Study on What is Critical Thinking
The word thinking can describe any number of mental activities. Much of our natural thinking, when left to itself, is biased, distorted, partial, uninformed, or downright prejudiced. Yet the quality of our lives depends precisely on the quality of our thought. Critical thinking is that mode of thinking--about any given subject--in which the thinker improves the quality of his or her thinking by skillfully taking charge of its very structures and by imposing intellectual standards upon them. However, effective critical thinking involves consideration of the full range of possibilities to a problem, including emotional, cognitive, intellectual and psychological factors.
Thus, critical thinking belongs to the category of higher-level thinking skills. Critical thinking is analytical and logical; it evaluates ideas and identifies the most reasonable ones. Critical thinking is clear, precise, accurate, relevant, consistent, and fair.
In short, critical thinking is self-directed, self-disciplined, self-monitored, and self-corrective thinking that entails effective communication and problem-solving abilities. While thinking in general is a natural activity of human beings, excellence in thinking must be cultivated and practiced.
Study on Why is Critical Thinking Important
Shallow thinking is costly, both in money and in quality of life. Not only academic success but also success in our work lives depends greatly on solid thinking skills. It is hardly enough for college graduates to have wide knowledge in their fields. Successful people are able to apply what they know to the challenges of their jobs. Today's employers are not looking for walking encyclopedias, but rather for independent decision-makers and problem-solvers.
Critical thinkers have what employers want. A well-cultivated critical thinker
Critical thinking is essential to workplace fairness because we can hold organizational decision-makers accountable and probe behind cliques and rhetoric.
While the above skills clearly apply to our professional environments, they play an important role in our personal and civic lives as well. For example, illogical thinking plays a big part in abusive behavior. Other examples for which critical thinking skills are useful are the manipulative appeals in TV commercials and the rhetoric used by politicians and the media in general. In general, we can avoid manipulation and much frustration by testing ideas for their reasonableness before we accept and act on them. This systematic evaluation of ideas is appropriate whenever someone makes a claim that is open to question. Many such claims are made daily at home, school, and work.
One part of critical thinking comprises the basic principles of logic. Logic, in the traditional philosophical sense, is the study of correct argument. In today's complex world, it is necessary to react to problems and situations from more than a narrow, emotional perspective. "Because I said so!" might (or might not) work with your children, but it probably won't go over really well with your boss. You need to be able to analyze problems and defend your proposed solutions rationally and logically. This requires an understanding of basic logic, including the structure of arguments and logical fallacies. We will take a closer look at arguments in in the Argument Workshop and fallacies in the Informal Fallacies Workshop.
Perception is reality! Oh really?
One of our greatest perceivers, Albert Einstein, when speaking of a subject thought to be literally concrete and figuratively black and white, stated:
"As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."
Many critical thinkers say that perception begins the very unique human experience and continues influencing our uniqueness throughout our lives. We begin life with stimulation of our senses, thereby becoming aware and interpreting the world around us. We move through life by growing, changing, and sometimes rejecting our perceptual building blocks.
Perception refers to the way we receive and translate our experiences--how and what we think about them. For some, plain yogurt is delicious, while for others it is disgusting.
For the most part, perception is a learned process. Through personal experiences and being told by others we learn that the sky is blue, water is refreshing, birds sing, sulfur stinks, and chocolate is tasty--at least to some folks. In the workplace, one employee will perceive a co-worker to be a constructive decision-maker, while at the same time another sees the same employee as an adversarial roadblock to progress.
Perception is also a significant filtering system. There is no doubt that we filter information as we select, organize, interpret, and subsequently, act on it. The question is how we do this. How we perceive, then, defines how we think. Developing critical thinking skills, therefore, requires increased understanding, acceptance, and evaluation of the perception process, influences on perception, and perception blockbusting techniques.
Study on The Perception Process
The perception process is typically outlined through three experiential steps: how we select, organize, and interpret information that is presented to us.
There are numerous factors we use in selecting the information we allow to enter our perception process--what we notice and what we ignore. Our attention is drawn to something louder, brighter, bigger, or in some other way, more intense in stimulating our senses. Each of our senses seeing, hearing, feeling, and smelling – influences our thinking process. The frequency or consistency of stimulation also causes us to notice one thing or person over another. Yet another determining factor in data selection is expectation: we noticed it, we noticed it often, and now we expect to notice it again, given a similar situation.
