that matter, why they would want to destroy it. There may be a third option that the author did not mention; namely, that society may be able to tolerate the "subversives" and it may even be improved by the diversity of opinion they offer. The answer is (C).

Appeal To Authority

To appeal to authority is to cite an expert's opinion as support for one's own opinion. This method of thought is not necessarily fallacious. Clearly, the reasonableness of the argument depends on the "expertise" of the person being cited and whether she is an expert in a field relevant to the argument. Appealing to a doctor's authority on a medical issue, for example, would be reasonable; but if the issue is about dermatology and the doctor is an orthopedist, then the argument would be questionable.

Personal Attack

In a personal attack (ad hominem), a person's character is challenged instead of her opinions.

Example:

Politician: How can we trust my opponent to be true to the voters? He isn't true to his wife!