Friday, September 29, 2006

Critical Reasoning - Approach


Logistics of the Arguments Section

The arguments comprise one-third of the Verbal section of the GMAT i.e approximately 14 questions.

What is an Argument ?

An argument is an attempt to provide a reason for believing something by citing something else.No of claims are put forward in an argument,the claim that is being supported is the conclusion.Claims alleged to support the conclusion are the premises.

Words ,Phrases supporting Conclusions:

This shows that;
We can infer that;
It follows that;
This indicates that;
For that reason,we may say;

Words ,Phrases introducing Premises:

The reason is that;
On the basis of;
t follows from;
In view of;
We may infer from;

Gap between Premises and Conclusions is Assumptions—identify the gaps and use it to find the solution.

Classification of Arguments

Deductive arguments are those in which the conclusion necessarily follows from the premises/evidence. It shows tight connection between the Premises and Conclusions. Most arguments on the test are inductive, where the author presents the evidence as support for the conclusion. The validity of the conclusion depends on the strength of the evidence.

Unlike deductive arguments, the conclusion of an inductive argument is always uncertain. You must be prepared to handle both reasonable arguments (when the conclusion is likely) and false arguments (when the conclusion is improbable). Each classification of inductive reasoning carries its own associated fallacies.

Evaluation of an Argument—To find errors in Arguments

(1) If-Then Statements

Most arguments are based on some variation of an if-then statement, which may be either directly stated or embedded. Understanding the if-then premise reveals the underlying simplicity of arguments.

If the premise of an if-then statement is true, then the conclusion must be true as well.

If A, then B

While three possible statements can be derived from the implication "if A, then B", only one is valid.

The statement that IS logically equivalent to "if A, then B" is called the contrapositive. It is stated as:

If not B, then not A

Let's explore why this is true.

"If there is a hurricane, then Samantha will cry"

There are four different hypothetical possibilities to consider when making deductions based on this statement:

1) A hurricane occurs
2) A hurricane does not occur
3) Samantha cries
4) Samantha does not cry

Let's consider each individually:

1. If a hurricane occurs.

You know that if this is true, the result will be that Samantha will cry.

2. If a hurricane does not occur.

If a hurricane does not occur, you can deduce nothing about Samantha. In particular, you cannot deduce that she does not cry. There are many other reasons why Samantha could cry, besides a hurricane (fight with her mom, she sees a sad movie, she gets sick).

3. If Samantha cries.

Again, you can't deduce anything about the occurence of a hurricane if Samantha cries. The if-then statement doesn't assert that Samantha cries only if a hurricane occurs, just that if it does, Samantha will cry. Samantha can cry even on clear, sunny days.

4. If Samantha does not cry.

If Samantha does not cry, you can deduce that a hurricane did not occur. Why? If it had occurred, then Samantha would definitely have cried. Yet she didn't. So, we know that, given Samantha's disposition, a hurricane did not occur.

To review, any time you see a statement in the form of "If A, then B", contrapose the statement into "If not B, then not A".

You know only two things:

a) what will happen if X occurs
b) what will happen if Y does not occur.

Those are the only valid deductions that you can make based on that original statement.

You can only assume two things about the implication "if A, then B":

1) If A is true, then B must be true.
2) If B is false, then A must be false.

2) Embedded If-Then Statements

If-then statements are frequently embedded in other structures, making their detection more difficult.

Example: (Embedded If-then)

Jamie and Kyle cannot both go to the mall.

At first glance, this sentence does not appear to contain an if-then statement. But it essentially says:

"if Jamie goes to the mall, then Kyle does not."

The contrapositive ("if Kyle goes to the mall, then Jamie does not") correctly expresses the same thing.

Example: (Embedded If-then)

Heather will go to Europe only if she gets a raise at work.

Given this statement, we know that if Heather goes to Europe, she must have gotten a raise at work.Students often wrongly interpret this statement to mean:

"If Heather gets a raise at work, then she will go to Europe."

We have no guarantee of this. The only guarantee is that if Heather doesn't get the raise, she will not go to Europe.

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

Fallacies from no.3 to no.15 are not important for Critical reasoning Questions but a student should know about them

3) Circular Reasoning

Here an unsubstantiated assertion is used to justify another unsubstantiated assertion,which is,or atleast could be ,used to justify the first statement.For instance,

Full scholarships are appropriate for disadantaged scholars because it is right to offer a top-notch education to those most capable.

This argument is circular because "right" means essentially the same thing as "appropriate." In effect, the author writer is saying that scholarships are appropriate because they are appropriate.

(4) The Biased Sample Fallacy

This is commited whenever the data for a statistical inference is drawn from a sample that is not representative of the population under consideration.

For example:

In a recent survey conducted by The Times of India of its readers,60% of the respondents indicated strong support to Lalu Prasad Yadav.Hence the survey clearly shows that Lalu yadav is the most popular leader among the masses.