Our ability and effort in organizing information, putting things in order, is another aspect of our perception process. We tend to put things in order through groupings such as place, time, similarity, and cause. Further, we look at some logical orders or associations, from the alphabet to the five Ws--who, what, where, when, and why--to help us organize all the data. Finally, we bring closure to our organizing efforts by developing patterns or frameworks that allow us to "move quickly and move on," so that we can interpret the information.
Once we select and organize our perceptions, the next step is to interpret the information. As with selection and organization, interpretation plays a significant role and includes several factors. Our frame of reference, comparisons to past experiences, assumptions about the unknown, and need fulfillment are but a few of the circumstances that determine if we move our thinking in a more rational direction.
By and large, these process factors introduce the numerous forces of influence in the way we shape our thoughts and formulate our behavior.
Study on Forces of Influence
The forces of influence on our perceptual process can be organized and presented--as we learned above--in various ways. Some thinkers suggest broad domains such as psychology, physiology, and sociology. Others propose much more specific criteria such as gender, age, birth order, culture, education, economic status, religion, etc. In their book, Thinking, Kirby and Goodpaster provide eight "personal barriers" to critical thinking: enculturation, self-concept, ego defenses, self-serving biases, expectation, emotional influences, cognitive consistency, and stress.
Whatever criteria or factors we use to understand and transcend our perception filters, it is important to realize that we distort the way we perceive the world. Or, at best, we certainly differ in our views of reality. We can, however, make hurdles instead of walls out of these perceptual barriers and blocks.
Study on Perception Blockbusting
In order to build our critical thinking skills, it is vital to sharpen our perceptual blockbusting tools. The three basic elements to perceptual blockbusting are
Awareness helps us identify our critical thinking strengths and weaknesses. Acceptance gives us the permission and motivation to avoid or modify these blocks. Developing these skills allows us to grow. Helping others to develop their awareness and acceptance of their blocks helps our relationships grow.
Increasing our awareness and acceptance begins the process of perceptual blockbusting--building stronger critical thinking bridges. Adding to the blockbusting process, we can take specific actions to overcome our perceptual biases. Actions to manage and, at times, transcend the forces of influence can be organized similarly to the influences themselves. As an example: physiological perceptual checks can be physical conditions including rest and nutrition; psychological checks can include emotion management to overcoming denial and rationalization; and sociological checks can include improvement of our listening skills or embracing cultural diversity.
Remember that better critical thinking does not require perfection, only steps to upgrade our best efforts.
Trying to identify the assumptions that underlie the ideas, beliefs, values, and actions that we and others take for granted is central to critical thinking. Assumptions are those taken-for-granted values, common-sense ideas, and stereotypical notions about human nature and social organization that underlie our thoughts and actions. Stemming from our personal and cultural experiences, they pretend to be "givens" rather than well-supported arguments. What makes assumptions difficult to detect is that they are implied rather than expressed, and therefore, we are usually not consciously aware of them.
Assumptions are not always bad. In fact, we all make daily assumptions. For example, when you buy a new car, you assume that it will run without problems for a while. When you go to sleep at night, you assume that your alarm will wake you up in the morning. When you are employed, you assume that you will receive a paycheck at the end of the month. Unless there was a good reason not to make these assumptions--for example, a defective alarm clock--they would be valid.
The assumptions that hinder critical thinking are unwarranted assumptions. Unwarranted assumptions are ideas we take for granted without justification. Sometimes, these assumptions cut off other avenues of inquiry. Let's suppose, for example, you firmly believe in the common statement that women are naturally more nurturing and emotional than men and men are naturally more aggressive than women. Many people assume this claim to be true because in our culture, women have widely taken on nurturing roles for centuries. Sociological and psychological research has suggested, however, that our gender roles are culturally determined and learned, rather than biologically ingrained. Now suppose your new boss is a very rational, aggressive businesswoman. Does her behavior clash with your assumptions? Very likely so! In this one or similar situations, a critical thinker will identify the assumption and adjust his or her view.
