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Critical Thinking Critical Thinking - Lecture notes ...€¦  · Web viewAuthor: Thanuja Jerad Created Date: 02/20/2018 08:56:00 Title: Critical Thinking Critical Thinking - Lecture

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Page 1: Critical Thinking Critical Thinking - Lecture notes ...€¦  · Web viewAuthor: Thanuja Jerad Created Date: 02/20/2018 08:56:00 Title: Critical Thinking Critical Thinking - Lecture

LOGIC AND CRITICAL THINKING

(DR E.B. AMEZA-XEMALORDZO)

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SECTION A

1.0 What is Critical Thinking?

We assume a belief is worth having provided it’s most likely true. We also assume a belief is most likely true if there are good reasons to accept it. “Critical thinking is the systematic evaluation or formulation of beliefs, or statements, by rational standards.”

It’s systematic because it involves distinct procedures and methods (not just gut feelings). It’s used to evaluate existing beliefs and formulate new ones. It evaluates beliefs in terms of how well they are supported by reasons. We Should Think Critically Because: Who we are is determined largely because of our actions and choices. Our actions and choices are in turn determined by our thoughts and beliefs. If we don’t choose our beliefs carefully were giving up control. Critical Thinking is all about thinking OUTSIDE of the box: Its about challenging our assumptions

Asking hard questions Rejecting biases, stereotypes, and other unreasonable assumptions To Think Critically you need to be able to think, listen, and read slowly and attentively. It helps you understand a few definitions and concepts.

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1.1 The Descriptive/Normative Distinction We all know what it is like to revise our opinions or beliefs, ranging from the trivial to the deep. The question is how we can do this in an intelligent and responsible way. The answer lies with critical thinking. To appreciate the value of critical thinking, it is helpful to draw a distinction that applies in many areas of life (not in Vaughn):

Descriptive: This concerns how we actually think or behave. Normative: This concerns how we ought to think or behave.

This distinction applies in the realm of ethical conduct: how people actually behave (people tell lies) does not necessary coincide with how they morally ought to behave (we ought to tell the truth). In fact, people’s actual behavior is no guide to proper moral conduct. 1.2 Critical Thinking is a Normative Enterprise This distinction applies in the realm of thinking as well: how people actually acquire their beliefs does not necessarily coincide with what they rationally ought to believe. In critical thinking, one aims to form beliefs that are true and objective. Unfortunately, many people do not aim for truth and objectivity when it comes to evaluating their opinions. Think about the role of television in the way it forms many people’s (and children’s) beliefs. Television is a big source of people’s opinions, ranging from current affairs to expectations about romance. It explains how people actually come to believe the things that they believe. To that extent, television only gives as a descriptive explanation of people’s beliefs. But that is not what we want. What we want is a set of guidelines for what we rationally ought to believe – what is correct to believe.

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This is where critical thinking comes in. It specifies the principles of correct thinking – the rationally proper ways in which we can gauge whether a belief is true, reasonable, rational, and worthy of preserving.

1.3 Critical Thinking StandardsCritical thinking can be seen as a disciplined thinking governed by clear intellectual standards. Among the most important of these intellectual standards are clarity, precision, accuracy, relevance, consistency, logical correctness, completeness, and fairness. Let’s begin our introduction to critical thinking by looking briefly at each of these important critical thinking standards.

▪ Clarity: Before we can effectively evaluate a person’s argument or claim, we need to understand clearly what he or she is saying. Unfortunately, that can be difficult because people often fail to express themselves clearly. Sometimes this lack of clarity is due to laziness, carelessness, or a lack of skill. At other times it results from a misguided effort to appear clever, learned, or profound.

Critical thinkers not only strive for clarity of language but also seek maximum clarity of thought.

• Could you elaborate further on that point?• Could you express that point in another way?• Could you give me an illustration?• Could you give me an example?

▪ Precision: An extraordinary commitment to precision. First, by careful and highly trained observation, precise logical inference, and able to reason from those clues to discover the solution to the mystery.

What exactly is the problem we’re facing? What exactly are the alternatives? What exactly are the advantages and disadvantages of each alternative? Only when we habitually seek such precision are we truly critical thinkers.

• Could you give more details? Could you be more specific?

▪ Accuracy: Critical thinkers don’t merely value the truth; they have a passion for accurate, timely information. As consumers, citizens, workers,

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and parents, they strive to make decisions that are as informed as possible.• Is that really true?• How could we check that?• How could we find out if that is true?

▪ Relevance: It is importance to stay focused on relevant ideas and information.

• How is that connected to the question?• How does that bear on the issue?

▪ Consistency: Critical thinkers prize truth and so are constantly on the lookout for inconsistencies, both in their own thinking and in the arguments and assertions of others. There are two kinds of inconsistency that we should avoid. One is logical inconsistency, which involves saying or believing inconsistent things (i.e., things that cannot both or all be true) about a particular matter. The other is practical inconsistency, which involves saying one thing and doing another.• How does your answer address the complexities in the question?• How are you taking into account the problems in the question?• Is that dealing with the most significant factors?

▪ Logical Correctness: To think logically is to reason correctly—that is, to draw well-founded conclusions from the beliefs we hold. To think critically we need accurate.• Does this really make sense?• Does that follow from what you said?• How does that follow?• But before you implied this and now you are saying that; how can

both be true?▪ Completeness: In most contexts, we rightly prefer deep and complete

thinking to shallow and superficial thinking. Thus, we justly condemn slipshod criminal investigations, hasty jury deliberations, superficial news stories, sketchy driving directions, and snap medical diagnoses.• Do we need to consider another point of view?

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• Is there another way to look at this question?• What would this look like from a conservative standpoint?• What would this look like from the point of view of...?

▪ Fairness: Critical thinking demands that our thinking be fair.• Open-minded • Impartial• Free of distorting biases and preconceptions

1.4 Benefits of Critical ThinkingAcademic Performance

understand the arguments and beliefs of others Critically evaluating those arguments and beliefs Develop and defend one's own well-supported arguments and

beliefs.

Workplace Helps us to reflect and get a deeper understanding of our own and

others’ decisions Encourage open-mindedness to change Aid us in being more analytical in solving problems

Daily life Helps us to avoid making foolish personal decisions. Promotes an informed and concerned citizenry capable of making

good decisions on important social, political and economic issues. Aids in the development of autonomous thinkers capable of

examining their assumptions, dogmas, and prejudices.

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2.0 SOME DEFINITIONS:

2.1. VAGUENESS AND AMBIGUITY VaguenessWhen a definition is vague it has no specific meaning for the intended audience. Here are few examples of vague definitions from the goldmine of pseudo-wisdom that is Depak Chopra: Happiness is a continuation of happenings, which are not resisted. To think is to practice brain chemistry. A person is a pattern of behavior, of a larger awareness.

Notice that none of these definitions gives us any clarity as to what the defined term actually means.  If you were an outer-space alien and asked for a definition of "happiness", "thinking", and a "person", your knowledge would not in any way be improved over your current position of ignorance. 

Vagueness can apply to both individual words like "happenings" as well as to entire phrases, e.g., "a larger awareness."  It should be noted that Depak isn't the only entity that employees vagueness as a means to appear to say something meaningful.  

This is also a favourite technique of advertisers.   How many times do we hear "new and improved!" with no description of what is new and improved?  Or that something "'boosts' your immune system"?

A term or phrase can be described as being vague if its meaning is not clear in its context. Vagueness involves a term’s lack of precision. AmbiguityTerms are ambiguous when they have more than one plausible interpretation. ("Ambi" means "two").  Ambiguity comes in two flavours: syntactic and semantic.   Semantic ambiguity is when a word can have two possible meanings.  For example, suppose a store has a sign that says "Watch

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repairs here."  We could interpret this as "this is a venue in which we can view someone doing repairs" or "timepieces are repaired here."  Generally, context sorts out semantic ambiguity (but not always).

Syntactic ambiguity is when the sentence structure offers more than one plausible meaning.  For example:  I tackled the thief with my pyjamas on.  We could interpret this as meaning the thief was wearing my pyjamas or that I was wearing pyjamas when I tackled the thief.   Again, context can usually help us sort this out, but not always. 

a. Word Ambiguity -Relates to the fact that many words have more than one meaning. A word is ambiguous when (1) it has more than one meaning and (2) it is not obvious which one is intended in a situation in which the word is used. For example: Joe went to the bank. In addition to word ambiguity, we can also say that this is an example of referential ambiguity since we don’t know what the word “bank” is referring to. An error in reasoning occurs when two distinct meanings of a word are used. For example:

Man is the only rational animal. No woman is a man. Therefore, no woman is rational. Two different senses of ‘man’ here: human versus adult male.

The fallacy of equivocation occurs whenever a word has one meaning in one premise and another meaning in another premise or the conclusion. This switch of senses always invalidates the argument.

b. Grammatical Ambiguity

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Grammatical ambiguity occurs when (1) a sentence has a grammatical structure allowing it to be understood in more than one way and (2) it is not clear from the context which understanding is the intended one. For example: A sign outside of a nightclub reads “Smart is the most exclusive club in town, everyone welcome.” -Local high school dropouts cut in half. -Miners refuse to work after death. Morgan ate the ice cream with relish.

1. Kids make nutritious snacks.

2. John met the girl he married at a dance.

3. Helen saw the bird with powerful binoculars.

4. The guy was all over the road; I had to swerve several times before I hit him.

5. Officers help dog bite victims.

Note: 'Vague' is used where something lacks precision or detail, while 'ambiguous' is something that could have two meanings, or is open to interpretation

2.1.1 Fallacy of EquivocationThe fallacy of equivocation is when a key term in the argument isn't used with a consistent meaning throughout the premises and conclusion.  That is, the meaning changes from one premise to another or from the premises to the conclusion. 

Example: Scientists say that energy can neither be created or destroyed, therefore it's impossible for there to be an energy crisis. 

In the premise "energy" is being used in the general scientific sense which refers to a closed system (i.e., the universe).  In the conclusion, "energy" is used in the natural resources sense (i.e., oil and coal).  Also, the earth isn't a closed system,

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but an open one.  Because the meaning of the term "energy" isn't held constant from premise to conclusion, this is an example of the fallacy of equivocation. 

2.2 Claims or AssertionsAn Assertion is a declarative sentence that is intended to make a claim of some sort. Sometimes these are called statements or propositions. When we take a position on an issue, we assert or claim something. The claim and thinking on which it is based are subject to rational evaluation. When we do that evaluating, we are thinking critically.

Only certain sorts of sentences can be used in arguments. We call these sentences propositions, statements or claims. Example,

“I’m taller than you”, “it is raining”, “she will win the race.

Statements or claims have the following characteristics:1. They are either true or false.2. They are declarative (that is to say, they are not questions or commands;

they are sentences that describe how things are, were, will be, would be, could be or should be.)

3. They are clearly written or stated such that there is no ambiguity as to their meaning (i.e. they don’t have two or more highly distinct interpretations, as in sentences like “I saw the waiter with the glasses”) and they are not so vague as to make it impossible to say under what conditions they would be true.

There are lots of ways for a sentence to fail to be a claim, just as there are a lot of way for a sentence to fail to be a question, or description of a dog, or a command.