The data for the inference in this argument is drawn from a sample that is not reprentative of the entire electorate.

6) The Insufficient Sample Fallacy

The Fallacy of the Insufficient Sample is committed whenever an inadequate sample is used to justify the conclusion drawn.
Here's an argument that commits the fallacy of the insufficient sample:

I have worked with three people from Bangalore City and found them to be obnoxious, pushy and rude. It is obvious that people from Bangalore City have a bad attitude.

The data for the inference in this argument is insufficient to support the conclusion. Three observations of people are not sufficient to support a conclusion for whole city population..

(4) Ad hominem

One of the most often employed fallacies, ad hominen means "to the man" and indicates an attack that is made upon a person rather than upon the statements that person has made.

An example is "Don't listen to my opponent; he's handicapped."

(7) The Fallacy of Faulty Analogy

Reasoning by analogy functions by comparing two similar things. Because they are alike in various ways, the fallacy is that it is likely they will share another trait as well. Faulty Analogy arguments draw similarities between the things compared that are not relevant to the characteristic being inferred in the conclusion.

Here's an example of a Faulty Analogy fallacy:

Ram and Shyam excel at both football and basketball. Since Ram is also a singer, it is likely that Shyam also excels at singing.

In this example, numerous similarities between Ram and Shyam are taken as the basis for the inference that they share additional traits.

(8) Straw Man

Here the speaker attributes an argument to an opponent that does not represent the opponent's true position.

For instance, a political candidate might charge that his opponent "wants to let all prisoners go free," when in fact his opponent simply favors a highly limited furlough system. The person is portrayed as someone that he is not.

(9) The "After This, Therefore, Because of This" Fallacy (Post hoc ergo propter hoc)

This is a "false cause" fallacy in which something is associated with something else because of mere proximity of time. One often encounters people assuming that because one thing happened after another, the first caused it, as with "I stood up; Sachin got out. My standing up resulted in a loss of wicket." The error in arguments that commit this fallacy is that their conclusions are causal claims that are not sufficiently substantiated by the evidence.

Here are two examples of the After This, Therefore Because of This Fallacy:

Ten minutes after walking into the auditorium, I began to feel sick to my stomach. There must have been something in the air in that building that caused my nausea.

In the first example, a causal connection is posited between two events simply on the basis of one occurring before the other. Without further evidence to support it, the causal claim based on the correlation is premature.

(10) The Either or Thinking

This is the so-called black or white fallacy. Essentially, it says "Either you believe what I'm saying, or you must believe exactly the opposite."

Here is an example of the black or white fallacy:

Since you don't believe that the earth is teetering on the edge of destruction, you must believe that pollution and other adverse effects that man has on the environment are of no concern whatsoever.

The argument above assumes that there are only two possible alternatives open to us. There is no room for a middle ground.

(11) The "All Things are Equal" Fallacy

This fallacy is committed when it is assumed, without justification, that background conditions have remained the same at different times/locations. In most instances, this is an unwarranted assumption for the simple reason that things rarely remain the same over extended periods of time, and things rarely remain the same from place to place.

The last time winner of south delhi constituency won the general election. This year, the winner of the south delhi constituency will win the general election.

The assumption operative in this argument is that nothing has changed since the last primary. No evidence or justification is offered for this assumption.

(12) The Fallacy of Equivocation

The Fallacy of Equivocation occurs when a word or phrase that has more than one meaning is employed in different meanings throughout the argument.

"Every society is, of course, repressive to some extent - as Sigmund Freud pointed out, repression is the price we pay for civilization."

In this example, the word repression is used in two completely different contexts. "Repression" in Freud's mind meant restricting sexual and psychological desires. "Repression" in the second context does not mean repression of individual desires, but government restriction of individual liberties, such as that in a totalitarian state.

(13) Non Sequitor

This means "does not follow," which is short for the conclusion does not follow from the premise. To say, "The house is white; therefore, it must be big" is an example of the Non Sequitor fallacy. It may be a big house, but there is no intrinsic connection with its being white.

(14) Argument ad populum

A group of children are playing, trying to determine no of balls in an opaque box. "I wonder if there are less than 4 or more than 4 balls in the box," says one student. "I know how we can tell!" pipes up another. "All right, how?" asks the teacher, resigned to the worst. Beams the child: "We can vote."

This is argumentum ad populum, the belief that truth can be determined by more or less putting it to a vote. Democracy is a very nice thing, but it doesn't determine truth. Polls are good for telling you what people think, not whether those thoughts are correct.

(15) Contradiction

Contradiction occurs when a writer asserts two opposing statements simultaneously. For example, saying "it is wet and it is dry" is a contradiction. Typical arguments on the test obscure the contradiction to the point that the argument can be quite compelling. Here's a great example:

We cannot know anyone, because we intuitively realize that people are unreliable.

At first glance this argument sounds reasonable, but "intuitively realize" means "to know." Thus the author is actually saying that we know that we don't know anyone. This is classic contradiction.