Study on Testing Assumptions
Critical thinkers are willing to uncover their own assumptions and those of others. Remember, assumptions depend on the notion that some ideas are so obvious and so taken for granted that they don't need to be explained. Yet in many cases, insisting on an explanation reveals that we may need more factual evidence in order to develop well-supported viewpoints and to come to sound decisions.
A good first step in challenging assumptions is to ask the impertinent question: WHY? Why do we do things the way we do? Why do we believe that something is true? Why do we act the way we do? The purpose of the "why" technique is not to arrive at a correct explanation, but to explore an issue. If you've ever been with a child who repeatedly asks "why" in response to a long-accepted but unexamined explanation for something, then you have probably experienced just how startling this simple question can sometimes be. By asking "why," we can challenge deeply ingrained assumptions.
As a rule of thumb, the following steps are needed if we want to start testing assumptions:
1. Becoming aware that assumptions exist
2. Making assumptions explicit
3. Assessing their accuracy and validity by asking:
Generating questions such as these is well worth the effort. If we get used to applying these questions routinely, we will assume a more critical and active stance in our lives. For example, we won't reproduce any more of those damaging reactions we have learned to have; we won't accept at face value all justifications given to us by political leaders and organizations; we will look more critically at television commercials; and we won't accept any more that if a textbook says it or if an organization does it, it must be right.
Study on Developing AlternativesThe problem with assumptions is that they make us feel comfortable with our present beliefs and keep us from thinking about alternatives. Critical thinkers, however, are able to independently generate and evaluate alternatives to their taken-for-granted beliefs. Let's look at an example: Praising people for work well done increases their motivation. Sounds good, doesn't it? If we were to scrutinize this statement with the testing questions in the last section, however, we'd get a different picture. Most of these questions yield comfortable answers. The last one, however, is the key: "are there conditions under which the statement seems false?" Here, we could think of answers such as if the praise is too effusive, it could yield smug satisfaction; if the praise is not clearly recognized by the receiver, it could be worthless; if praise is given to the wrong person-for example, the group leader and not the participants-its purpose is destroyed; if praise is given too often, it may become meaningless, and so on. While these answers may destroy our convenient assumptions, they will also generate new ideas that will help expand our viewpoints. Most importantly, they will keep us from making weak judgments on the mere basis of assumptions. Purposefully exploring alternative viewpoints on any given subject is an important characteristic of critical thinkers.
For virtually all of us, there are topics about which we "just cannot be rational." Think, for example, of religion and politics. In these instances, our psychological commitment to a certain belief against another belief may keep us from weighing objectively the evidence for each side of the issue. We call these topics "touchy" because our emotions make it hard for us to reason rationally about them. Some people are unable to accept any significant criticism of a particular political or economic system, regardless of the merit of the criticism. In this case, their emotions stand in the way of a fair and rational evaluation of the system.
Clearly, not all emotions should be avoided as blocks to clear thinking and insight. There is nothing wrong with our enthusiasm for our friends, family, or even for our political and moral views. Emotions can become dangerous, however, when we allow them to cloud evidence, to suggest unwarranted conclusions, and to prevent us from solving issues. The most common cases in which our emotions affect our ability to argue logically are prejudice and defensiveness. Neither prejudice nor defensiveness fosters open-minded, critical thinking. They are discussed in the next sections.
Study on Prejudice and Stereotype
One of the most common barriers to logical thinking based on our emotions involves prejudices and stereotypes.
A prejudice is an unreasonable bias. Not all biases are unreasonable: sometimes our tendency to hold on to a certain view is based on evidence that supports such a bias. We are prejudiced, however, when we make up our minds before we have examined and reflected on the information that could help us to come to a rational understanding. In this case, we have "prejudged" (as the word prejudice suggests) the issue, person, group, or idea.
Prejudice is nourished by stereotypes. Stereotypes are simplistic overgeneralizations that harden into convictions shared by many people. They sometimes lead to patterned expectations: individuals of a group are expected to vary little--if at all--from a preconceived idea of what individuals in that group are like. In social relations, this can result in unfair attitudes or actions toward individuals or groups.
Study on Defensiveness
Defensiveness occurs when we take a combative stance in conversation. When an argument turns in a personal either-win-or-lose "word war," we are not concerned anymore with solving issues rationally. When we become defensive, we concentrate more on defending one point of view than openly evaluating other views. Instead of opening our minds, defensive attitudes prevent us from gaining new insight and understanding.
