SDCAR2010【逻辑入门】（八）Assumptions

sdcar2010

An assumption is an unstated premise. In other words, an assumption is a piece of evidence that strengthens the author’s argument but that the author never sates explicitly in the stimulus.

Sufficient vs. Necessary Assumptions

Imagine that you were accused of cheating during a GMAT test. At the hearing before a panel of disciplinary committee, only one piece of evidence is presented – your one-sentence testimony: “I did not cheat at the GMAT exam.” After hearing your testimony, the panel concludes that you did not cheat. You are definitely elated. But logically, the panel’s conclusion is on shaky ground because they assume, for better or worse, that you are telling the truth! In fact there are at least three different assumptions the panel could be making.
1. You always tell the truth.
2. You told the truth at the hearing.
3. It is possible for you to tell the truth.

The first assumption that you always tell the truth is a sufficient assumption because it is sufficient or enough to justify the panel’s conclusion. If you always tell the truth, then the panel must be right. However, this assumption is not a necessary assumption or an assumption that we have to make, because the panel could still be right even if you do not always tell the truth. As long as you told the truth at your hearing, the judge is still right. In other words, the panel’s conclusion does not depend on the assumption that you always tell the truth.

The second assumption that you told the truth at your hearing is both a necessary and sufficient assumption. It is sufficient because if you told the truth at the hearing, then the panel is right; it is also necessary because if you did not tell the truth at the hearing, then the panel is wrong. In other words, the panel’s decision depends on this assumption being true.

The third assumption that it is possible for you to tell the truth is a necessary assumption because if it were not possible for you to tell the truth, then the panel would be wrong. However, this assumption is not sufficient because it alone does not justify the panel’s conclusion. Just because you can tell the truth does not mean you actually tell the truth at the hearing. Therefore, the panel could still be wrong, even if the last assumption is true.

As this example illustrates, sufficient assumptions typically have strong language (always, never, none, all), while necessary assumptions typically have weak language (possible, likely, often, many).

Sufficient Assumption

Prompts for sufficient assumptions
• Which one of the following, if assumed, would justify the conclusion?
• The author’s conclusion would be properly drawn if which one of the following was true?

Sufficient assumption prompts almost always use the word IF, while necessary assumption prompts never use IF. Also, sufficient assumption prompts avoid qualifiers such as MOST. MOST JUSTIFIES, for example, is a strengthen question, while JUSTIFY by itself is a sufficient assumption question.

Before you look at the answers:
1. Pinpoint the main conclusion in the passage. (Read my previous Main Point post.)
2. Separate the premises from everything else. After you find the main point, don’t assume that all the other statements are premises; they might include opposing viewpoints, background information, and concessions.
3. Are there any jumps between the premises and the conclusion or between each premise? To find these jumps, look for any concepts that are discussed only once. There are usually two. The correct answer usually fills in the gap in the argument by linking those two concepts together. Alternatively, slowly read each word of the conclusion. Which phrase was not used in the premise? That word or phrase will likely reveal where the argument jumped to the conclusion: at the gap!

Look for the answer that links those two concepts together.
1. The correct answer will almost always use the exact same language used in the passage to describe each concept. If “many smart CDers” were one the concepts you found in the gap, the correct answer would likely use those three exact words, while the wrong answers would likely use similar but different words such as “many diligent CDers” or “smart CDers who read SCAR’s posts.” For the former, diligent is different from smart; for the latter, it refers to a smaller subset of CDers than the entire groupof “smart CDers.”
2. Because a sufficient assumption must justify the conclusion, the correct answer often has all, only, no, none, most, always, or some other strong words.

Jumps in Reasoning

Jumps can occur between the premises and the conclusion or between each premise. Here is a jump between premises:
1. Our school requires some of the highest tuitions in the country.
2. High tuitions in any school discourage poor students from attending.
3. Discriminatory schools cannot attract the best and the brightest students.
Therefore, our school cannot attract the best and the brightest students.

The first and second premises are related, but not perfectly: schools that impose the highest tuitions do not necessarily impose high tuitions – only tuitions that are higher than other schools. That said, it is not unreasonable to assume that a school with some of the highest tuitions in the country would have high tuitions. So this is a jump, but it is a small one. The second and third premises make a larger jump: a school discourages poor students from attending is not necessarily a discriminatory school.