Which of the following are claims?

1. All dogs have four legs.

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2. John F. Kennedy was the 35th president of the United States.

3. Don’t go into Central Park at night.

4. Why do people always talk on their cell phones on the J train?

5. Barack Obama is very tall.

6. There is life on other planets.

Answers:1. Is a claim. It’s false (there are dogs that have lost a leg, thus three-legged

dogs.) The fact that it’s false means that it must be a claim. ONLY claims can be false.

2. Is a claim. It’s true. The fact that it’s true means that it must be a claim. ONLY claims can be true.

3. Not a claim. It is a command; it is neither true nor false (though it might be good advice.)

4. Not a claim. It is a question. Questions are never true or false, though sometimes they imply claims.

5. Not a claim. “Very tall” is too vague. We have no standard, agreed upon method for determining if someone is “very tall.” By Danish standards (where the average male height is 5’11”) Obama is probably not “very” tall. By Vietnamese standards (where the average male is 5’4”) Obama might well be considered “very” tall. We could turn this sentence into a claim by changing it to “President Obama is 6’2” tall.”

6. This is a claim, but we don’t know if it’s true or not. Still, it’s clearly either true or false, so it must be a claim.

2.2.1 Subjective and Objective claims

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Claims are either subjective or objective. These words have a special, technical sense in philosophy. A claim is subjective if it is about thoughts, feelings, or other internal states of the mind. A claim is objective if it is about something that is not dependent on a state of the mind.

For example, “I'm itchy,” is a subjective claim. “I feel hot,” “John is tired,” “Anita loves Keyshawn,” “Thomas believes in God,” and “The Black Keys are my favorite band,” are all subjective claims. This is because their truth or falsity depends upon what someone thinks or feels.

The following claims are objective: “Dan is six feet tall,” “The Empire state building is made of cheese,” “New York is the largest city in the United States,” and “God exists.”

Note that the second claim is a false objective claim. The Empire State Building is not made of cheese. But the truth or falsity of the claim is independent of what anyone thinks or feels. It's a fact about the world outside of our minds. Similarly, “God exists” is an objective claim. Some people believe it to be true, some people believe it to be false, but their beliefs do not make the claim true or false any more than one's belief that New York is the largest city in the world would make that claim true. God exists, or fails to exist, whether or not we believe or think that God exists.

For the following claims, say if they are subjective or objective:

1. There are over 1200 species of beetles.

2. The Yankees will win the World Series in 2012.

3. Alissa's head hurts.

4. I'm tired of hearing about the economy.

5. There is no God but Allah and Mohammed is his prophet.

6. There are over 9 billion people living in Brooklyn.

Answers: 1. Is an objective claim.

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2. Is also objective: though it refers to a future event, it's not the case that our

thoughts or feelings cannot make it true or false; we just have to wait to see if it's true or false.

3. Is subjective: it refers to a feeling that Alissa has. 4. Is subjective; it refers to a feeling or thought had by the speaker. 5. Is objective: many people believe it to be true, many others do not, but it's

true if and only if there is, in fact, on God, that God's name is Allah, and Mohammed is the prophet of that God. My thoughts or feelings on this cannot alter its truth value.

6. Is objective: there are not, in fact, 9 billion people living in Brooklyn, and we can ascertain that by counting, looking at the census, or just noting the impossibility of getting 9 billion people into the existing housing in Brooklyn.

2.3 ARGUMENT

The goal of a critical thinking course is to enable you to understand and analyze arguments. By the end of the course you should be able to recognize such arguments and determine if they are good (i.e. if a rational person, upon hearing such an argument, should be convinced by it.).

Here’s another way of saying this: An argument is a group of statements in which some (the premises) are intended to support another (the conclusion). The conclusion is what the speaker wants you to accept. The premises state the reasons or evidence for accepting the conclusion. Typical argument will have mini claims to support it.

2.3.1 Basics of Argumentation

Argument: An attempt to convince, using reasons. An argument consists of two parts:

A conclusion, which is the sentence that the argument is arguing for, or that part of the argument that the arguer is trying to convince you of. The conclusion is always a claim.

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The premises. These are sentences that are supposed to support, lead to, provide evidence for, prove or convince that the conclusion is true. An argument is an attempt to convince someone (though not necessarily someone in particular) that a certain claim is true.

For example, this is an argument:

Mr. Johnson’s fingerprints, and only Mr. Johnson’s fingerprints, were found at the crime scene. A knife was found on Mr. Johnson’s person, and it matched the wounds on the victim, and contained traces of the victim’s blood. Mr. Johnson’s cellmate testified that Mr. Johnson confessed to the crime, and hidden cameras recorded this confession. Therefore, Mr. Johnson is guilty.

The last sentence is the conclusion. The other sentences are premises.

Here’s another:

When I left the house, there was cake in the refrigerator. You’re the only other person with a key to the house, and now the cake is gone. So, you ate the cake.

Again, the last sentence is the conclusion, the others are premises. Here’s another:

You should complete your college education. People who graduate from college not only earn, on average, more money than college dropouts, they also report much higher levels of satisfaction in life.

In this case, the first sentence is the conclusion, and the rest are premises. You should be able to note this because the other sentences give reasons that you should accept the first sentence. That is, they act as premises, or evidence, for the conclusion. Another way to see that this is the conclusion is to ask yourself: what is the person trying to convince me of? It’s not “college graduates earn more money.” He’s telling me that without any evidence. But, if that’s true, that’s a reason to graduate from college. In other words, it’s a premise. The premise is presented as evidence for the conclusion.

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2.3.2 IDENTIFYING PREMISES AND CONCLUSIONS

In identifying premises and conclusions, we are often helped by indicator words. Indicator words are words or phrases that provide clues that premises or conclusions are being put forward. Premise indicators indicate that premises are being offered, and conclusion indicators indicate that conclusions are being offered. Here are some common premise indicators:

since becausefor given thatseeing that considering thatinasmuch as asin view of the fact that as indicated by

judging from on account of

The following examples illustrate the use of premise indicators:

1. Having fun can be the spice of life but not its main course, because when it is over, nothing of lasting value remains.

2. Since effective reasoning requires reliable information, it’s important to be able to distinguish good sources and trustworthy experts from less useful ones.

3. Women are not by any means to blame when they reject the rules of life, which have been introduced into the world, seeing that it is men who have made them without their consent. (Michel de Montaigne)

4. I think that, as life is action and passion, it is required of a man that he should share the passion and action of his time, at peril of being judged not to have lived. (Oliver Wendell Holmes Jr.)

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And here are some common conclusion indicators: Therefore thusHence consequentlySo accordingly,it follows that for this reason,that is why which shows thatWherefore this implies thatas a result this suggests thatthis being so we may infer that

These examples illustrate the use of conclusion indicators:

1. There’s probably no God, so stop worrying and enjoy your life.2. Rapid economic improvements represent a life-or-death imperative

throughout the Third World. Its people will not be denied that hope, no matter the environmental costs. As a result, that choice must not be forced upon them. (Al Gore)

3. Your life is what your thoughts make it. That is why it is important for all of us to guard our minds from unhealthy habits of thinking, habits that hold us back from what we could be accomplishing. (Tom Morris)

4. As our birth brought us the birth of all things, so will our death bring us the death of all things. Wherefore it is as foolish to weep because a hundred years from now we shall not be alive, as to weep because we were not living

a hundred years ago. (Michel de Montaigne)

Understanding arguments would be easier if the expressions just listed were used only to signal premises or conclusions.

That is not the case, however, as the following examples illustrate:

I haven’t seen you since high school.You’ve had that jacket for as long as I’ve known you.Thus far everything has been great.It was so cold that even the ski resorts shut down.

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I wouldn’t mind seeing that movie again.There is water on the floor because the sink overflowed.

2.3.3. InferenceAn inference is the move from a premise (or premises) to a conclusion (or conclusions). Critical thinking is all about inferences. Inferences are identified and evaluated.

An argument attempts to prove that some claim is true, while an explanation attempts to specify how something works or what caused it or brought it about. Arguing that a dog has fleas is quite different from explaining how it came to have fleas. Explanations and arguments are different things.

An inference is the move from a premise (or premises) to a conclusion (or conclusions).

• Critical thinking is all about inferences.

• Inferences are identified and evaluated.

2.4 FUNDAMENTAL DISTINCTIONS Claims and Reasons The central focus is upon the truth or credibility of a claim. A claim is expressed in a statement that asserts the truth (or falsity) of some situation. Examples:

Oranges grow in Southern California. Electric cars emit less carbon than fuel-powered cars. Every Ghanaian citizen should have health care.

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Claims merit belief or disbelief, and the way one displays the credibility of a claim is by offering a reason that can support the claim’s truth. Reasons and Arguments

When one gives a complete and coherent reason for a claim, be it long or short, one has essentially given an argument. An argument, thus, consists of a reason supporting a claim. The statements that express the reason are called premises, and the claim that the argument is attempting to prove is called the conclusion. To make things explicit, we will often write up an argument in the following way:

Depending on the claim, a supporting reason can be short (expressible in a single premise) or it can be long (expressible only in many premises). The term, “reason,” refers to the premises of an argument. The important thing is that the premises offer a coherent reason to accept the conclusion. Here are some examples:

Argument 1 1. John is a bachelor.

2. Therefore, John is unmarried.

Argument 2 1. All surfers are enthusiastic swimmers. 2. All enthusiastic swimmers like being in water. 3. All those who like being in the water want clean oceans. 4. John doesn’t care about clean oceans.

5. John is not a surfer.

Argument

Conclusion Premise Premise

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The first argument is pretty short; the reason supporting the conclusion is expressed in just a single premise. The second argument, however, is pretty long; there are four premises that combine together to give a single coherent reason for the conclusion. It is also possible to have a completely different reason for one and the same conclusion:

Argument 3 1. Those who don’t know how to swim are not surfers. 2. John does not know how to swim. 3. John is not a surfer.

Argument 2 and argument 3 have the same conclusion; they are arguing for the same claim. However, they appeal to different reasons. Just because an argument fails to support a claim does not mean that there cannot be a different argument that does a better job. Critical reasoning gives us the rules, principles, and strategies to help us judge which are the good reasons and which are the bad ones so that we know which arguments to accept or reject.

2.4.1 HOW TO IDENTIFY ARGUMENTS There are some typical indicator words that are used to signal that one is giving an argument. Some common premise indicators are:

because since for the reason that due to the fact that as

in view of the fact that given that seeing that assuming that for the reason that

inasmuch as as indicated by for the reason being

Some common conclusion indicators are:

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therefore, thus which implies that consequently it follows that

we can conclude that so hence it must be that as a result

which means that ergo

Even though these are commonly available indicator words, identifying arguments is not an easy task. Some arguments do not contain any premise or conclusion indicators, even though they are perfectly good arguments. And some collections of statements contain such words, even though they do not constitute an argument. Furthermore, people do not successfully give proper arguments even when they want to. When people give arguments (in newspaper editorials, in everyday speech, in books or articles), they do not present it in numbered premise form. Sometimes people present the conclusion first, and then rattle off some supporting premises; at other times, they present some premises first, and then draw their desired conclusion. In addition, people are not always careful about giving all the necessary premises for an argument; in other words, they only give us a partial reason, and so leave out missing premises. Often, we have to fill in the missing premises to see how the argument really works. This can take some ingenuity on the part of the critical thinker, but when important arguments are at stake, this is a highly valuable thing to do. 2.4.2 Arguments v Non-Arguments A mere collection of statements does not constitute an argument. In an argument, there is a logical inference to draw from reasons (premises) to conclusion. When no such inference is present, there is no argument.