Consider one helpful test for detecting defensiveness: When the other person is speaking, are you listening in order to find strong points in the reasoning, or are you trying to think of a "comeback" response that would devastate the other position and demonstrate clearly that you were right all along? If you are only seeking victory over an opponent, you are being defensive. In addition to this unwillingness to listen, other signs of defensiveness are communicated simply by the tone of a voice: irritation, condescension, ridicule, and disgust. More explicitly verbal signs of defensiveness include continual interruptions of someone's attempt to argue or plain insults that attack a person or a person's ideas.
Logical thinking cannot be separated from language. The philosopher Ludwig Wittgenstein referred to this relationship when he said: "The limits of my language mean the limits of my world." Developing sensitivity to language and its usage can help foster invaluable insights into ourselves and others. Such insights can be extremely helpful in understanding arguments, in uncovering their hidden assumptions, and in detecting their errors.
Language is a system of symbols--or words--with standardized meanings and rules for their usage. By standardizing the meanings and usage, we are able to communicate. Yet words, although standardized, can signify two kinds of meaning: denotative and connotative meaning. Denotations, that is, the dictionary meaning, usually mean the same thing to everyone. For example, the word apple denotes the firm, round, edible fruit of the apple tree.
But words have connotations as well--overtones or suggestions beyond their dictionary meanings. A word can have different connotations for different people. So, depending on our subjective associations, apple might connote Adam and Eve, apple pie, Macintosh computers, or simply good health. These connotative meanings play an important role in argument. Speakers and writers whose goal it is to persuade, use the possible meanings their audiences find in words to elicit the emotions of the audience.
Study on Emotions and Values in Language
We must understand that language is not entirely neutral. Language not only reports what we see, but it actually shapes our ideas and mental images. It's as if we see what we say. Oftentimes, the words we use are charged with a high emotive value. Emotive language is any word or phrase that arouses moods or feelings. Take, for example, words such as abortion, atheist, family values, feminism, government, motherhood, sex, or socialism. In some cases, our feelings are so identified with such words that their mere mention sets off an emotional reaction. This reaction may be positive or negative. Often, emotive language is used to influence thoughts, actions, and beliefs. Emotive language becomes a problem when it interferes with clear thinking or is used to deceive and manipulate. When this happens, we may believe that we are making rational decisions when in fact we are being emotionally manipulated.
The language people use also reflects how they see and think about things. It reveals their assumptions and biases. For example, words such as Negro and colored have virtually vanished from contemporary American language usage. They have been replaced with the more neutral African American and Black in order to rid the terms of their mental associations of segregation and inferiority. Black--at least on the language level--suggests equality with White. Hence, our use of the new terms shows a change in our assumptions about race relations: this shift in language reflects (and influences) cultural value shifts. The point is that using fair language shows fair thinking.
Study on Persuasive Language
We can sometimes be persuasive without good reasoning. We can also have good reasoning without successfully persuading. This means we have to consider not only how to reason well but also how to present our position in a fair but effective way.
In order to be persuasive, we should use arguments that are as precise and factually oriented as possible. There can and often will be situations in which it is necessary or appropriate to interject emotive language. However, while emotionally charged language is certainly of value in sermons, inspirational speeches, moments of condolence or affection, and so forth, we should be suspicious of any argument that tries to persuade us primarily on the basis of emotionally loaded words and phrases. If there are sound reasons for a position, we have a right to hear them and to evaluate them objectively. In fact, we should demand them. In their absence, and in the presence of emotive language, we should assume that someone is trying to manipulate our emotions to persuade us of the truth of the conclusion.
Study on Informative Language
Informative language functions to provide facts and details. It conveys information by reporting facts, describing events, explaining processes and characteristics, and so on. If our language is vague and ambiguous--when it lacks clear and precise meaning--then our thinking can't be evaluated. If it can't be evaluated, then it cannot be assumed to be reasonable.