So in a sufficient assumption question, the correct answer for this argument would likely link these last two phrases together by saying that “any school that discourages poor students from attending is a discriminatory school” or “only discriminatory schools discourage poor students from attending.” Note that both expressions say the same thing because any means if and only means then.

Necessary Assumption
Prompts for necessary assumptions:
• The conclusion relies on which one of the following assumptions?
• The argument presupposes which one of the following?
• The conclusion does not follow unless

Before you look at the answers:

1. Pinpoint the main conclusion in the passage. (Read my previous Main Point post.)
2. Separate the premises from everything else. After you find the main point, don’t assume that all the other statements are premises; they might include opposing viewpoints, background information, and concessions.
3. Are there any jumps between the premises and the conclusion or between each premise? To find these jumps, look for any concepts that are discussed only once. There often two such concepts in the same passage. Unlike the jumps in sufficient assumption passages, however, the jumps in necessary assumption passages are often less obvious.

Look for the answer that must be true for the conclusion to stand.

1. Ask yourself, “Does this answer have to be true?” Or could the conclusion still be true without it? In other words, if the answer were not true, would it undermine the conclusion? Is it an assumption that the conclusion depends on?
2. Negate your last two best answers choices. The negated answer that undermines the conclusion is the correct answer.
3. If you spot any jumps, the correct answer will often link those two concepts together.

Negating an answer choice

Imagine you are eating ice cream and your friend asks you how it tastes. You reply, “It is sweet.” The negation of this statement is that the ice cream “is not sweet.” The complete opposite of this statement is that the ice cream “is sour.”

When you negate an answer, just negate it. Try not to turn it into its opposite. Also, negate either the verb or the quantity, but not both.

SDCAR2010【逻辑入门】（七) Strengthen and Paradox

SDCAR2010【逻辑入门】（九）Flaw (part 1)

jaze

追

horsecc

good

jaze

1. Our school requires some of the highest tuitions in the country.
2. High tuitions in any school discourage poor students from attending.
3. Discriminatory schools cannot attract the best and the brightest students.

1. E -> F
2. A -> B
3. C -> D
conslusion: E --> D

first gap:  F --> A
second gap: B --> C

but at the first glance, i thought  B = D, and then i got  E--> F--> A--> B = D.
Is it right as another direction of solving those questions?

jaze

“any school that discourages poor students from attending is a discriminatory school” or “only discriminatory schools discourage poor students from attending.” Note that both expressions say the same thing because any means if and only means then.

i make sense such things as this:
If a school that discourages poor students from attending is a discriminatory school,
then a discriminatory school discourages poor students from attending.

I think there is a assumption in this reasoning: whether a school is a discriminatory school can only defined by
whether it discourages poor students.
That is, if there is anther way for us to define a school a discriminatory school, for example, discriminate women(it is just a example, do not be serious), then, i think we can not conclude that a discriminatory school discourages poor students from attending just from the evidence that a school that discourages poor students from attending is a discriminatory school.

Is that right, if not, please correct my fault.
I just want to learn from u.

sdcar2010

1. Our school requires some of the highest tuitions in the country.
2. High tuitions in any school discourage poor students from attending.
3. Discriminatory schools cannot attract the best and the brightest students.

1. E -> F
2. A -> B
3. C -> D
conslusion: E --> D

first gap:  F --> A
second gap: B --> C

but at the first glance, i thought  B = D, and then i got  E--> F--> A--> B = D.
Is it right as another direction of solving those questions?

-- by 会员 jaze (2011/6/24 9:59:14)

From the  formal logic standpoint, if B-->D, then E-->D is correct. So B-->D could be a sufficient assumption.

sdcar2010

“any school that discourages poor students from attending is a discriminatory school” or “only discriminatory schools discourage poor students from attending.” Note that both expressions say the same thing because any means if and only means then.

What I meant is that
“any school that discourages poor students from attending is a discriminatory school” = IF a school discourages poor students from attending, then it is a discriminatory school.

"only discriminatory schools discourage poor students from attending" = THEN they are discriminatory schools if the school discourage poos students from attending.

All two statements tell the same thing.

jaze

Thanks for replying. I learn a lot

jameshzd

顶！！！

jameshzd

这个帖子是精华！