Published: Friday, 17 June, 2016 10:00 AM
Premises + Assumptions = Conclusions
Logical Reasoning and Critical Reasoning questions in an MBA entrance exam, invariably, have the following structure:
b. Question Stem
c. Answer Choices
Premise, Assumption and Conclusion, together form a part of a typical argument.
A premise is a stated reason or evidence that supports the conclusion. An assumption is an unstated premise that supports the conclusion. Both premise and assumption are unquestionable facts but the assumption, unlike the premise, is not explicitly stated and needs to be deciphered.A conclusion is the claim, the main point of the argument. It is the proposition that is affirmed on the basis of the other propositions of the argument. Thus, the conclusion is drawn based on the stated premise and the unstated assumptions, in other words, Premises+Assumptions= Conclusion.
After reading the argument, the first step is to identify the conclusion. It is not necessary for conclusion to come at the end of the argument, it may even precede the premise. For instance, ‘Amazon.com is the largest online bookstore with over 3,00,000 titles available. Hence, you will be able to find the book you want,’ can be written as, ‘You will find the book you want at Amazon.com. It is the largest online bookstore with over 3,00,000 titles.’ Some of the indicators through which a conclusion can be identified are, ‘therefore,’ ‘hence,’ ‘thus,’ ‘so,’ ‘accordingly,’ ‘consequently,’ ‘as a result’ and so on. Some of the indicators through which a premise can be identified are, ‘since,’ ‘because,’ ‘for,’ ‘as,’ ‘follows from’ and so on. After identifying the conclusion, identify the premises and assumptions, if any. The premises and the assumptions must provide enough evidence for the conclusion.
3. Types of questions
Critical reasoning questions can be of the following types:
-Identify the assumption
-Strengthen/Weaken the argument/conclusion
-Complete the argument
To tackle all these type of questions, the candidate must know what is a premise, assumption and conclusion because it is these three components that make up an argument.
Let’s look at the following:
-Statement- Virat has been elected as captain of the Indian cricket team, so he must be a cricketer of calibre.
Assumptions- i. Only cricketers of calibre can be members of the Indian cricket team
ii. Only cricketers of calibre can be captain of the Indian cricket team
iii. Only members of the Indian cricket team can be cricketers of calibre
In the above question, identify the assumption of the given argument. Mark the best answer out of the choices: a. i only, b. ii only, c. iii only, d. i and iii only, e. i, ii and iii
In this question, since the prerequisite of becoming captain of the Indian cricket team is to be a cricketer of calibre, so only ii is the right choice. Hence, the answer is b.
-All children are happy when they get new clothes. Therefore, Amar will be thrilled when he gets the new leather jacket.
In this argument, the premise is about children and the conclusion is about Amar. The hidden premise (or assumption) here is that Amar is a child. Without this assumption, the argument will make no sense.
Thus, in critical and logical reasoning, it is imperative that the candidate understands the three parts of the argument, which will help solve the question.
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There are different ways to think about reasoning. This handout discusses the one that I find most useful: analyzing assumptions. But another popular method is to look for fallacies (logical errors). I have written a brief introduction to fallacies for those who would like more information on that topic, with links to detailed articles elsewhere on the web.
This handout discusses assumptions using a sample article about environmental racism and Hurricane Katrina. (Its the same article used in the handout on writing a paragraph outline.)
What Is Reasoning
Reasoning is the process of moving from the evidence to the conclusion. Notice the terms I have emphasized here: process, from and to.
Reasoning is a process or movement of thought, from one idea or group of ideas (the evidence or premises) to another (the conclusion, or what you are trying to prove). Its all about the relationship between those ideas, rather than either one taken by itself.
When people talk about reasoning, or logic, they tend to be thinking of a process with at least two steps:
Assessing reasoning, then, can focus on two aspects of the argument:
- The premises, or if statements (are they true? are they reasonable?)
- The movement from the stated premises to the conclusion (is it valid? does it follow the rules?)
In this document I talk about premises. The document on fallacies discusses the rules for moving from premises to conclusion.
What Are Assumptions
All arguments require assumptions. In a moment we will look at different types of assumption, with some examples. But first, a definition:
An assumption is a claim that the author doesnt even try to prove.
Rather than proving the claim, the author simply assumes it is true.