The key to effectively communicating information is using language that is clear and precise. Often, however, the language we use is marked by vagueness and ambiguity. An expression is vague when it is not specific enough to meet the needs or desires of the reader or listener; it is ambiguous when it has two or more possible meanings. Let's look at an example: a friend is telling you about a book that you have wanted to read and calls it disappointing. Wouldn't it be worth considering the contrast between what the reader expected and what the book actually offered? Is it disappointing because of a lame plot? A boring style? The lack of insights? In other words, why exactly is it disappointing? As you can see, there are many questions open because the one word used to describe the book is vague, that is, not specific enough. These open questions can be avoided if we clarify the meaning at the time we make the statement.
Before we can look at the structure of argument, we need to define the term. Many people think arguing means fighting or quarreling. In the context of critical thinking, however, this definition does not work. An argument is used to persuade others that something is (or is not) true or should (or should not) be done. When someone gives reasons for believing something--hoping that another person will come to the same conclusion by considering those reasons--the discourse is geared toward persuasion. Not every claim is an argument. Some statements are merely factual information.
For example, to say that the NBA team located in Phoenix, Arizona, is the Suns would not qualify as an argument. There is nothing to argue about since it's an easily verifiable fact. However, the assertion that the Phoenix Suns are the best (or worst, or the fastest, or the slowest, or whatever!) team in the NBA moves into the realm of argument because it involves a disputable claim.
Study on Structure: An Overview
An argument contains three basic elements:
In the example in the previous section, the issue is whether or not the Phoenix Suns are the best (or the worst, or the fastest, or the slowest, or whatever!) team in the NBA. Using such a "whether or not" statement helps you to isolate the issue in a longer, more complicated argument. Remember, an argument involves a disputable claim, which is the issue to be argued.
Unless you are able to distinguish among the elements of the argument, you are in danger of succumbing to fallacious arguments. The next two sections will discuss premises and conclusions.
Study on Premises
The reasons given in an argument to support the conclusion are called premises. As statements that present the evidence, they answer the question why we should believe a claim. Why do I think that the Phoenix Suns are the best team in the NBA? Because they have good rebounding, a good playmaker, depth on the bench, and so on.
Good arguments will give you clues about identifying premises. Often--but not always--we can find certain words that indicate to the reader or listener where the premises are. They are called logical indicators. Some logical indicators that typically identify the position of the premises are:
An argument may have more than one premise since we often use a list of reasons to explain our position.
Study on Conclusion
In someone's attempt to persuade, the conclusion is the statement that presents the point to be proven. In other words, it is essentially the arguer's decision about the issue, and it answers the question presented by the issue. Whether we are reading written material or listening to a friend talk, we should quickly scan--visually or mentally--for the conclusion. In fact, we cannot hope to analyze the reasoning unless we can first identity the conclusion. If someone stopped you by the side of the road and asked, "Is this the best route to get there?" you would probably respond, "To get where?" Similarly, we certainly can't tell if a person's reasoning leads correctly to its destination--the point to be proven--unless we know what the destination is.
Like premises, conclusions often have logical indicators to help identify the conclusion's position. Some conclusion indicators are:
Finding conclusions can be tricky. By its name, it would seem that a conclusion should conclude an argument, that is, that it should appear at the end. However, while this is sometimes the case, at other times it is not. The conclusion, in fact, can appear almost anywhere in an argument. In many cases, mentally inserting a conclusion indicator such as the ones listed above can help. You must ultimately rely on your own good sense of the arguer's intention when you listen or read.
Study on Deduction and Induction: An OverviewTraditionally, philosophy has distinguished between two methods of reasoning: deductive logic and inductive logic. Together, these two forms of inference comprise what is known as the scientific method. In deductive reasoning, we draw a certain conclusion that must necessarily follow from known facts stated in the premises. In inductive reasoning, we derive a probable conclusion from our general observation of diverse facts. Thus, deduction and induction are two different processes of logical reasoning with different levels of conclusiveness.
Study on InductionInductive arguments intend to support their conclusions only to some degree, that is, the premises do not necessitate the conclusion. Hence, the conclusion is probable, but not certain. The idea behind valid induction is that of learning from experience. We observe many patterns, resemblances, and other kinds of regularities in our experiences, some quite simple (sugar sweetens coffee), some very complicated (the laws of planetary motion).
For example, many inductive arguments arrive at generalizations on the basis of a number of observations. A typical generalization argument will occur again given the same circumstances. The strength of such arguments depends on the number of observations of an occurrence, and the impact of other factors. Consider this example: The professor says, "I have no doubt that the vast majority of students will pass this test. They've passed the last three tests I've given, haven't they?" In this case, the professor ties past observations to predicting the probable outcome of the test.
