Sunday, September 28, 2008

Cooking and Critical Reasoning

online cat 2008 cat 2009 cat coaching delhi critical reasoningTG and I have these long discussions over almost everything. These discussions generally take place either when we go out for our long evening walkds or when we are cooking or enjoying our wine at Pizza Express. This time it was cooking.

TG (probably thinking about a mathematical problem): “What are we preparing for lunch today?”

Now that I want to have this discussion with him, it’s very important that I suggest his favourite dish only.

Aaloo Gobhi, Matar, Zeera Pulao, Pudina Chutney and Cold Ribbon Pasta Salad.”

TG is smiling now. “Aah tempting! Are you trapping me into something?”

“Umm… actually, I have forgotten many things related to critical reasoning and TGites have long been asking us to write an article. So I thought may be we could discuss it first!”

TG smiles and nods his head. I knew he would never be able to say no, now that we are talking about cooking his favourite dish. Ha! I like these traps. winkwink

TG and I head to the kitchen to pick up vegetables and fruits for chopping. He picks up potatoes, onions, ginger, peas, green chillies, coriander leaves, cauliflower, and tomatoes. I open the fridge and take out cabbage, pineapple can, pomegranate, apples, boiled potatoes, bell peppers, olives, and strawberries for cold salad.

TG: “Hmm, so what is an argument?”

ME (placing the bowl containing pasta on the gas for boiling)- An argument is a sequence of two or more phrases, clauses, sentences or statements, one of which is a claim or conclusion, which follows the premise. The simplest kind of argument consists of one premise and a conclusion. An example could be ‘No one was present when life first appeared on Earth. Therefore, any statement about life’s origins should be considered as a theory.’

TG- So the premise in your example is ‘No one was present when life first appeared on Earth.’ And the conclusion is ‘Any statement about life’s origins should be considered as a theory.’ In an argument some claims are put forward in support of others. The claim that is being supported is the conclusion. The claims that are alleged to support the conclusion are the premises. In simple words, premises are the facts or evidence that support or lead to the conclusion. In your example there was a cue word ‘therefore’ that made it easier for me to separate the premise from the conclusion. Conclusion can be preceded by cue words such as thus, hence, so and therefore. And cue words such as if, given that, suppose, for, since and because signal the presence of evidence and reasons in support of a fact. It is not necessary that conclusion will always be followed by premises. In some cases conclusion of the argument may come first. For example, Forbear to judge, for we are sinners all.

ME- Hmm..

We move back to the dining room with our chopping boards, bowls, and knives along with the eatables.

ME (chop-chop) - Let me classify the arguments. There are two types of arguments- deductive and inductive. When an argument claims that the truth of its premises guarantees the truth of its conclusion, it is said to involve a deductive argument. Deductive reasoning holds to a very high standard of correctness. A deductive argument is valid when, if its premise is true, conclusion must be true. In deductive argument the truth of the premises guarantees the truth of the conclusion. For example, ‘All men are mortal. Socrates is a man. Therefore, Socrates is mortal.’ When an argument claims merely that the truth of its premises make it likely or probable that its conclusion is also true, it is said to involve an inductive inference. An inductive argument is one whose premises are meant to show that the conclusion is probably true. For example, ‘It has snowed in Himachal every year in recorded history. Therefore, it will snow in Himachal this coming year.’

TG (with watery eyes, chopping onions)- We will check the inference part from the Fact-Inference- Judgement chapter. For students, here is the link-

ME- I think pasta must be done. Be right back.

I go back to the kitchen to check whether the pasta was boiled. I strain the extra water, run cold water on it and add a table spoon of oil so that each ribbon stays separate and doesn’t get sticky. I soak the rice quickly in water for Pulao and leave the kitchen.

TG- Is it ready?

ME- Yeah! Okay the last definition. What is an assumption?

TG (Don’t know how does he chop and grate these vegetables so finely!) - An assumption bridges the gap between an argument's evidence and conclusion. It's a piece of support that isn't explicitly stated but that is required for the conclusion to remain valid. It is an unstated premise that supports the author's conclusion.

Henry plays basketball for his college. Therefore, Henry must be over six feet tall.

Here you are assuming that all the basket ball players are over six feet tall.

Me- Also, assumption provides additional premises needed to draw the conclusion and the assumptions take that the premises in an argument can actually be true. For the ‘Evaluation of the argument’ part, I think we will give the link of the Fallacies chapter and I remember most of it so let’s just directly move to the types of questions.

TG- But before that let me ask you something. Consider this example.

Painting classes take place on Mondays. Today is Monday. Therefore, painting classes take place today. Now tell me, is the conclusion correct?

ME - Yes.