Argument: A group of statement in which there are premises that constitute a reason for believing the truth of a claim. The premises support an inference to the conclusion. Non-Argument: A group of statement in which there is no inference that can be drawn that supports any claim.

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This can get a bit tricky when a non-argument reports an argument or reports someone drawing an inference. Merely reporting an argument is not the same thing as giving an argument. It’s important to note that not all passages contain an argument. Newspaper reports are generally not arguments: they simply describe what happened. There is no one sentence that all the other sentences aim at. It’s also the case that sometimes polemical writings that seem angry and pointed do not contain an argument, because they have no premise-conclusion relations.

For the following, distinguish the arguments from the non-arguments by underlining the conclusions of the arguments.1. All liberals want the United States to be defeated. John Kerry is a liberal:

you can see that quite clearly in his congressional voting record. So if you voted for John Kerry, you voted for someone who wanted the United States to be defeated.

2. One in seven American adults in the US—about 32 million people—have such low literacy skills that they cannot read a newspaper story or a prescription bottle, a new federal study says. "They really cannot read paragraphs (or) sentences that are connected," says an Education Department researcher. The numbers aren't improving: The US adult population increased by 23 million between 1992 and 2003, 3.6 million of whom were functionally illiterate, USA Today reports.

3. You shouldn’t smoke, because it can cause lung cancer.

4. Joe Biden arrived in Pakistan today at the start of a tour of Southwest Asia, AFP reports. The vice-president-elect is leading a congressional delegation that includes Republican Sen. Lindsey Graham. Talks with President Asif Ali Zardari and other Pakistani leaders are likely to focus on the war on terror and relations with India, expected to be Biden's next stop.

5. Anyone who voted for Barack Obama is an idiot. Why would you vote for him? A lot of people don’t care about this country. I bet they’ll all be sorry in four years when he’s destroyed the economy.

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6. Water boils at 100 degrees Celsius because at that temperature the weak bonding between the water molecules can’t overcome the force of their movement, and the molecules push off one another, causing the water to go from a liquid to a gas.

7. Cellular respiration is the set of the metabolic reactions and processes that take place in organisms' cells to convert biochemical energy from nutrients into adenosine triphosphate (ATP), and then release waste products. The reactions involved in respiration are catabolic reactions that involve the oxidation of one molecule and the reduction of another.

8. Pat Robertson is opposed to abortion in all cases. In other words, he wants women to be treated as second class citizens whose bodies are nothing but baby making machines. So we have to oppose Robertson’s view, because really it’s just a way of making women into slaves.

9. I hate Reggaeton music! I can’t imagine why anyone would listen to it. People should listen to good music. And they blast that Reggaton so loud on the car stereos on my block. It’s annoying!

10. Enrique is a member of the American Communist Party. All members of the American Communist Party are communists. All communists are in favor of overthrowing the U.S. government. All terrorists are in favor of overthrowing the U.S. government. It stands to reason that Enrique is a terrorist.

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2.4.3 Arguments v Explanations This is a subtler distinction. The word, “because,” can be used in both cases. But there is a difference. An argument attempts to prove that something is the case. An explanation, on the other hand, already assumes that that something is the case, but proceeds to explain why it is the case.

Argument: A group of statements that attempt to prove that something is the case by appealing to reasons. Explanation: A group of statements that assume that something is the case and that proceed to explain why.

In an explanation, something is already proven; you just want further information about how it got to be that way. In an argument, you cannot take the proof for granted; you have to give the proof.

1. An explanation tells you why something happened 2. An argument tells you why you should believe something, an argument tries

to persuade you. 3. Arguments have something to prove; explanations do not

Example; Adam stole the money, for three people saw him do it Adam stole the money because he needed it to buy food

2.4.4 Good and Bad arguments

Clearly, we can have valid or very strong arguments that are not convincing because the premises are implausible. So, in determining if an argument is good, then, we need to know more than the way in which the premises relate to the conclusion.

Strong, weak and valid refer only to the relation between premises and conclusion.

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A good argument (and here we’ll be adopting a technical sense of “good argument”) is one that is (1) either valid or strong, (2) with all premises being plausible, and (3) the premises being more plausible than the conclusion.

The last condition requires some explanation:

Begging the question: an argument is said to “beg the question” if the conclusion simply repeats one of the premises, or (less commonly) if any of the premises are less plausible than the conclusion.

The following arguments beg the question:

Of course, God exists. We know this because God wrote the Bible, and God would never lie, and the Bible says that God exists.

Here, the conclusion “God exists,” is more plausible than the premise “God wrote the Bible.” If you accept that God wrote the Bible, you accept not only that God exists but that he wrote a book. Since that sentence contains two conditions (God’s existence, and his authorship of the Bible) it is necessarily less plausible than the conclusion, which contains only one of those conditions.

Here’s another question-begging argument:

Why should I be in charge? I should be in charge because I’m the boss!

If the conclusion is “I should be in charge,” and the premise is “because I’m the boss,” then the premise and the conclusion are essentially saying the same thing: the boss is, by definition, the person in charge. So the question hasn’t been answered, nor the conclusion supported.

We now have the three conditions for a good argument. A bad argument, then, is any argument that fails to meet any one of the three conditions.

Bad arguments fail one or more of the tests for good arguments.

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Exercises

For the following arguments, say if the argument is valid, strong or weak and then say if it is good or bad. If it is bad, say which test it fails.

1. All John Jay students are lawyers. And all lawyers are corrupt. So all John Jay students are corrupt.

2. Ishmael attends a fundamentalist mosque in Brooklyn. Ishmael has repeatedly said that he thinks the U.S. should withdraw all financial support for Israel, and pull all troops out of all Muslim countries. Therefore, Ishmael wants the U.S. government to be replaced by a fundamentalist Muslim government.

3. Historian David Irving claims that the Holocaust, that is, the systematic murder of Jews in Hitler’s Germany, did not take place. But there are thousands of eyewitness reports of the death camps from U.S. and allied soldiers. There are documents from top Nazi officials detailing the orders for the death camps. The remains of the camps still stand. Further, there are hundreds of survivors whose stories cohere and who all report the extermination of Jews and others at the camps. And soldiers and reporters photographed the camps, including photographs of piles of dead, emaciated prisoners and mass graves. So, clearly, David Irving is wrong, and the Holocaust did take place.

4. A group of 6000 college students from across the United States was randomly, and blindly, divided into two equal groups. One received Coldstop anti-cold medicine; the other group received a placebo. Neither group knew which they had received. At the end of the semester it was found, by self-report and nurse follow-up, that 35% of the placebo group had had a cold during the course of the semester, whereas only 4% of the Coldstop group had had a cold. Therefore, Coldstop is effective in preventing colds.

5. UFOs land on the White House lawn all the time. I've totally seen them landing there. And weird space aliens get out of the UFOs and they go into the White House. This happens two or three times a week! Recently, Barack

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Obama signed a bill giving space aliens a fast-track to US citizenship. He gave a speech about how space aliens, “if they exist,” (that's what he said) should be greeted and treated as friends. So obviously space aliens have been meeting with the president.

6. All humans are mammals. And all humans have opposable thumbs. John is a mammal with opposable thumbs. So John must be a human.

7. You should vote for Senator McMahon. She's a former pro-wrestler and she once killed a mugger. She's not afraid of anything. And she's a huge fan of the local football team!

2.5 Deduction, Induction, Validity, Truth, Soundness and Cogency

An argument is said to be deductive if it is claimed that the truth of the premises would guarantee the truth of the conclusion. If in fact the truth of the premises would guarantee the truth of the conclusion, the argument is said to be valid.

In other words: A valid argument is one where it is IMPOSSIBLE for the premises to be true and the conclusion false at the same time.

So: If we argue:John was found with a gun in his hand, running from the apartment where Tom's body was found. Three witnesses heard a gunshot right before they saw John run out. The gun in John's possession matched the ballistics on the bullet pulled from Tom's head. John had written a series of threatening letters to Tom. In prison, John confessed to his cellmate that he had killed Tom. Therefore, John is the murder of Tom.

I have NOT produced a valid argument! Because it is still possible, though unlikely, that John is not the killer. Think of how this could be.

If you can imagine a scenario where all the premises are true and the conclusion is false, no matter how unlikely that scenario is, the argument is not valid.

An argument like the one above is called an inductive argument. That's an argument where the premises are meant to give good reason to believe the

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conclusion, but their truth does not guarantee the truth of the conclusion. If the premises make the conclusion very likely, the argument is said to be strong.

But if we argue:

John is from Mars.Everyone from Mars is the murderer of Tom.Therefore, John is the murderer of Tom.

Then I've produced a valid argument. There is no possible scenario wherein the premises would all be true and the conclusion false. One way to think of this is: imagine you had absolute power. You still couldn't make it so that it was true that

(1) All dogs are mammals and (2) All mammals are animals and simultaneously false that (3) Some dogs are not animals.

There is simply no way for the premises to be true and conclusion false, no matter how will the scenario you dream up. If the conclusion is false, at least one of the premises has to wrong.

Valid arguments are never said to be strong. The word "strong" applies only to inductive arguments.

Notably, the actual truth of the premises is irrelevant when determining if the argument is strong or if it is valid. Strength and validity are only about the relation between premises and conclusion, not about the truth of any of the statements in the argument.

Remember the following definitions, and learn to apply them:

Cogency: If an argument is strong and the premises are true, the argument is said to be cogent.

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Soundness: If an argument is valid and the premises are true, the argument is said to be sound.

Exercises in Validity

Remember: if the argument is valid there is no conceivable way for the premises to be true and the conclusion false. If you can conceive of some way for the premises to be true and the conclusion false, no matter how far-fetched the conception, then the argument is not valid! One way to show that an argument is not valid is to describe a situation in which the premises would be true and the conclusion false at the same time.

Example: Mary and John are married. Mary sees John holding another woman’s hand, and then kissing that woman. John then gets into bed with the other woman, and they continue to kiss. Therefore, John is cheating on Mary.

Not valid: Mary might be watching John in a play where he and the other woman are acting the part of a married couple.

A common mistake in this exercise is to write a description that contradicts one of the premises. So for example, if I said:

All dogs are friendly. John has a dog. So John’s dog is friendly.

And you wrote:

Not valid: Maybe John has an unfriendly dog.

You would be incorrect, because the first premise states that all dogs are friendly. Just because we know that to be false doesn’t mean that the argument is invalid! Validity is not about the truth of the claims in the argument. It is only about whether or not those claims, if they were true, would guarantee the conclusion. So the following are valid arguments:

George Bush is from the planet Krypton. Everyone from the planet Krypton can fly and shoot heat beams from their eyes. So George Bush can fly and shoot heat beams from his eyes.