Another example of induction is hypothetical reasoning. A hypothesis is a tentative conclusion that helps us organize ideas until we can come to a definite conclusion based on more experience and evidence. Hypotheses are highly speculative. We all come up daily with hypothetical explanations and expectations. For example, if you notice that your hair has become dry and brittle, you might begin to speculate on why. You might think of recent changes in your lifestyle that could affect your hair: a new shampoo, changes in diet, stress, medication. If you identify such a change, say new shampoo, you could hypothesize that the new shampoo is the reason for your hair problem. If you switched back to your old brand and this solved the problem, then experience would have verified your hypothesis. We must keep in mind, however, that when we are using hypothetical arguments, the conclusions we draw are not certain. Yet, they can be inductively strong if we have enough relevant evidence to support the conclusion, that is, if the premises establish good reason to believe the conclusion.
Study on DeductionIn contrast to inductive reasoning, the conclusions we derive from deductive reasoning must follow from the premises. The premises prove the conclusion. Thus, we can rely on not only probability but on certainty. Note, however, that this certainty does not necessarily refer to the truth of an argument. It's important to understand that the deductive validity of an argument has nothing to do with whether its premises are true. Validity has to do with the connection between premises and conclusion, that is, the structure of the argument and not its content. An argument can be valid and still have a false conclusion.
Let's look at an example: All cats can fly (premise). Dusty is a cat (premise). Therefore, Dusty can fly (conclusion). This is a valid argument because-regardless of the false first premise-the conclusion follows from the premises. When the structure of an argument--as in the above example--suggests that if the premises were true, then the conclusion would have to be true, we call it a valid argument. This is not to say, however, that the conclusion is acceptable. A conclusion is acceptable only if 1) the argument is valid, and 2) we accept the premises as true. In this case, we call the argument sound. An example of a sound argument is the following: All cats purr. Dusty is a cat. Therefore, Dusty purrs. In this example, we can easily accept the premises, and the structure of the argument necessitates the conclusion. Since a deductively valid argument cannot move from true premises to a false conclusion, this argument is acceptable. There are hundreds of fallacious patterns, and each fallacy is given a name that in some way describes the error. The names often are derived from Latin because of the roots of logical study. Let's identify what we consider to be the five most common fallacies: non sequitur ("does not follow"), ad hominem ("relating to the person" rather than to the argument), post hoc ergo propter hoc ("after this therefore because of this"), slippery slope, and appeal to emotion.
Non sequitur (irrelevant reason). In this fallacy, the premises have no direct relationship to the conclusion. Example: A waterfall in the background and a beautiful girl in the foreground have nothing to do with an automobile's performance.
Ad hominem. This fallacy is committed when a person's characteristics are irrelevantly attacked in order to discredit the arguer rather than his or her argument. Example: John's objections to capital punishment carry no weight since he is a convicted felon.
Post hoc ergo propter hoc. A form of hasty generalization in which it is inferred that because one event followed another, it is necessarily caused by that event. Example: They quit using the Iowa tests last year in my kids' school, and this year my son received 3 Ds. I knew that was going to cause problems.
Slippery slope (black-and-white fallacy). A line of reasoning in which there is no gray area or middle ground. It argues for (or against) the first step because if you take the first step, you will inevitably follow through to the last (which is usually quite horrible...). Example: We can't allow students any voice in decision-making on campus; if we do, it won't be long before they are in total control.
Appeal to emotion. In this fallacy, the arguer uses emotional appeals rather than logical reasons to persuade the listener or reader. Generally, the issue is oversimplified to the advantage of the arguer. Example: Ladies and Gentlemen of the jury, the defendant comes from a poor background. He was badly mistreated as a child. If he is found guilty, there will be no one to care for his wife and three young children. Surely, so long as there is any mercy and justice left in the world, you cannot find it in your hearts to return any verdict but "not guilty."
When you understand a fallacy, it is difficult to commit that error of reasoning without realizing what you are doing. It will also give you power in arguments with "smooth talkers" who commit fallacies but disguise them well. Responding to fallacies is easy. Simply insist that the arguer give you adequate support for his or her claim and ask for further, factual justification. Remember, the burden of proof is on the arguer.