TG– Wrong (my jaw drops!) Let us analyse the premise (1) If we assume that painting classes usually take place on Monday, then there is a probability that if today is Monday it will be one of those Mondays when painting classes take place, but this is obviously not certain. Premise 1 does not state that painting classes take place every Monday; classes could be held every other Monday or every fourth Monday. Therefore, the conclusion may be wrong.

ME– Let me conclude. Assumptions are premises that are accepted as true or as certain to happen, without proof. Inferences are unstated partial conclusions that can be drawn from the given premises. And conclusions are judgments or decisions reached on the basis of the premise/s. An example would be

TG is a student of IIT Delhi.
Therefore TG is intelligent.

Here Premise- TG is a student of IIT Delhi. Conclusion- TG is intelligent.
Assumption- All IIT Delhi students are intelligent.

TG looks at me from the corner of his eyes.

ME- But what is the difference between assumption and inference and conclusion and inference?

TG- An inference is an additional observation in the line of reasoning but is not the same as a conclusion. A conclusion invariably addresses the central idea of a thought stimulus whereas an inference serves only to support the conclusion. The difference between assumption and inference is that the validity of the conclusion does not depend on inference as it depends on the assumption. Hmmm (thinking) example Students who drink at least two glasses of milk everyday tend to be more active than those who don’t drink two glasses of milk in a day. The ability to get a good score in any competitive exam depends on one’s level of activeness. So what do you infer and conclude from this?

ME: Inference-If you are a student you are likely to be more active if you drink two glasses of milk. Conclusion- Students wishing to do well in competitive exams should try to drink at least two glasses of milk daily to stay active during the exams. Got it!

We completed the chopping part and moved to the kitchen to start our cooking. I take a glass bowl, add mayonnaise, and pass it on to TG while he heats the oil for Aaloo Gobhi. TG adds pasta, fruits, and vegetables, just the right amount of salt and freshly grounded pepper in mayo and mixes them cautiously. While I add potatoes, ginger, green chillies, cauliflower, tomatoes, grated ginger, coriander leaves, salt, red chilli powder, and turmeric. I simmer the gas, cover the vegetables with a lid, and let it cook.

TG (looking pleased while decorating his salad with strawberries and mint leaves) - The major types of questions are find an assumption, draw a conclusion, weaken the conclusion, strengthen the conclusion and analyse the argument structure.

ME- What about the inferential questions?

TG- Restate the conclusion, mimic the argument, make an inference about the premise, resolve a problem, explain an event or a discrepancy, provide an example are all minor types of questions. We also look for boundary and extreme words while solving CR.

ME (heating the oil for pulao) - Boundary words narrow the scope of the argument. For example, The percentage of CAT takers are increasing in India. In this statement, the boundary words are percentage, CAT takers, and India. The word percentage restricts the meaning to percentage only as opposed to the actual CAT takers. (it is not necessary that if the percentage has increased that the actual number has also increased.) The word CAT takers also limits the scope of the premise, it restricts the meaning to the CAT takers only as opposed to the people who take rest of MBA entrance exams as well. Extreme words are essentially opposite of boundary words. Extreme words open the argument unreasonably. The good questions in CR will always have moderate options. All, always, never, only etc are a few such words. For example, ‘everyone who has weak eyesight always wear specs.’

The extreme word ‘always’ unreasonably opens the scope of the argument. The more reasonable argument would have been that People with weak eyesight usually wear specs. Also, the extreme work everyone is also unnecessarily opening the argument further. The more reasonable argument would have been ‘most people who have weak eyesight wear specs.’

Invariably, the biggest thumb rule in solving a CR question is to read the question correctly. It is important to dissect the argument before moving on to the question because many a times the options will have seemingly ‘correct’ wrong answers. Dissecting the argument beforehand prevents you from going wrong. Identify to identify the premises, conclusion and assumptions (if any) in the argument and try to guess the answers before moving on to the options.

TG puts the salad in refrigerator and takes out mint leaves for Pudina Chutney. Aaloo Gobhi is ready, I add freshly grounded garam masala, close the lid, and turn off the gas. I add khada masala, zeera, sliced onions, and dry red chillies in the oil along with salt and wait for the onions to turn brownish.

TG (taking out the hand-grinder from the cupboard) – Good. There are also these ‘except’ kind of questions. ‘Each of the following strengthen/weaken the conclusion except’ or ‘Each of the following makes the argument logically correct except’ or ‘Each of the following helps to explain event X except’. (TG stopped speaking and I knew he hasn’t finished…)

He adds mint leaves, salt, onion, grounded pomegranate seeds and starts the grinder. Tangy! The onions have turned brown, I add water and peas to the contents, cover the container with the lid and wait for the water to boil.