Remember:An assumption is not a point that the author tries to prove and fails. Its a point he or she doesnt even try to prove.
Assumptions and Theses: Comparison and Contrast
For a refresher on theses, here are links to my �What is a Thesis� handout for English 101 and English 102.
Here are two important ways that an assumption is like a thesis:
- An assumption can be proved and disproved.
- An assumption can be expressed only as a complete, declarative sentence (not a question, not a word or phrase or fragment). Another way of saying this is that both assumptions and theses are claimsassertions of truth. (I gave a definition of claim in the handout on assessing evidence.)
And here are two ways that an assumption is not like a thesis:
- The author never tries to prove an assumption, whereas the author always tries to prove the thesis.
- The thesis is what the paper is aiming at; the assumptions are what it starts from.
An assumption on which the argument depends is also sometimes called a premise. For example, in the classic syllogism:
All men are mortal;
Socrates is a man;
therefore, Socrates is mortal.
the first two statements are premises. They are assumptions, because no attempt is made to prove them. We just assume they are true. But the third statement depends on them: if they are true, it is true. If either of them were false, the third statement would be either false or unproven.
A different syllogism might not have such acceptable premises:
All men are purple.
Socrates is a man.
Therefore, Socrates is purple.
Yesif all men were purple, then Socrates would be purple. But theyre not. In making this assumption, the syllogism fails to convince us, though it might be logically perfect. By evaluating the assumption, or premise, we have evaluated one aspect of the reasoning.
Of course, reallife arguments are rarely so neat or simple. Most of them involve more than two premises, and often some premises are left unstated. The relationships are fundamentally the same, but it can be tricky sorting out all the pieces.
All argumentsall attempts to prove somethingrequire assumptions. They are not bad; they are, on the contrary, essential. If you tried to prove every point you would never finish, because every proof would depend on another point or points, which would have to be proved, and so on to infinity. So you need assumptions, but you also need to be careful with them. Know what they are, test them to be sure you think theyre valid, and try to use only those that your reader is likely to share.
Consider the simple example of proving it is going to rain that I used in the handout on evidence. In that example, I suggested that sufficient evidence might include the use of a thermometer and a barometer (for measuring air pressure). But notice that this involves certain assumptions:
- To begin with, I assume that the particular instruments I am using are working correctly.
- More fundamentally, I assume that all thermometers and barometers have some meaningful relationship to the physical world they seem to measure.
- I also assume that there is a connection between changes in temperature and air pressure and changes in precipitation.
- There are many other assumptions involved in this use of evidence. In fact, you could say they go on forever.
Think about proving a thesis. One simple procedure for doing so is as follows. We begin with the thesisthe claim we want to prove. Then, we list smaller claims we would have to prove in order to prove the thesis. Then we list even smaller claims needed to prove those claims. That process could go on foreverbut at some point you have to stop. At that point you decide no further proof is needed. The trick is knowing when to stop, which claims do not need proof.
Thesis: The overall claim the essay is trying to prove.
- First main claim that you have to prove, to prove the thesis
- First sub-claim to prove the first main point
- Assumption: At some level you stop proving claims. You just assume theyre true.
Second sub-claim Third sub-claim
- Second main claim
- First sub-claim
- Second sub-claim
- Third sub-claim
- Third main claim
- First sub-claim
- Second sub-claim
- Third sub-claim
As you can see, most arguments actually involve many assumptions, at least one for each sub-claim.
To keep things simple, Ill usually refer to assumptions. But most of the time, when talking about assumptions Im talking about the special subset of assumptions called premisesthe ones that are needed to prove the thesis.
Types of Assumptions
Assumptions can be either explicit (directly stated) or implicit (not directly stated but implied). When you identify someones assumptions, look for both kinds.
An explicit premise in the sample article is the statement that the stranded [people after Hurricane Katrina] were poor, black, disproportionately elderly (paragraph 5). The author states this but makes no attempt to prove it, probably because she figures it�s a well-established fact. No proof needed here.
An implicit premise in the article is the assumption that racism is a bad thing. She never says this, and she certainly never tries to prove it, but it is basic to the point she is trying to make.
Notice that an assumption can be, and often is, perfectly reasonable. Assumptions are not necessarily errorsthey are an indispensable part of any argument, the bedrock on which it rests.
Assumptions can also be either factual, analytical, or moral (based on values).