Study on DefinedWe all make errors in reasoning on occasion. Those of us with strong opinions and beliefs tend to fall into problems when we are creating arguments. When these errors fall into a common pattern, they are called logical fallacies. A logical fallacy, then, is a pattern of incorrect or illogical reasoning. Almost all fallacies can be seen as devices for getting you to accept conclusions that are unwarranted by what are offered as premises. In a fallacious argument, the premises leading to the conclusion look okay at first glance, but we sense that something is not quite right about them. Finding a fallacy in our own or someone else's reasoning does not mean that a presented conclusion is false. It simply shows that the conclusion is not adequately supported by the evidence, that is, by the premises.
Consider the following example:
You can be sure that we will give you an honest deal on a used car since we will always deal with you in a forthright and honest way when you purchase a used car from us.
The fallacy committed here is called begging the question, or circular reasoning. Note that the reason offered for the conclusion is the conclusion expressed in different words. People are often so taken in by the magic of words that they fail to see when they aren't given independent evidence for a conclusion. If you take the time to analyze carefully the content of the premises of an argument and consider its relation to the content of the conclusion, you will not be fooled by argumentative devices as flimsy as the above.
Study on Approaching Logic Problems
This last workshop is among the most important; it is the one for which you prepared in the above sections. Much like in the perception process, our problem-solving abilities depend on how effectively we organize and interpret information that is presented to us. In organizing information, it is essential to recognize the core of the problem--that is, to "weed out" any irrelevant data, sometimes by the process of elimination--and to group relevant data in meaningful patterns that are connected by common characteristics, for example, spatial relationships. Doing so requires that we overcome our perceptual blocks and that we apply both deductive and inductive reasoning.
You might wonder why this is important. After all, solving logic problems is not part of your day to day work life, right? Wrong. While you won't very often have to determine which cities Sally and Harry visited in which order (one of the logic problem staples!), you are most likely faced with problems that can be more easily solved by a practiced, logical mind all the time. Think about it. How did you decide which vendor's price was the best deal, or where that important report was misplaced? Learning how to solve simple logic problems in the abstract will help you build transferable skills that will serve you well in school, work, and life. The term "logic problem" is used in this tutorial to identify a particular type of question. Logic questions are often called "analytical reasoning" questions. These questions are designed to measure your ability to understand a system of relationships and to draw conclusions about those relationships.
Anatomy of a Logic Problem
Analytical reasoning questions typically appear in sets. Each set presents a distinct problem which includes three elements: (1) the premise, (2) the conditions, and (3) the questions.
1) The Premise
The premise is a brief introductory paragraph establishing the setting for the problem, identifying the subjects involved, and describing generally how the subjects are related to one another. The number of subjects in a problem generally ranges from four to ten.
2) The Conditions
The premise is followed by a series of conditions (or rules) that impose specific restrictions upon the relationships among the subjects. A logic problem may include as few as two or as many as ten conditions (the sample problem in Example 9-1 uses four conditions).
3) The Questions
The conditions are followed by a series of questions about the relationships defined by those conditions. The questions require that you use deductive and occasionally inductive analysis. As in math problems, one and only one response can be proven beyond any doubt to be the correct one.
You should realize that logic problems-even the most simple ones-are not easy. Do not be discouraged. Developing analytical reasoning ability is like riding a bike or learning a new language. You simply need to develop certain skills. While this tutorial will not delve into complex logic, there are a number of important basics that you will have to understand in order to succeed. You will have to understand fully all the implications of a conditional rule. In particular, you will have to learn to appreciate not only what you know directly from application of a rule, but what additional inferences or conclusions the rule permits you to make or not make. The single most important conclusion that you are always permitted to make is the contrapositive rule. There are two other conclusions that you are not permitted to make that are also important. When you draw a conclusion that you are not allowed to make, you have committed a logical fallacy. Let's examine both the permissible conclusions and the impermissible ones before proceeding further.