TG (looking happy)- See, just the right colour of green. (I look and smile and he speaks again) If you closely inspect the phrases then they mean the same as ‘which of the following does not weaken or strengthen the conclusion or which of the following does not make the argument logically correct or which of the following does not help to explain the event X.

Phew! Agree! Its 1 p.m and we have almost an hour before lunch so we decide to solve some questions. I quickly add the rice to the water, simmer the gas and close the lid. TG prepares his special Elachi tea for both of us and we go to the living room.

TG (leaning back on the couch comfortably searching something in the laptop) – Let’s solve this question.

To prevent some conflicts of interest, Congress could prohibit high-level government officials from accepting positions as lobbyists for three years after such officials leave government service. One such official concluded, however, that such a prohibition would be unfortunate because it would prevent high-level government officials from earning a livelihood for three years.
The official’s conclusion logically depends on which of the following assumptions?

A. Laws should not restrict the behavior of former government officials.
B. Lobbyists are typically people who have previously been high-level government officials.
C. Low-level government officials do not often become lobbyists when they leave government service.
D. High-level government officials who leave government service are capable of earning a livelihood only as lobbyists.
E. High-level government officials who leave government service are currently permitted to act as lobbyists for only three years.

We stare a question for a while and I answer first.

ME- Is the answers D?

TG- Correct! Approach?

ME- I kept the conclusion in my mind because an assumption has to be closely tied to the conclusion. Here the conclusion is ‘that such a prohibition would be unfortunate because it would prevent high-level government officials from earning a livelihood for three years.’ What I roughly thought was that if they cannot earn their lively hood for three years as we know from the official statement, it means that they cannot earn their lively hood in any other way but by being lobbyists. Among all the 5 options, only D is the prefect choice because it logically fills the gap between the premise and a conclusion.

TG- (scribbling something on the scribble pad) Hmmm correct. Did you notice the words Congress- prohibit-high-level government officials -from earning a livelihood for three years? (Whew!). Questions on assumptions can be phrased in many ways. 1) Which of the following most accurately states a hidden assumption that the author must make in order to advance the argument above? 2) The argument above assumes which of the following? 3) Which of the following is an assumption that, if true, would support the conclusion in the passage above? In assumption type of questions, follow this routine:

· Identify the Conclusion and the evidence
· Ask if the conclusion follows from the evidence?
· Check if you need some missing evidence to support the conclusion.
· Apply the denial test. If the given option is removed or falsified then the conclusion is invalid.

TG- Another Question:

A computer equipped with signature-recognition software, which restricts access to a computer to those people whose signatures are on file, identifies a person’s signature by analyzing not only the form of the signature but also such characteristics as pen pressure and signing speed. Even the most adept forgers cannot duplicate all of the characteristics the program analyzes.
Which of the following can be logically concluded from the passage above?

(A) The time it takes to record and analyze a signature makes the software impractical for everyday use.
(B) Computers equipped with the software will soon be installed in most banks.
(C) Nobody can gain access to a computer equipped with the software solely by virtue of skill at forging signatures.
(D) Signature-recognition software has taken many years to develop and perfect.
(E) In many cases even authorized users are denied legitimate access to computers equipped with the software.

TG quickly reads the question and starts writing something again, I solved the question sipping tea from the mug.

ME- C? (TG nodding in affirmation and we discuss my approach) Premise 1: A computer equipped with signature-recognition software identifies a person’s signature by analyzing not only the form of the signature but also such characteristics as pen pressure and signing speed.

Premise 2: Even the most adept forgers cannot duplicate all of the characteristics the program analyzes. (It means that even if you have a skill to forage the signatures, you would not be able to gain an access because the software needs to identify your signature.)

Here I worked with the options keeping in mind that I don’t have to go beyond the premise. Option A and D look out of the context of the passage because the passage gives no information about how fast the software operates or about how long the software was under development. Option B- where did banks come from? Option E is wrong because no such information given about the errors of that sort (too distant from the mentioned premise). Option C looks best because it summarizes the premises.

TG- Let’s move on to strengthen/ weaken the conclusion types of questions.

I suddenly realized that the pulao must be ready and I rush to the kitchen. I open the lid to check and the rich aroma of cloves, cinnamon, zeera, peas mixed with rice enriched the senses. I put off the flame, covered the rice with the lid, and back to discussion!

TG - The average life expectancy for the United States population as a whole is 73.9 years, but children born in Hawaii will live an average of 77 years, and those born in Louisiana, 71.7 years. If a newlywed couple from Louisiana were to begin their family in Hawaii, therefore, their children would be expected to live longer than would be the case if the family remained in Louisiana.
Which of the following statements, if true, would most significantly strengthen the conclusion drawn in the passage?