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Basketballs are made of yarn. Everything that’s made of yarn is flammable. And all flammable things are the emperor of Jupiter. So basketballs are the emperor of Jupiter.

Exercise

1. All people over 6 feet tall are from Mars. Barack Obama and George W. Bush are both over six feet tall. So both Barack Obama and George W. Bush are from mars. Valid or Invalid?

If Invalid, describe how the premises could be true and conclusion false:

2. My friend Don owns a gun shop, and he’s a member of the NRA. Plus, he owns 30 guns. So Don must like guns. Valid or Invalid?

If Invalid, describe how the premises could be true and conclusion false:

3. Yesterday was 17th of May. So today is the 18th of May. Valid or Invalid?If Invalid, describe how the premises could be true and conclusion false:

4. I have five dollars in my pocket, and gumballs cost exactly 25 cents, so I have enough money to buy a gumball. Valid or Invalid?

If Invalid, describe how the premises could be true and conclusion false:

5. Keisha is six feet tall. Lawrence is four feet tall. Lawrence is taller than Jaime. So Keisha is taller than Jaime. Valid or Invalid?

If Invalid, describe how the premises could be true and conclusion false:

6. John gave Frederique one hundred dollars. Frederique then gave John a gram of cocaine. So John bought cocaine from Frederique. Valid or Invalid?

If Invalid, describe how the premises could be true and conclusion false:

7. John and Frederique went to the opera. So John went to the opera. Valid or Invalid?

If Invalid, describe how the premises could be true and conclusion false:

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8. Frederique killed John. So Frederique is a murderer. Valid or Invalid?If Invalid, describe how the premises could be true and conclusion false:

Exercises in Soundness

For the following, decide if the argument is sound or not. If it’s not sound, say why not. Remember, there can be two reasons for an argument to be unsound: it is invalid, or at least one of the premises is false.

1. All dogs are canines. Lassie was a dog. So Lassie was a canine.

2. All cats are felines. So if Felix is a feline, then Felix is a cat.

3. President Obama is the 44th President of the United States. Thus, whoever succeeds him as President will be the 45th President of the United States.

4. All dogs are friendly. Lassie was a dog. So Lassie was friendly.

5. All United States Presidents were born in the United States. Barack Obama is the President of the United States. So Barack Obama was born in the United States.

2.4.2 Strength and Weakness

Inductive arguments are said to be either strong or weak. There’s no absolute cut-off between strength and weakness, but some arguments will be very strong and others very weak, so the distinction is still useful even if it is not precise.

A strong argument is one where, if the premises are true, the conclusion is very likely to be true. A weak argument is one where the conclusion does not follow from the premises (i.e. even if the premises were true, there would still be a good chance that the conclusion could be false.)

Most arguments in courts of law attempt to be strong arguments; they are generally not attempts at valid arguments.

So, the following example (which we saw above as well) is a strong argument.

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John was found with a gun in his hand, running from the apartment where Tom's body was found. Three witnesses heard a gunshot right before they saw John run out. The gun in John's possession matched the ballistics on the bullet pulled from Tom's head. John had written a series of threatening letters to Tom. In prison, John confessed to his cellmate that he had killed Tom. Therefore, John is the murder of Tom.

Given that all the premises were true, it would be very likely that the conclusion would be true.

Importantly, strength has nothing to do with the actual truth of the premises!

A STRONG ARGUMENT NEEDN’T HAVE ANY TRUE PREMISES! ALL THE PREMISES OF A STRONG ARGUMENT CAN BE FALSE!

2.4.4 SummaryA. Truth Versus Logical Strength; Premises and conclusions may be true, or they may be false. Evaluating the truth-value of premises and conclusions is distinct from evaluating the logical strength of arguments. Ryerson University is in Guelph, ON. The RAC is located within Ryerson U.

Therefore, The RAC is located in Guelph, ON. B. Validity and Soundness. Deductive Validity: An argument is deductively valid if and only if it is not possible for the premises to be true and the conclusion false. i.e., if all the premises were true, the conclusion would have to be true too.

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An argument is deductively invalid if and only if it is not deductively valid. A deductively valid argument:

(1) All bachelors are unmarried. (2) Ivan is a bachelor.

Therefore, (3) Ivan is unmarried.

Note: This is a special use of the word ‘valid’ Remember, a valid argument need not have true premises, and it need not have true conclusions: what’s important is the logical relationship between the premise(s) and conclusion(s).

(1) All Americans are ten feet tall. (2) Prof. Hunter is an American.

Therefore, (3) Prof. Hunter is ten feet tall

Two False Premises and False Conclusion.

C. Deductive Soundness: An argument is deductively sound if and only if it is deductively valid and all its premises are true.

Deductive Versus Inductive Arguments

In a deductively valid argument, the truth of the premise(s) guarantees the truth of the conclusion(s). But, not all arguments are deductive:

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D. Inductive Strength: An argument is inductively strong if and only if the conclusion is probably true, given the premises. An argument is inductively weak if and only if it is not inductively strong. E. Inductively Strong Argument:

(1) Quitting smoking usually improves your health. (2) Mary has quit smoking.

Therefore, probably (3) Mary’s health will improve.

Inductively Weak Argument: (1) A few police officers are corrupt. (2) Jim is a police officer.

Therefore, probably, (3) Jim is corrupt.

2.4 Conditional Statements; Necessary and Sufficient Conditions

A conditional statement is an “if…then” statement, or a statement that can be rewritten as an “if…then” without changing its meaning. A conditional statement, all by itself, is generally not an argument (if it is an argument it’s of the type we call “enthymemes,” which is to say arguments that are missing either premises or a conclusion.) Conditionals, however, figure in many arguments, and are centrally important to logic.

The part following the “if” is called the antecedent, and the part following the “then” is called the consequent.

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Sometimes, the “then” is left out. Sometimes the words “when” or “whenever” are used in place of “if.” And sometimes the antecedent, or “if clause,” comes after the consequent, or “then clause.”

Identify the antecedents and consequents of the following conditional statements. If the statement is not in standard “if…then” form, think of how you’d rewrite it to put it in that form, and use that as the basis for identifying the antecedent and consequent.

1. If it rains, I’ll go outside.

2. I’ll give you a dollar if you tell me what mom got me for Christmas.

3. Whenever Keisha comes over I feel sick to my stomach.

4. If you don’t know what time it is then you should buy yourself a watch.

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2.4.1 Necessary and Sufficient Conditions

In a conditional statement, two conditions are given: a necessary and a sufficient condition.

Sufficient Conditions:A is a sufficient condition for B whenever A is all that is needed to make B true, or whenever the occurrence of A is all that is needed for the occurrence of B.

If Fido is a dog, then Fido is a mammal.“Fido is a dog” is all that’s needed to make it true that “Fido is a mammal.” So “Fido is a dog” is a sufficient condition for “Fido is a mammal.” Similarly, “Fluffy is a cat,” “Pokey is a rhinoceros,” “Trunky is an elephant,” and “Ollie is an ocelot” would be sufficient conditions to make each one of them mammals.

If it rains, the sidewalk will be wet.If a dog pees on it, the sidewalk will be wet.If someone spills soda on it, the sidewalk will be wet.If someone sprays a hose on it, the sidewalk will be wet.

In each case, the antecedent expresses a sufficient condition for “the sidewalk will be wet.”

Necessary conditions: B is a necessary condition for A whenever A cannot occur without B also occurring, or whenever A cannot be true without B also being true. So, in all the cases above, the consequent is a necessary condition.

If Fido is a dog, then he is necessarily a mammal.If I spray a hose on it, the sidewalk will necessarily get wet.If John is older than Kevin, and Kevin is older then Lanai, then John is necessarily older than Lanai.

In each case, the word “necessarily” is not needed, because the conditional sentence already asserts the necessity.

For the following, fill in the blanks with “necessary” or “sufficient.”

1. Being a quarterback in the NFL is a ___________ condition for being a football player.

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2. Being a football player is a ___________ condition for being an NFL quarterback.

3. Being able to fly a plane is a ___________ condition for being an airplane pilot.

4. Spraying a hose on a dog is a __________ condition for making the dog's fur wet.

5. Being a guitarist is a _________ condition for being a musician.

6. Being a musician is a ___________ condition for being a guitarist.

7. Firing an unsilenced gun is a ____________ condition for making a loud noise.

8. Being famous is a ____________ condition for being a movie star.

9. Being a movie star is a __________ condition for being famous.

Now, rewrite each of the above as a conditional sentence.

Because necessary conditions are distinct from sufficient conditions, the antecedent and consequent of a conditional statement cannot be reversed if you wish to maintain the truth and meaning of the sentence. In other words, saying:

- Whenever a patient is feeling pain, the pre-occipital lobe of the brain is active.

is not the same as saying:

- Whenever the pre-occipital lobe of the brain is active, the patient is feeling pain.

These cases should make that clear:

If that’s a dog, then it’s a mammal.

If that’s a mammal, then it’s a dog.

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If you have five dollars, you have some money.

If you have some money, you have five dollars.

If you go outside in winter then you’ll feel cold.

If you feel cold, then you’ve gone outside in the winter.

If you find a sentence where the meaning stays (essentially) the same when you’ve reversed antecedent and consequent, then you’ve found a case of what we call a biconditional. The biconditional is usually written as “if, and only if…”

2.5 FURTHER PARTTENS IN BASIC LOGICAL CONCEPTS

2.5.1 HOW CAN WE TELL WHETHER AN ARGUMENT IS DEDUCTIVE OR INDUCTIVE?

We have seen that an argument is deductive if its premises are intended to provide conclusive grounds for the truth of its conclusion, and inductive if its premises are intended to provide merely probable grounds for the truth of its conclusion. But it is not always easy to know what a given speaker or writer intends. For that reason it is sometimes diffi cult to tell whether a particular argument is deductive or inductive. Fortunately, there are four tests that greatly simplify the task of determining whether an argument should be regarded as deductive or inductive:

• the indicator word test• the strict necessity test• the common pattern test• the principle of charity test

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2.5.2 The Indicator Word Test Just as we use indicator words to signal the assertion of premises or conclusions, we use indicator words to signal when our arguments are deductive or inductive. For example, a phrase like “it necessarily follows that” almost always indicates that an argument is deductive. Here are some other common deduction indicator words:

certainly it logically follows thatdefinitely it is logical to conclude thatabsolutely this logically implies thatconclusively this entails that

These are some common induction indicator words:

Probably one would expect that likely it is a good bet that it is plausible to suppose that chances are that it is reasonable to assume that odds are that

The indicator word test is often extremely helpful. Nevertheless, two limitations of the test should be noted. First, many arguments contain no deduction or induction indicator words. Here are two examples:If you call a dog’s tail a leg, how many legs does it have? Answer: Four. Calling a tail a leg doesn’t make it a leg. (Attributed to Abe Lincoln) Pleasure is not the same thing as happiness. The occasional self-destructive behaviour of the rich and famous confirms this far too vividly. (Tom Morris)

Neither of these arguments contains any indicator words that would help us decide whether it is deductive or inductive. For arguments such as these, we must rely on one or more of the other tests discussed in this section. Second, arguers often use indicator words loosely or improperly. For example, it is common to hear speakers use strong phrases like “it must be the case that” and “it is logical to assume that” when the context makes clear that the argument is not intended to be strictly deductive. For these reasons the indicator word test must be used with caution.