Conditional Statements and The Contrapositive Rule
A conditional statement is one in which an event occurs (or does not occur if some other event occurs (or does not occur). It defines the parameters of the relationship between and among conditions. Consider the following three statements
All three statements above mean essentially the same thing-a shirt's being blue is conditioned upon the shirt's having buttons. Given this premise, consider whether each of the following statements may be logically deduced:
The first of the three statements immediately above is referred to in formal logic as the contrapositive-it reverses the premise and the conclusion, and negates both. A contrapositive statement is always inferable from its premise. In formal logic, this rule is set forth as follows: RULE: If A, then B. CONTRAPOSITIVE. If not B, then not A.
As a common example: Statement: All boys are male. Contrapositive conclusion: If not a male, then not a boy.
Statements 2 and 3, however, are both fallacious - buttoned shirts may also be any other color. In order to recognize these statements as they appear in some other scenario in a logic problem, it is helpful to consider the statements in a general form:
In Statement 2, we have:
RULE: If A, then B.
CONCLUSION: If B, then A.
This conclusion is not inferable.
In formal logic, it is such a common fallacy that it even has a formal name: AFFIRMING THE CONSEQUENT. The name is not especially important, but the principle is critical. While buttons and blue shirts may not stick in your head, think of a more common example to highlight why this is an example of false reasoning: Statement: All boys are males. Conclusion: All males are boys.
In Statement 3, we have RULE: If A, then B. This conclusion is not inferable. It, too, is such a common logical fallacy that it has a formal name: DENYING THE ANTECEDENT. Again, the principle is critical and a common example highlights the falsity of the conclusion: Statement: All boys are males. Conclusion: If someone is not a boy, then he is not a male. Obviously, adult males would disagree.
1) If A, then B. If not B, then not A. (Contrapositive-valid)
2) All A are B. If B, then A. (Affirming the consequent-not inferable)
3) If A, then B.
Study on Linear Sequence Problems
What is a "Linear Sequence
Study on Matching ProblemsWhat is "Matching"?
Matching problems involve assigning to each subject in the problem one or more attributes or characteristics. There is no single diagramming approach that works well for all matching problems. The proper approach depends upon how many attributes are involved as well as other factors.
Matching must be distinguished from grouping. Matching involves assigning characteristics to a subject, while grouping involves grouping two (or more) subjects together according to a common characteristic. These two different problem types are similar in that each involves assigning characteristics to a problem's subjects.
Matching Problems that Contain Conditional Statements
A matching problem may contain one or more conditional statements. Remember that a conditional statement is one in which an event occurs (or does not occur) if some other event occurs (or does not occur). (At this point you might want to review the discussion regarding conditional statements and the contrapositive rule of formal logic.)
Study on Grouping and Selection ProblemsIn the earlier sections of this tutorial, your task was either to order the subjects of the problem in their proper sequence or to match the subjects to one or more attributes. In this section, your task is to divide the subjects of a problem into two or more groups. The fundamental distinction between grouping and selection is as follows:
Simple Grouping Problems
As noted above, "grouping" involves dividing a problem's subjects into at least three different groups. The number of subjects to be included in each group may or may not be specified.
Selection problems involve dividing subjects into exactly two groups. The term "selection" is used here because your task is to select particular subjects from a roster or pool, while the remaining subjects remain unselected. Two groups result - those subjects that are selected, and those subjects that are not selected. In other words, for each subject you must make a yes-or-no decision - for example, is the subject:
Study on Non-Linear Spatial Problems
Earlier, we explored the linear sequence problem, which involved ordering the subjects of a problem along a straight line (usually from left to right). In this section, you will discover that a problem involving spatial relationships among the subjects (that is, how the subjects are arranged relative to one another in the concrete world) may instead involve a two-dimensional plane rather than simply a straight line. The problem may require that you arrange the subjects:
A map problem involves arranging the subjects on a plane according to their relative compass direction (north, south, east, west). Map problems bear some resemblance to linear sequence problems in that your task is to rank the subjects. However, in a map problem, two simultaneous and interconnected rankings are involved - (1) a horizontal (east-west) ranking and a vertical (north-south) ranking.
Line-and-node problems involve spatial connections between the subjects of the problem. Your task is to determine how to get from one subject (or node) to the other subjects following the connecting lines. Some lines may be two-way streets, while others may be one-way streets.
Also, some subjects might be impossible to reach from certain other subjects. The rules tend to be permissive in nature rather than mandatory-that is, the rules speak in terms of where you can go from any given point of departure, rather than compelling you to go.
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