A. As population density increases in Hawaii, life expectancy figures for that state are likely to be revised downward.
B. Environmental factors tending to favour longevity are abundant in Hawaii and less numerous in Louisiana.
C. Twenty-five percent of all Louisianans who move to Hawaii live longer than 77 years.
D. Over the last decade, average life expectancy has risen at a higher rate for Louisianans than for Hawaiians.
E. Studies show that the average life expectancy for Hawaiians who move permanently to Louisiana is roughly equal to that of Hawaiians who remain in Hawaii.

ME- In simple words the conclusion is that people who live in Hawaii live longer than people who live in Louisiana and that is the reason that even if people living in Louisiana shift to Hawaii, they are expected to live longer. The main aim is to add a premise that would support the conclusion. I solved it by eliminating the options. Option A is weakening the conclusion because it says that life expectancy in Hawaii is likely to be falling. Option B strengthens the conclusion because the greater abundance of longevity-promoting environmental factors it mentions is probably at least partly responsible for the higher life expectancy in Hawaii. Children born in Hawaii benefit from these factors from birth, and thus Louisianans who have children in Hawaii increase their children’s chances of living longer. Option C talks about only 25% of the cases and option E weakens the argument. Option D does not support the argument as it talks about increased rate of lie expectancy in Louisiana rather than in Hawaii.

TG– (taking the last sip from his mug) another question. Same passage, different options, and different question.

The average life expectancy for the United States population as a whole is 73.9 years, but children born in Hawaii will live an average of 77 years, and those born in Louisiana, 71.7 years. If a newlywed couple from Louisiana were to begin their family in Hawaii, therefore, their children would be expected to live longer than would be the case if the family remained in Louisiana.
Which of the following, if true, would most seriously weaken the conclusion drawn in the passage?

A. Insurance company statisticians do not believe that moving to Hawaii will significantly lengthen the average Louisianan’s life.
B. The governor of Louisiana has falsely alleged that statistics for his state are inaccurate.
C. The longevity ascribed to Hawaii’s current population is attributable mostly to genetically determined factors.
D. Thirty percent of all Louisianans can expect to live longer than 77 years.
E. Most of the Hawaiian Islands have levels of air pollution well below the national average for the United States.

ME (this was tough!)- Same conclusion, that people who live in Hawaii live longer than people who live in Louisiana and that is why if people living in Louisiana shift to Hawaii, they are expected to live longer. So basically I have to consider either two things either to find a faulty premise or find evidence that will belittle the conclusion. I work with eliminating the options. D does not guarantee that a Louisianan will not have a longer life in Hawaii. E is incorrect because it supports the conclusion. A is out of the context. Because the governor’s allegation is false, it cannot affect the conclusion so, B also eliminated. Only option C weakens the argument because since the Louisianans’ children will acquire their genetic characteristics from their parents, not from their birthplace, this choice presents a reason to doubt that Hawaiian born children of native Louisianans will have an increased life expectancy.

We take a break from all the logic and go to the kitchen to serve lunch. I garnish Aaloo- Gobhi with freshly chopped coriander leaves, rice with sliced tomatoes and green chillies, Pudina Chutney with 2 mint leaves, and cold salad in a glass bowl with white base and different colours of green, red, yellow, black etc. We sit down to enjoy our lunch and discuss easier topics like catching up a next movie and buying some books from the Oxford book store. After the gourmet lunch we move to the living room yet again, switch on the AC, and sit lazily on the couch. He compliments me for the good

ME- You were telling me about those minor types of questions?

TG- Yes, Many a times you come across questions where you have to explain an event (Which of the following statements, if true, would best explain the 1984 decrease in productivity?), find an Inference (If the statements above are all true, which of the following can properly be inferred on the basis of them?), evaluate the conclusion (Which of the following investigations is most likely to yield significant information that would help to evaluate the researcher’s hypothesis?) etc. But if you become comfortable at solving major types of questions, minor types come in handy. And the strategy or solving each CR question remains more or less the same.

Me- And the strategy is?

TG (mockingly)- Gadha Rules:

· Look for particular types of questions, and then use the strategies appropriate for that type
of question to choose the right answer.

· You can rephrase the text if you want and make things simpler for yourself.
· Break the argument in premise and conclusion. Look for cue words if any.
· Identify the argument.
· Read the question carefully (know what you are looking for) and anticipate the answer

· Focus on what the question is asking you to do and find an answer choice that best answers
the question. That’s it.

· Use the process of elimination.
· Avoid the options containing extreme words.
· Don’t go beyond the scope of the argument. If the passage tells you ‘The sun rises in the
East’, believe it.

· Remember that there is only ONE correct answer and that is the best answer.

I think the chapter is more or less covered. Ah! Ek chai ho jaaye?

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