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2.5.5 How to Distinguish Deductive from Inductive Arguments

1. If the conclusion follows necessarily from the premises, the

argument should always be treated as deductive.

2. If the conclusion does not follow necessarily from the premises, the

argument should be treated as inductive unless (a) the language or

context of the argument makes clear that the argument is deductive

or (b) the argument has a pattern of reasoning that is

characteristically deductive.

3. If the argument has a pattern of reasoning that is characteristically

deductive, the argument should be treated as deductive unless there

is clear evidence that the argument is intended to be inductive.

4. If the argument has a pattern of reasoning that is characteristically

inductive, the argument should be treated as inductive unless there is

clear evidence that the argument is intended to be deductive.

5. Arguments often contain indicator words—words like probably,

necessarily, and certainly —that provide clues in determining

whether an argument is deductive or inductive. Keep in mind,

however, that indicator words are often used loosely or improperly.

6. If there is significant doubt about whether an argument is deductive

or inductive, always interpret the argument in the way most

favourable to the arguer.

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2.5.6 COMMON PATTERNS OF DEDUCTIVE REASONING

Often, the quickest way to determine whether an argument is deductive or inductive is to note whether it has a pattern of reasoning that is characteristically deductive or inductive. In this section we discuss five common patterns of deductive reasoning:

• hypothetical syllogism• categorical syllogism• argument by elimination• argument based on mathematics• argument from definition

I. Hypothetical Syllogism A syllogism is a three-line argument, that is, an argument that consists of exactly two premises and a conclusion. A hypothetical syllogism is a syllogism that contains at least one hypothetical or conditional (i.e., if-then) premise.

Here are two examples of hypothetical syllogisms:If the Tigers beat the Yankees, then the Tigers will make the playoffs. The Tigers will beat the Yankees. So, the Tigers will make the playoffs.

If I want to keep my financial aid, I’d better study hard. I do want to keep my financial aid. Therefore, I’d better study hard.

Notice that these two arguments each have the same logical pattern or form:If A then B. A. Therefore, B.

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This pattern, as we have seen, is called; modus ponens. Arguments with this pattern consist of one conditional premise, a second premise that asserts as true the antecedent (the if part) of the conditional, and a conclusion that asserts as true the consequent (the then part) of the conditional. Other common varieties of hypothetical syllogisms include

• chain argument• modus tollens (denying the consequent)• denying the antecedent• affirming the consequent

Chain arguments consist of three conditional statements that link together in the following way:If A then B. If B then C. Therefore, if A then C.

Here is an example of a chain argument:If we don’t stop for petrol soon, then we’ll run out of gas. If we run out of petrol, then we’ll be late for the wedding. Therefore, if we don’t stop for petrol soon, we’ll be late for the wedding.

Modus tollens arguments have the following pattern:

If A then B. Not B. Therefore, not A.

Arguments of this pattern are sometimes called “denying the consequent” because they consist of one conditional premise, a second premise that denies (i.e., asserts to be false) the consequent of the conditional, and a conclusion that denies the antecedent of the conditional.

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Here is an example:If we’re in Sacramento, then we’re in California. We’re not in California. Therefore, we’re not in Sacramento.

Modus ponens, chain argument, and modus tollens are all logically reliable patterns of deductive reasoning. That is, any argument that has one of these patterns is absolutely guaranteed to have a true conclusion if the premises are also true. But not all patterns of deductive reasoning are completely reliable in this way. Two patterns that are not logically reliable are denying the antecedent and affirming the consequent.

Denying the antecedent arguments have the following pattern:If A then B. Not A. Therefore, not B.

Here is an example:

If Shakespeare wrote War and Peace, then he’s a great writer. Shakespeare didn’t write War and Peace. Therefore, Shakespeare is not a great writer.

Notice in this example that the premises are true and the conclusion is false. This shows straightaway that the pattern of reasoning of this argument is not logically reliable.

Another faulty pattern of deductive reasoning is affirming the consequent. Its pattern is as follows:

If A then B. B. Therefore, A.

Here is an example:If we’re on Neptune, then we’re in the solar system. We are in the solar system.

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Therefore, we’re on Neptune.

Given that this argument has true premises and a false conclusion, it is clear that affirming the consequent is not a logically reliable pattern of reasoning. Because modus ponens, modus tollens, and chain argument are logically reliable patterns of reasoning, they should always be treated as deductive. Denying the antecedent and affirming the consequent are not logically reliable patterns of reasoning; nevertheless, they should generally be treated as deductive because they have a pattern of reasoning that is characteristically deductive.

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II. Categorical Syllogism Another common pattern of deductive reasoning is categorical syllogism. For present purposes, a categorical syllogism may be defined as a three-line argument in which each statement begins with the word all, some, or no. Here are two examples:All oaks are trees. All trees are plants. So, all oaks are plants. Some Democrats are elected officials. All elected officials are politicians. Therefore, some Democrats are politicians.

Because categorical reasoning like this is such a familiar form of rigorous logical reasoning, such arguments should nearly always be treated as deductive.

III. Argument by Elimination An argument by elimination seeks to logically rule out various possibilities until only a single possibility remains. Here are two examples:Either Joe walked to the library or he drove. But Joe didn’t drive to the library. Therefore, Joe walked to the library.

Either Dutch committed the murder, or Jack committed the murder, or Celia committed the murder. If Dutch or Jack committed the murder, then the weapon was a rope. The weapon was not a rope. So, neither Dutch nor Jack committed the murder. Therefore, Celia committed the murder.

Because the aim of such arguments is to logically exclude every possible outcome except one, such arguments are always deductive.

IV. Argument Based on Mathematics Mathematics is a model of logical, step-by-step reasoning. Mathematicians don’t claim that their conclusions are merely likely or probable. They claim to prove their conclusions on the basis of precise mathematical concepts and

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reasoning. In an argument based on mathematics, the conclusion is claimed to depend largely or entirely on some mathematical calculation or measurement (perhaps in conjunction with one or more nonmathematical premises).

Here are two examples:Eight is greater than four. Four is greater than two. Therefore, eight is greater than two.

Light travels at a rate of 186,000 miles per second. The sun is more than 93 million miles distant from the earth. Therefore, it takes more than eight minutes for the sun’s light to reach the earth.

Because mathematical arguments are generally models of precise logical reasoning, arguments based on mathematics are usually best treated as deductive. Arguments based on mathematics can be inductive, however, as this example shows:My blind uncle told me that there were 8 men, 6 women, and 12 kids at the party. By simple addition, therefore, it follows that there were 26 people at the party.

Here, the conclusion clearly does not follow from the premise because it is possible for the premise to be true and the conclusion false. (Maybe my blind uncle miscounted, for example.) For that reason, the argument is best treated as inductive.

V. Argument from Definition In an argument from definition, the conclusion is presented as being “true by definition,” that is, as following simply by definition from some key word or phrase used in the argument. Here are two examples:Janelle is a cardiologist. Therefore, Janelle is a doctor. Bertha is an aunt. It follows that she is a woman.

Because a statement that follows by definition is necessarily true if the relevant definition is true, arguments from definition are always deductive.

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Our discussion of common patterns of deductive reasoning can be summarized as follows:

- Arguments by elimination and arguments from definition should always be treated as deductive.

- Logically reliable hypothetical syllogisms, categorical syllogisms, and arguments based on mathematics should always be treated as deductive.

- Logically unreliable hypothetical syllogisms, categorical syllogisms, and arguments based on mathematics should be treated as deductive unless there is clear evidence that they are intended to be inductive.

2.5.7 COMMON PATTERNS OF INDUCTIVE REASONING

In this section we look at six common patterns of inductive reasoning:

• inductive generalization• predictive argument• argument from authority• causal argument• statistical argument• argument from analogy

I. Inductive Generalization

An inductive generalization is an argument in which a generalization is claimed to be probably true based on information about some members of a particular class. Here are two examples:All dinosaur bones so far discovered have been more than sixty-five million years old. Therefore, probably all dinosaur bones are more than sixty-five million years old.

Six months ago I met a farmer from Iowa, and he was friendly. Four months ago, I met an insurance salesman from Iowa, and he was friendly. Two months ago, I met a dentist from Iowa, and she was friendly.

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I guess most people from Iowa are friendly.

Because all inductive generalizations claim that their conclusions are probable rather than certain, such arguments are always inductive.

II. Predictive Argument A prediction is a statement about what may or will happen in the future. In a predictive argument, a prediction is defended with reasons. Predictive arguments are among the most common patterns of inductive reasoning. Here are two examples:It has rained in Vancouver every February since weather records have been kept. Therefore, it will probably rain in Vancouver next February.

Most U.S. presidents have been tall. Therefore, probably the next U.S. president will be tall.

Because nothing in the future (including death and taxes) is absolutely certain, arguments containing predictions are usually inductive. It should be noted, however, that predictions can be argued for deductively. For e xample:If Amy comes to the party, Ted will come to the party. Amy will come to the party. Therefore, Ted will come to the party.

Even though this argument contains a prediction, it is clearly deductive because the conclusion must be true if the premises are true.

III. Argument from Authority An argument from authority asserts a claim and then supports that claim by citing some presumed authority or witness who has said that the claim is true. Here are three examples:More Americans die of skin cancer each year than die in car accidents. How do I know? My doctor told me.

The Encyclopaedia Britannica says that parts of Virginia are farther west than Detroit.

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In general, the Encyclopaedia Britannica is a highly reliable source of information. Therefore, it’s probably true that parts of Virginia are farther west than Detroit.

There are bears in these woods. My neighbour Frank said he saw one last week.

Because we can never be absolutely certain that a presumed authority or witness is accurate or reliable, arguments from authority should normally be treated as inductive. Arguments from authority are sometimes deductive, however. For example:Whatever the Bible teaches is true. The Bible teaches that we should love our neighbours. Therefore, we should love our neighbours.

Because the conclusion of this argument follows necessarily from the premises, the argument is deductive.

IV. Causal Argument A causal argument asserts or denies that something is the cause of something else. Here are three examples:I can’t log on. The network must be down.

Rashid isn’t allergic to peanuts. I saw him eat a bag of peanuts on the flight from Dallas.

As we shall see THAT we can rarely, if ever, be 100 percent certain that one thing causes, or does not cause, something else. For that reason causal arguments are usually best treated as inductive. It cannot be assumed, however, that causal arguments are always inductive.

The following causal argument, for example, is clearly deductive:Whenever iron is exposed to oxygen, it rusts. This iron pipe has been exposed to oxygen. Therefore, it will rust.

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V. Statistical Argument

A statistical argument rests on statistical evidence—that is, evidence that some percentage of some group or class has some particular characteristic. Here are two examples:Eighty-three percent of St. Stephen’s students are Episcopalian. Beatrice is a St. Stephen’s student. So, Beatrice is probably Episcopalian.

Doctor to patient: Studies show that condoms have an annual failure rate of 2 to 3 percent, even if they are used consistently and correctly. So, you should not assume that condoms will provide complete protection from the risk of pregnancy or sexually transmitted diseases.

Because statistical evidence is generally used to support claims that are presented as probable rather than certain, statistical arguments are usually inductive.