Some assumptions deal with facts, like the statement all men are mortal. An example of a factual assumption in the sample article would be the statement about those stranded in New Orleans. Another is the claim that The ‘toxic soup’ that has received much public attention is filled with the effluence from the oil and petrochemical industry (paragraph 4). Both these assumptions deal with straightforward factual information that can be measured or observed directly.
Other assumptions are analytical. They are based on facts, but they go a step further in making some sort of statement about those factsinterpreting them, analyzing them, explaining them, evaluating them. An example of an analytical assumption in the sample would be that larger systemic problems ... , such as the exclusion of voices and perspectives of racial minorities and working-class populations from environmental policy-making, caused environmental racism (paragraph 5). This assumption goes beyond measurable or observable data to examine meanings and relationships. As such, it is always more open to debate than factual assumptions whichat least in theorycan be proved or disproved by direct observation.
Still other assumptions deal with values. Unlike factual and analytical assumptions, which can be defended with evidence and reason, it is almost impossible to prove values. Either you share them or you dont. One of the sample articles implicit assumptions about values is that poor people and people of color should not experience unfair impacts simply because of their socio-economic status. This assumption depends on ideas about what is fair that are very difficult, if not impossible, to defend with evidence and reason. This does not mean they are wrong, just that you are unlikely to convince anyone of them through logical argument.
The assumptions you identify in your reading can be explicit or implicit, and they can be factual, analytical or relating to values. These two ways of categorizing assumptions intersect. The table below shows how, using the examples I discussed above. (If a cell in the table is blank, it�s just because I didn�t give an example of that type.)
|Explicit||the stranded [people after Hurricane Katrina] were poor, black, disproportionately elderly||larger systemic problems caused environmental racism|
|Implicit||Racism is bad|
One thing to note is that the factual and analytical assumptions tend more often to be explicit, while the moral assumptions tend often to be implicit. This is by no means always the case, but it�s a pretty common pattern.
As with assessing evidence, assessing reasoning consists of two steps:
- Analyzing it, and
- evaluating it.
Analyzing it consists of identifying the assumptionsespecially those that are important to the argument. That�s what most of this handout has been about.
Evaluating reasoning means deciding if those assumptions are true. In one of the examples above, we said it�s not true that all men are purple. In another, we saw the assumption that racism is bad. Most people would agree with that one.
Often, however, we can�t be sure if the assumptions are true or not. In such cases, we fall back on a looser standard: are they reasonable?
By �reasonable� we mean, does it seem likely? Based on what you know about the subject, can you see how someone would think this?
Consider the assumption about �toxic soup� in the article about Hurricane Katrina: The ‘toxic soup’ that has received much public attention is filled with the effluence from the oil and petrochemical industry. Do you know if this is true? Probably not, unless you�ve studied the subject. But does it seem reasonable? That depends on what you know about the area. For example, you may know that southern Louisiana is home to many oil refineries and chemical plants. That would make the assumption seem more reasonable. On the other hand, you may just be familiar with the effects of flooding, and know that it tends to spread nasty stuff around, whether it�s chemicals or mud. That�s less to go on but might still be enough to decide that the assumption is reasonable.
Another aspect of the �reasonable� standard is we may disagree but still see that point of view. For example, some readers might disagree with the idea that �larger systemic problems� caused environmental racism, but they could still see how someone else might think that. So you can criticize the reasoningthe assumptionwhile recognizing that it�s not completely off base. On the other hand, the assumption that all men are purple is not just wrong, it�s completely unreasonable.
As always, this kind of evaluation is not black or white. It�s a matter of degree and judgement, based on your knowledge of the world.
Here is a quick checklist for assessing reasoning.
Identifying, Evaluating and Revising Your Own Assumptions
Like the articles you read and analyze, any argument you make will also contain assumptions. Often we are not aware of the assumptions we make, and sometimes we make bad assumptions without realizing it. One important part of persuasive writing is to examine your own assumptions to make sure that they are valid and consistent with the argument, and to revise those that are mistaken.
You can analyze your own assumptions in the same way that you analyze others. After writing a draft of your argument, go through the main sections and try to spot the claims you make, or those you imply, that you do not try to prove. Make a list of the most important ones.
Once you have identified your assumptions you will want some strategies for dealing with them. Revising Assumptions discusses four things you can do with your own assumptions.