Typical Questions

Despite the wide variety of arguments used on the test, there are essentially only eight types of questions that are asked.

1) Assumption Questions

When a question asks you to find an author's assumption, it's asking you to find the statement without which the argument falls apart.Make use of denial technique. Simply negate the statement and see if the argument falls apart. If it does, that choice is the correct assumption. If, on the other hand, the argument is unaffected, the choice is wrong.

Below are stated some of the ways in which assumption questions are worded:

Which one of the following is assumed by the author?
Upon which one of the following assumptions does the author rely?
The argument depends on the assumption that. ..
Which one of the following, if added to the passage, will make the conclusion logical?
The validity of the argument depends on which one of the following?
The argument presupposes which one of the following?

2) Strengthen and Weaken Questions

An argument can be weakened by destroying a central piece of evidence or by attacking the validity of the author's assumptions. In contrast, an argument can be strengthened by providing additional support, by affirming the truth of an assumption or by presenting additional persuasive evidence.

Here are some of the ways in which strengthen/weaken the argument questions are worded:

Which one of the following, if true, would most weaken the argument?
Which one of the following, if true, would most strengthen the argument?
Which one of the following, if true, would most seriously damage the argument above?
Which one of the following, if true, casts the most doubt on the argument above?
Which one of the following, if true, is the most serious criticism of the argument above?
Which one of the following, if true, would provide the most support for the conclusion in the argument above?
The argument above would be more persuasive if which one of the following were found to be true?

3) Inference Questions

Inference questions require you to consider the statements as evidence and then draw a conclusion from them. A valid inference is something that must be true if the statements in the passage are true. It is an extension of the argument rather than a necessary part of it.

Inference questions probably have the most varied wording of all the Logical Reasoning question stems. Some are obvious, others are subtle, and still others may resemble other question types.

Below is the quick rundown of the various forms that inference questions are likely to take on your test:

Which one of the following can be inferred from the argument above?
The author suggests that. ..
If all the statements above are true, which one of the following must also be true?
The author of the passage would most likely agree with which one of the following?
The passage provides the most support for which one of the following?Which one of the following is probably the conclusion toward which the author is moving?

4) Flaw Questions

This question asks you to recognize what's wrong with an argument. Most critique the reasoning by pointing out a fallacy. Other flaw questions are more specific and attack the argument's reasoning.

Here are typical flaw questions:

Which one of the following contains a flaw that most closely parallels the flaw contained in the passage?
The speakers will not be able to settle their argument unless they
The conclusion above is unsound because
Which one of the following best identifies the flaw in the above argument?
In presenting her position the author does which one of the following?

5) Method of Argument Questions

Method-of-argument questions ask you to pick the choice that describes how the authorpresents her case. To tackle these, you must be able to analyze the structure of an argument. If you can't identify the evidence and conclusion, you'll have difficulty describing how an argument works.

Most questions involve classic argumentative structures, such as "arguing from a small sample to a larger group," or "inferring a causal relationship from a correlation." The other type of method-of-argument question gives a description of the argument in much more specific terms. Anexample of this might read, "The author presents his case in order to show that......"

6) Similar-Reasoning Questions

Similar-reasoning questions require you to identify the answer that contains the reasoning most similar to that in the stimulus. The key is to summarize the argument's overall form and match it to that of the correct choice. A good approach to these questions is to see if the argument can be symbolized algebraically, using Xs and Ys.

Example: All fish swim. This creature swims. Therefore, it must be a fish.

This (flawed) argument can be symbolized in the following way:

All X do Y. This does Y. Therefore, this must be an X.

If the stimulus can be symbolized this way, your job will be to search for the choice that can be symbolized in the same way. Your answer might look something like this:

Every mother (all X) loves singing (does Y). Jenny is singing (this does Y). So she must be a mother. (therefore, this must be an X).

7) Paradox Questions

When an argument contains two or more seemingly inconsistent statements, it presents a paradox. Most paradoxical arguments end with a contradiction. Another type of paradox has the argument build to a certain point, then change to the exact opposite of what you expect.

In a typical paradox question, you'll be asked either to find the choice that "explains the paradoxical result", "explains the inconsistent findings", or "resolves the apparent discrepancy." This will be the choice that reconciles the seemingly inconsistent statements in the argument while allowing them all to still be true.

8) Principle Questions

Principle questions ask you to apply a specific situation into a global generality (or vice versa). You may be given an argument and asked to find the principle that justifies the author's reasoning.

Possible question stems:

The author's position most closely conforms to which one of the following principles?
What principle best accounts for or justifies the author's position?
Which one of the following principles would justify Al's refusal to follow the author's recommendation

The correct answer to principle questions expresses the key concepts and contains the key terms that the other choices omit. Avoid choices that are beyond the scope of the argument. Most of the wrong choices contain principles that sound formal and look reasonable, but they don't address the author's main concern.