It should be noted, however, that statistical evidence can be used in deductive reasoning. For example:If 65 percent of likely voters polled support Senator Beltway, then Senator Beltway will win in a landslide. Sixty-five percent of likely voters polled do support Senator Beltway. Therefore, Senator Beltway will win in a landslide.

VI. Argument from Analogy An analogy is a comparison of two or more things that are claimed to be alike in some relevant respect. Here are two examples of analogies:Habits are like a cable. We weave a strand of it every day and soon it cannot be broken. (Horace Mann)

As man casts off worn-out garments and puts on others that are new, similarly the embodied soul, casting off worn-out bodies, enters into others, which are new. (Bhagavad-Gita)

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In an argument from analogy, the conclusion is claimed to depend on an analogy (i.e., a comparison or similarity) between two or more things.

Here are two examples:Hershey Park has a thrilling roller-coaster ride. Dorney Park, like Hershey Park, is a great amusement park. Therefore, probably Dorney Park also has a thrilling roller-coaster ride.

Bill is a graduate of Central University, and he is bright, energetic, and dependable. Mary is a graduate of Central University, and she is bright, energetic, and dependable. Paula is a graduate of Central University. Therefore, most likely, Paula is bright, energetic, and dependable, too.

Note the basic logical pattern of these arguments:These things are similar in such-and-such ways. Therefore, they’re probably similar in some further way.

Because the conclusions of arguments of this pattern are claimed to follow only probably from the premises, such arguments are clearly inductive. Not all analogical arguments are inductive, however. For example:

1. Automobiles cause thousands of deaths each year and produce noxious and offensive fumes.

2. Smoking causes thousands of deaths each year and produces noxious and offensive fumes.

3. Thus, if smoking is heavily regulated, automobiles should also be heavily regulated.

4. But automobiles shouldn’t be heavily regulated.5. Therefore, smoking shouldn’t be heavily regulated, either.

This is an analogical argument because the main conclusion, statement 5, is claimed to depend on an analogy between automobiles and smoking.

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Nevertheless, the argument is deductive because it would be logically inconsistent to assert all the premises and deny the conclusion. Our discussion of common patterns of inductive reasoning can be summarized as follows:

Inductive generalizations, by definition, are always inductive.Predictive arguments, arguments from authority, causal arguments, statistical arguments, and arguments from analogy are generally, but not always, inductive. It takes practice to be able to recognize the patterns of deductive and inductive reasoning that we have discussed, but it is important to be able to do so because such patterns often provide the best clue available as to whether an argument is deductive or inductive.

2.6 DEDUCTIVE VALIDITY

We have seen that all deductive arguments claim, implicitly or explicitly, that their conclusions follow necessarily from their premises. A logically reliable deductive argument is one in which the conclusion really does follow necessarily from the premises. In logic, a logically reliable deductive argument is called a valid deductive argument.

More formally, a valid deductive argument is an argument in which it is impossible for all the premises to be true and the conclusion false. Put another way, a valid deductive argument (or valid argument for short) is an argument in which these conditions apply:

If the premises are true, the conclusion must be true.The conclusion follows necessarily from the premises.The premises provide logically conclusive grounds for the truth of the conclusion.It is logically inconsistent to assert all the premises as true and deny the conclusion.

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In everyday language, valid often means “good” or “true.” We say, for instance, that a person makes a “valid point” or offers a “valid suggestion.” In logic, however, valid never means simply “good” or “true.” It is always used in the precise technical sense indicated above.

It is not necessary to know whether an argument’s premises or conclusion are true to know whether the argument is valid. In fact, some valid arguments have obviously false premises and a false conclusion. For example:All squares are circles. All circles are triangles. Therefore, all squares are triangles.

Some valid arguments have false premises and a true conclusion. For example:All fruits are vegetables. Spinach is a fruit. Therefore, spinach is a vegetable.

And some valid arguments have true premises and a true conclusion. For example:If you’re reading this, you are alive. You are reading this. Therefore, you are alive.There is, however, one combination of truth or falsity that no valid argument can have. No valid argument can have all true premises and a false conclusion. This important truth follows from the very definition of a valid argument. Because a valid argument, by definition, is an argument in which the conclusion must be true if the premises are true, no valid argument can have all true premises and a false conclusion.

A deductive argument in which the conclusion does not follow necessarily from the premises is said to be an invalid deductive argument.

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Here are examples:All dogs are animals. Lassie is an animal. Therefore, Lassie is a dog.

If I’m a monkey’s uncle, then I’m a primate. I’m not a monkey’s uncle. So, I’m not a primate.

Each of these arguments is invalid. The first argument has true premises and a true conclusion. The second argument has true premises and a false conclusion. The third argument has false premises and a true conclusion. And the fourth argument has false premises and a false conclusion.

2.6.8 INDUCTIVE STRENGTH

Inductive arguments, like deductive arguments, can be well reasoned or poorly reasoned. A well-reasoned inductive argument is called a strong inductive argument. More precisely, in a strong inductive argument, the conclusion follows probably from the premises. Put otherwise, a strong inductive argument is an argument in which the following conditions apply: If the premises are true, the conclusion is probably true. The premises provide probable, but not logically conclusive, grounds for the truth of the conclusion.The premises, if true, make the conclusion likely.

Here are two examples of strong inductive arguments:Most college students own MP3 players. Andy is a college student. So, Andy probably owns an MP3 player.

All recent U.S. presidents have been college graduates. Thus, it is likely that the next U.S. president will be a college graduate.

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An inductive argument that is not strong is said to be weak. In a weak inductive argument , the conclusion does not follow probably from the premises. In other words, a weak argument is an inductive argument in which the premises, even if they are assumed to be true, do not make the conclusion probable.

Here are two examples of inductively weak arguments:All previous popes have been men. Therefore, probably the next pope will be a woman.

Fifty-five percent of students at East Laredo State University are Hispanic. Li Fang Wang, owner of Wang’s Chinese Restaurant, is a student at East Laredo State University. Therefore, Li Fang Wang is probably Hispanic.

Because the conclusions of these arguments are not probably true even if we assume that the premises are true, the arguments are weak. Like deductively valid arguments, inductively strong arguments can have various combinations of truth or falsity in the premises and conclusion. Some strong arguments have false premises and a probably false conclusion.

For example:All previous U.S. vice presidents have been women. Therefore, it is likely that the next U.S. vice president will be a woman.

Some inductively strong arguments have false premises and a probably true conclusion. For example:Every previous U.S. president has been clean-shaven. So, the next U.S. president probably will be clean-shaven.

And some inductively strong arguments have true premises and a probably true conclusion. For example:No previous Ghanaian president has been a native Accra. So, the next U.S. president probably will not be a Ga.

SUMMARY

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1. All arguments are either deductive or inductive. In a deductive argument,

the conclusion is claimed to follow necessarily from the premises. In an inductive argument, the conclusion is claimed to follow only probably from the premises.

2. In deciding whether an argument is deductive or inductive, one should apply four simple tests. The indicator word test asks, Are there any indicator words—words such as probably, necessarily, and likely —that signal whether the argument is intended to be deductive or inductive? The strict necessity test asks, Does the conclusion follow with strict necessity from the premises? The common pattern test asks, Does the argument have a pattern that is characteristically deductive or inductive? The principle of charity test urges us to treat doubtful arguments in whatever way is most favourable to the arguer.

3. We looked at five common patterns of deductive reasoning. A hypothetical syllogism is a three-line argument that contains at least one conditional (if-then) statement. A categorical syllogism is a three-line deductive argument in which each line in the argument begins with all, some, or no. An argument by elimination seeks to logically rule out various possibilities until only a single possibility remains. In an argument based on mathematics, the conclusion is claimed to depend largely or entirely on some mathematical calculation or measurement (perhaps in conjunction with one or more nonmathematical premises). In an argument from definition, the conclusion is presented as being true by definition.

4. We studied six common patterns of inductive reasoning. An inductive generalization is an argument in which a generalization is claimed to be likely on the basis of information about some members of a particular class. In a predictive argument, a prediction is defended with reasons. An argument from authority asserts that a claim is true and then supports that claim by alleging that some presumed authority or witness has said that the claim is true. A causal argument asserts or denies that something is the cause of something else. A statistical argument rests on statistical evidence—that is, evidence that some percentage of some group has some particular characteristic. In an argument from analogy, the conclusion is claimed to depend on an analogy (i.e., a comparison or similarity) between two or more things.

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5. Deductive arguments are either valid or invalid. In a valid deductive argument, the conclusion follows necessarily from the premises. In other words, it is an argument in which it is impossible for all the premises to be true and the conclusion false. In an invalid deductive argument, the conclusion does not follow necessarily from the premises.

6. A sound deductive argument both is valid and has all true premises. An unsound deductive argument either is invalid or has at least one false premise, or both.

7. Inductive arguments are either strong or weak. In a strong inductive argument, the conclusion follows probably from the premises. In other words, it is an inductive argument in which, if the premises are (or were) true, the conclusion would probably be true. In a weak inductive argument, the conclusion does not follow probably from the premises.

8. A cogent argument is an inductive argument that both is strong and has all true premises. An uncogent argument is an inductive argument that either is weak or has at least one false premise, or both.

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3.0 The Environment of Critical Thinking:

3.1 Impediments to Critical Thinking

Recall our first definition: Critical thinking is the systematic evaluation or formulation of

beliefs or statements by rational standards.

Common impediments to critical thinking:

Category 1: hindrances that arise because of how we think.

Category 2: hindrances that occur because of what we think.

3.1.1 Category 1 Impediments to Critical Thinking

(a) Self-Interested thinking: accepting a claim solely on the grounds that it advances, or

coincides with, our interests.

Overcoming self-interested thinking:

Watch out when things get very personal.

Be alert to ways that critical thinking can be undermined (ex: wishful thinking).

Ensure that nothing has been left out:

Avoid selective attention.

Look for opposing evidence.

(b) Group Thinking:

Peer pressure

Fallacy: an argument form that is both common and defective.

Fallacy of appeal to popularity

Fallacy of appeal to common practice

Fallacy of appeal to tradition

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Genetic fallacy

Stereotyping: drawing conclusions about people or groups without sufficient reasons.

3.1.2 Category 2 Impediments to Critical Thinking.

Hindrances that occur because of our views about truth and knowledge.

Subjective Relativism.

Social Relativism.

Skepticism.

If you do not believe there is an objective truth, than you are a relativist.

Relativism: the view that intentions have a truth-value, but that what this is depends upon

(i.e. is relative to) some person or social group.

(i) Subjective Relativism

The view that the truth-value of a proposition depends solely upon (is relative to) what

some subject believes. “that’s true for you “ “that’s my truth” Objections:

(a) This is unlikely: consider the jar of jelly beans

(b) This view would make us (Infallible-> meaning you believe you can’t make an error)

(c) This view is self-defeating (i.e. if it’s true, then it is an example of a truth that

is not relative).

Subjective relativist is saying there is no absolute truth.

(ii) Social Relativism

The view that the truth-value of a proposition depends solely upon (is relative to) societies.

It is talking about something broader.

Why might someone hold this view?

2

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Objections:

(a) Implausible

(b) Intolerant views

(c) Would make societies infallible (infallible means you believe that you cannot make an

error.) (c) Self-defeating.

Philosophical Skepticism:

o The view that propositions have truth-values, but that we know what very few, or

none, of them are.

o (In other words, we know a lot less than we think, or nothing at all.)

Why Hold this View?

(a) Dream Hypothesis

(b) Evil Genius Hypothesis

e.g. Machine hypothesis

Consider the following argument for skepticism:

(1) Unless I am completely certain that I am not being deceived by an evil genius, my beliefs lack justification (they do not count as knowledge).

(2) I am not completely certain that I am not being deceived by an evil genius. Therefore,

(3) My beliefs lack justification (they do not count as knowledge).

Objection:

Requiring absolute certainty for a belief to count as knowledge is asking too much.

Each category 2 impediment to critical thinking denies something about truth or knowledge: Relativism- subjective

Relativisim-

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4.0 Reasons for Belief and Doubt:

When Claims Conflict Experts and Evidence Personal Experience Fooling ourselves 4.1 Reasons for Belief and Doubt If we care whether our beliefs are true or reliable, then we must care about the reasons for accepting those beliefs. - When Claims Conflict

When two claims conflict, they simply cannot both be true If a new claim conflicts with other claims we have good reason to accept, we have good grounds for doubting the new claim. With conflicting claims, you are not justified in believing either one of them until you resolve the conflict.

Two types of conflict: Two statements can be “inconsistent”- I.E. can’t both be true, but could both be false. E.G. E.g. “today is Monday” and “today is Wednesday” are inconsistent

Two statements can be contradictories- I.e. can’t both be true, but(also) can’t both be false. E.g. “there is a video of Rob Ford” and “there is not a video of Rob Ford” are both Contradictories.

Conflict with Background information Sometimes rather than two conflicting claims we see a conflict between a claim and your “background information.”

“background information’ includes: Facts about everyday things E.g. The sky is blue - Beliefs based on very good evidence E.g. Cigarettes aren’t good for you - Justified claims that we would regard as common sense or common knowledge E.g. If you study, then you will do better on the quiz. Example “some babies can bench press 500 pounds You are not going to be able to accept this claim because it conflicts with an enormous number of your background beliefs about physiology, gravity, and weight lifiting.

4

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The more background information the claim conflicts with the more reason we have to doubt it. But, it is always possible; of course, that a conflicting claim is true and some of our background information is unfounded.

4.2 Beliefs and Evidence We should proportion our belief to the evidence. Our degree of belief should vary according to the evidence. The more evidence a claim has in favour, the stronger our belief in it should be. It is not reasonable to believe a claim when there is no good reason for doing so Believing shouldn’t be your default setting. 4.3 Experts and Evidence When an unsupported claim doesn’t conflict with what we already know, we are often justified in believing it because it comes from experts. If an expert makes a claim then we are more justified in believing it, even if no evidence is given So long as it doesn’t conflict with background information

What is an expert? Expert defined is someone who has more knowledge. Someone who is more knowledgeable in particular subjects than other people. What good is an expert? In their specialty areas, experts are more likely to be right because: - They have access to more information on the subject - They are better at judging that information than we are.- This is primarily because of their greater experience and practice In a complex world people must rely on experts You can’t be a doctor and lawyer and mechanic… BUT good critical thinkers are careful about expert opinion. When to doubt an expert If a claim conflicts with expert opinion, we have good reason to doubt it Example: the earth is about 10,000 year’s old When experts disagree over a claim we have good reason to withhold judgment. Have you found the right expert? When a claim comes from someone deemed to be an expert who in fact is not an expert we commit the fallacy known as appear to authority Here is one of the two ways appeal the authority can happen:

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- First just because someone is an expert in one field he or she is not necessarily an expert in another

- The second way appeal to authority can happen is that. We may fall into a fallacious appeal to authority by regarding a non-expert as an expert Movie stars, acts, and famous athletes.

To be considered an expert: - Someone must have shown that he or she can assess relevant evidence and arguments

and arrive at well supported conclusions in a particular field

A few indicators to consider someone an expert are - Amount of education and training - Experience in making reliable judgments - Professional Experience

4.3 Personal Experience - We accept a great many claims because they are based on personal experiences- our own or someone else’s - But can you trust personal experience to reveal the truth? It is reasonable to accept the evidence provided by personal experience only if there’s no good reason to doubt it. For examples - If we seem to see a cat on the mat under good viewing conditions, then we’re justified

in believing that there’s a cat on the mat But sometimes our attention is flawed. Factors that can give us a good reason to doubt the reliability of personal experience - Impairment - Expectation - Innum

eracy

Impairment If our perceptual powers are somehow impaired, we have reason to doubt them The following are reasons to doubt the trustworthiness… Expectation We often perceive exactly what we expect, regardless of whether there’s really anything to detect. Innumeracy Another common error is the misjudging of coincidences.

6

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Another error is to think that previous events can affect the probabilities in the random event at hand E.g. The coin has turned up heads seven times in a row so it’s more likely that it will turn up tails the next flip.This is example of Gamblers Fallacy The lessons here is not that we should mistrust all judgment about probabilities but rather that. Fooling ourselves We too often fail to give evidence its due We Ignore evidence Deny evidence The most common and most serious mistakes are:- Resisting contrary evidence - Looking only for confirming evidence - Preferring available evidence - Resisting contrary evidence - We resist evidence that flies in the face of our cherished beliefs This can be psychologically comforting but it can prevent any further search for knowledge Often you will see evidence you want to see and be blind to what we don’t want to see. Looking only for confirming evidence We often seek out and use only confirming evidence. This is known as confirming bias The result we can end up accepting a claim that is now true Remember when we evaluate claims we should look for disconfirming and conforming evidence.

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5.0 Logical Structure:

Why worry about Logical Structure? Comprehension: Helps us to better see the underlying forms of arguments Positive evaluation: Helps us to readily spot (and create) valid arguments Negative Evaluation: Helps us to readily spot (and avoid creating )Invalid arguments Some Terminology: Simple Statement: Contains no other statement as a component part. (We represent it with a letter, like “P”.) Complex Statement: Contains at least one other statement as a component part. Logical Operator: Special expressions which work to combine simple statements into complex ones.

Examples:

Simple statements: Alice is happy (A)

Jim is sad (J)

Logical Operators: 1) Conjunction: Alice is happy AND Jim is sad A & J

[Exercise: When is this statement false?]

2) Negation: Alice is not happy. not-A ~A

[Exercise: When is this statement false?] 3) Disjunction: Alice is happy OR Jim is sad A or J A v J [Exercise: When is this statement false?] (4) Conditional: IF Alice is happy, THEN Jim is sad. If A then J

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A J

“antecedent” “consequent”

“” is the implication operator [Exercise: When is this statement false?] As soon as you see a antecedent is false the conditional MUST be true.. ONLY time conditional is true when consequent is false. Spotting Logical Operators Just like premise- indicators logical operators are not always explicitly present in a text. (a) Conjunctions Paul Martin is a prime minister now, but Stephen harper will be soon The lecture was poorly- presented even though the topic was interesting Other conjuct words:

however’, ‘although’, ‘nonetheless’, ‘moreover’.

(2) Negations Other expressions include: ‘it’s not true that’; ‘it’s false that’; ‘it’s not the case that’.

(3) Disjunctions English: ‘exclusive’ sense. “A v B, and not both.” Logic: ‘inclusive’ sense. “Sam will get a sunburn unless she applies lotion.” “unless” = “or”

(4) Conditionals “Since your lease expired the landlord is free to raise the rent” “Being a teenager means you have lots of problems” “Anyone who likes logic is a fool” “The truth of evolution implies the falsity of the Bible” “Whenever Lebowski drinks coffee, he gets antsy”

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5.2 Logical Structure (Summary)

(1) Comprehension: Helps us to better see the underlying forms of arguments

(2) Positive evaluation: Helps us to readily spot (and create) valid arguments

(3) Negative Evaluation: Helps us to readily spot (and avoid creating) Invalid arguments

Some Terminology:

Simple Statement:

Contains no other statement as a component part. (We represent it with a letter, like “P”.)

Complex Statement:

Contains at least one other statement as a component part.

Logical Operator:

Special expressions which work to combine simple statements into complex ones.

Examples:

Simple statements: Alice is happy (A)

Jim is sad (J)

Logical Operators:

(1) Conjunction: Alice is happy AND Jim is sad

A & J

[Exercise: When is this statement false?]

(2) Negation: Alice is not happy.

not-A ~A

[Exercise: When is this statement false?]

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3) Disjunction: Alice is happy OR Jim is sad

A or J

A v J

[Exercise: When is this statement false?]

(4) Conditional: IF Alice is happy, THEN Jim is sad.

If A then J

A J

“antecedent” “consequent”

“” is the implication operator

[Exercise: When is this statement false?]

As soon as you see a antecedent is false the conditional MUST be true..

ONLY time conditional is true when consequent is false.

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SECTION B

Unit 5 Generalising

A generalization, as that term is used in critical thinking, is a statement that attributes some characteristic to all or most members of a given class. Here are some examples of generalizations:All wild grizzly bears in the United States live west of the Mississippi River. Most college students work at least part-time. Men are so unromantic!

In this unit we start examining closely a particular kind of judgement, namely Generalisation.

Consider this example:

Brian manages a small architectural firm, which relies heavily on broadband internet for sharing files with clients and construction partners. Brian recently decided to switch from Telstra to PIG, a low-cost broadband provider. One day, a month after switching, the firm’s internet connection went down for almost an hour. Brian decided to switch back to Telstra, paying a hefty cancellation fee to PIG. When asked why, Brian said that PIG was too unreliable; Telstra had only gone down twice in the prior year.

Perhaps without realising it, Brian has generalised from PIG’s performance in the first month to PIG’s performance overall:

Generalisation is very frequent in business, as in other areas of life.

In every generalisation, the Conclusion is a claim about a whole group, or what is technically called the Population, and the Reason is a claim about a sub-group, or referred to as a Sample. In other generalisations all have the following form:

These terms should be familiar from one of the most well-known forms of generalisation, namely opinion polling. In a national opinion poll such as Newspoll, the Population is, quite literally, the entire population of Australia, and the sample is the random selection of around 1000 people whose dinner gets rudely interrupted by a question-asking robot.

In business generalisations, what the Sample and Population are may not be quite so obvious. In Brian’s case, the Sample is PIG’s performance in the first month, and the Population is PIGs performance in all months.

Conclusion: PIG was relatively unreliable in general.

Reason: PIG was relatively unreliable this month.

Conclusion: The same, or similar, claim about the population

Reason: A claim about the sample

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You might be thinking that Brian was a bit hasty in concluding that PIG is always unreliable. Perhaps PIG is just as reliable as Telstra; the fact that it happened to go down in the first month was just a bit of bad luck.

5.1 Good Generalisation There is a fundamental principle of good generalisation: the Sample should be similar to the Population in all relevant respects. Or, to use the technical term, we say that the Sample should be Representative of the population.

Put another way, every generalisation involves a Bridging Assumption that the Sample is Representative of the Population:

When generalisations go wrong, it is typically because the Sample is not Representative of the Population. This usually happens in one or both of two ways:

• The Sample is too small, allowing it to differ from the Population due to random variation • The Sample differs in some important way from the Population, usually because of the way it was chosen.

5.2 Pitfall: Small samples In the example above, Brian made a broad generalisation about PIG from quite a small experience of its performance. The generalisation is quite likely to be wrong.

Here is another simple example:

A government set up a program to help the long-term unemployed work, called ReStart. This program provided funding to subsidize the cost of hiring somebody who had been unemployed for over a year. Hastie Pty Ltd, a struggling landscape gardening business, took advantage of ReStart to hire two labourers, including Mary, who was going back to work now that her children were school age, and Joe, who had been out of work since leaving prison five years ago. A few months later, Joe disappeared taking some valuable equipment with him. Hastie’s manager Mr. Pastie decided that unemployed people are a “bad bet” and that government programs are more trouble than they are worth.

2

Reason A claim about the sample

Conclusion The same, or similar, claim about the population

Bridging Assumption The sample is representative of (relevantly similar to) the population.

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Again, this looks like a rash generalisation. In this case the Sample is the two long-term unemployed hired by Hastie under the ReStart program. The Population is all long-term unemployed people they could potentially hire. There are thousands of people in the Population. Clearly, there’s a good chance the tiny sample, consisting of just Mary and Joe, differs in important respects from the Population.

5.3 Generalisation and Statistics When is a Sample large enough? Unfortunately, there is no simple general answer.1 There are certainly technical statistical methods for addressing this, but these require specialist expertise. The advanced critical thinker will be proficient in these methods, but realistically most people will not be so fortunate.

In most cases, common sense will be only guide you have to whether a Sample is too small. The most important thing is to consider the issue, i.e. to use this critical thinking tool:

TOOL: CHECK SAMPLE SIZE Whenever you are making, or evaluating, a generalisation:

1. Diagram the inference. 2. Identify the Sample and the Population, and how large the Sample is in relation to the Population. 3. Use common sense to assess whether the sample is large enough to be representative of (relevantly similar to) the population. Put another way, assess whether chance alone would make it quite likely that the Sample differs from the Population in some important respect. 4. Be aware that you may need to apply more technical tools, or to call in expert assistance.

To go beyond using this simple and useful tool, you should consider

• taking subjects in statistics and research methods • Reading good popular introductions to statistics such as Naked Statistics: Stripping the Dread from Data.

5.4 Summary

1. A Generalisation is a judgement that a claim about all members of a group (Population) is true or probable based on a claim about a sub-group (Sample). 2. A common problem is generalising from a Sample which is Representative of (relevantly similar to) the Population. 3. Use the CHECK SAMPLE SIZE tool to avoid the pitfall of generalising from a sample so small that it is likely to be unrepresentative due to random variation.

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Unit 6 Anecdotal Arguments

In this unit we continue to consider Generalisations, focusing on another common pitfall.

6.1 Pitfall: Anecdote(s) The smallest sample you can have is just a single case. If you tell an interesting story about this case, it is called an Anecdote. Thus, imagine Hastie’s owner arguing as follows:

We tried the ReStart program. We hired this unemployed guy called Joe. He was real trouble. After a few months he just took off, taking our trimmer with him. That’s the last time we’ll ever try to get business assistance from the government.

You can see how ridiculous it would be write off all government programs just because of this one bad experience. In general, anecdotal arguments are very unreliable. Single anecdotes provide little if any support for generalisations.

This is obvious in simple examples like the one above. However, it is very easy to fall for anecdotal arguments in real-life situations when you are not on guard, partly because anecdotes are often quite vivid, interesting and persuasive.

6.2 A business example Here is a real business example. In his recent book Obliquity, the eminent economist John Kay argued that the path to great profits is oblique, i.e. not direct. Instead of focusing on shareholder value, companies should focus on other goals such as making the world a better place. If they do this well, then shareholder value will naturally follow.

To make his point, Kay describes the case of the British chemical company ICI. When it was focused on “the innovative and responsible application of chemistry and related science” it was very successful commercially. It then changed its focus to the direct pursuit of shareholder value. From there it went rapidly downhill, ceasing to exist in 2007.

Kay is offering the following anecdotal argument:

However the case of ICI, interesting as it may be, cannot alone establish such a broad conclusion.

Perhaps realising this, Kay continues with further anecdotes along the same lines, describing companies such as Boeing, Merck and Johnson & Johnson. Each of these cases individually is just another anecdote. Even when combined, they constitute just a tiny sample of the population of all 6—2

businesses. To properly support the conclusion, Kay would need to show results from a much larger and more systematic sample.

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There is a famous saying: “the plural of anecdote is not data”. Telling one Anecdote after another does not result in a decent Sample. (Unless you tell a LOT of anecdotes, in which case most people will have stopped listening anyway.)

6.3 Tool: Avoiding Anecdotal Arguments TOOL: AVOID ANECDOTAL ARGUMENTS

1. Recognise when an anecdote is being provided. 2. Ask whether a general claim is also being made. 3. Ask: is the anecdote being used as an argument for the general claim? Are you inferring, or being invited to infer, from the anecdote to the truth of the general claim? 4. If so, reject the argument (though the conclusion may still be true). Be aware that the anecdote may have made the general claim more plausible to you than it really should be.

6.4 When anecdotes are OK Anecdotes are not always bad. They have at least two valid uses in relation to generalisations.

1. Illustrating. They can be used to illuminate a generalisation. If Kay (see above) had provided good independent reason to believe that the path to shareholder value is always indirect, then the story of ICI might provide a great example illustrating how the generalisation applies in a particular case.

2. Refuting. While you cannot prove a generalisation with an anecdote, you might be able to refute one (i.e, prove it false). Suppose somebody was arguing that all car companies sell into a global market. A single anecdote about a small company making and selling cars within one country (e.g. in Cuba) could – if true - refute the generalisation.

6.5 Summary

1. An Anecdotal Argument is essentially a Generalisation based on the smallest possible sample, a single case.

2. Because anecdotes can be interesting and persuasive, generalising based on anecdotes is a common pitfall.

3. Use AVOID ANECDOTAL ARGUMENTS to avoid accepting a general claim on the basis of one or two compelling cases (anecdotes).

4. However, bear in mind that anecdotes to have valid uses, i.e. illustrating and refuting.

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Unit 7 Biased Samples

This unit is the third and last one to focus on Generalisations.

7.1 Pitfall: Biased samples Ever heard of US President Landon? Probably not, because there never was one.

Instead, in the 1936 election, there was a Republican contender for the US presidency, called Alf Landon. In the lead up to the election that year, Landon was the strong frontrunner in the most important opinion poll of the time, run by the prestigious magazine Literary Digest. Yet on election day, the Democrat Franklin D Roosevelt, instigator of the New Deal, was brought back in a landslide.

How did the Literary Digest poll manage to be so wrong? They had drawn their samples from two kinds of lists: phone books, and vehicle registrations. At that time, both telephones and cars tended to be owned by wealthier people, who tended to vote Republican. So the Literary Digest sample preferred Landon, even while the population at large was preferring Roosevelt.

This illustrates a common pitfall in generalisation: having a Biased Sample. This means that the sample is, in some systematic and relevant way, different from the population. This is usually due to the way the sample was selected – hence the term Selection Bias, and the related term Survivorship Bias.

Note that the pitfall of Biased Sample is conceptually different to the pitfall of Small Sample. As the above example shows, a Sample can be systematically biased even if it is very large. Conversely, a Sample can be selected in an unbiased way, but be so small that it differs from the Population due to random variation.

That said, a Generalisation can be based on a Sample that is both too small, and biased.

TOOL: CHECK FOR BIASED SAMPLE Whenever you are making, or evaluating, a generalisation:

1. Diagram the inference. 2. Identify the Sample and the Population. 3. Find out how the Sample was obtained. 4. Think hard about whether there is any relevant way the Sample might systematically differ from the Population due to the way it was obtained.

7.2 More Examples Samples can end up being biased in many ways.

Here are some more examples of poor generalisations based on Biased Samples. Can you see why?. (See end of unit for clues.)

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1. A funds management firm attempts to convince you to invest in a new fund it is creating. It claims it has a strong record in producing superior returns in its funds. It points at all its current funds, which are all showing strong returns.

2. A software company is convinced its new app will sell well into its target market of parents of small children, because the parents who work at the company love the beta version of the app and use it all the time.

3. International accounting firm MGI claimed that 91 percent of small business owners were dissatisfied with the Labor government. Their conclusion was based on responses to a survey mailed out to small business owners.

7.3 Summary

1.A Sample is biased if it is unrepresentative of the population due to the way it was selected. 2.Use the tool CHECK FOR BIASED SAMPLE to avoid the pitfall of drawing a false Generalisation from a biased sample.

Unit 8 Causal Explanations; Hasty Explanation

In the next three units, we focus on another kind of judgement, namely Causal Explanations.

This unit explains the concept of Causal Explanation, and introduces a tool to avoid one kind of pitfall, Hasty Explanation.

8.1 About Causal Explanation Causal explanation is the most important type of deductive-nomological or covering law explanation. Historically, the theory of deductive-nomological explanation was developed out of the theory of causal explanation.Very often in business we want to know why something happened. For example:

• Why did our department stores’ net profit go down this year? • Why did we win the contract to build the new cross-city tunnel?

Why did we have a blowout in our oil well? In such cases we are searching for causes – the factor or factors which brought about the event. When we know the cause(s), we have made some sense of the event.

So a common type of business judgement is Causal Explanation – judging that one thing E (effect) was caused by another thing C (cause).

Corresponding to the events above, we might have the following explanations:

• Net profit went down because of high wages, rent, and utility costs.

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• We won the tunnel contract because of our recent success in a similar project. Our well blew out because of a mechanical failure in the drill head.

Note that these judgements all take the form

E because C

Getting causal explanations right is important for any business. If we know why things happen, we are better positioned to control them, whether avoiding them or bringing them about. We also have a better idea who (if anyone) to blame or reward.

Unfortunately, we often get causal explanations wrong. For example, we may judge that profits in our department stores went down because of high wages, rent, and utility costs, when in fact these factors changed little and the real cause was losses due to lavish spending on spring fashion shows and other dubious marketing exercises.

8.2 How Causal Explanations go wrong In general, there are three ways a causal explanation goes wrong:

1. Mis-identifying. What we identify as the cause (C) is not in fact the cause. E was caused by something else entirely. 2. Over-simplifying. We judge that C is the only cause of E, when in fact there are other important factors involved as well. 3. Over-weighting. We judge that C had far more impact than it actually had, as compared with the other factors.

This unit looks briefly at some of the thinking pitfalls which lead to explanations going wrong in the above ways, and provides some tools for avoiding these misjudgements.

8.3 Inferring to Causal Explanations Very often an explanatory judgement is made on the basis of some evidence – some information (I) pointing to C as the cause. Thus there is an inference from I to [E was caused by C]. We can diagram this as follows:

For example, consider this passage:

Americans choke on $1-coin stockpile. The UK newspaper The Telegraph reported recently that a mountain of 1.2 billion-dollar coins is sitting unused in US government vaults because the American public is so attached to the traditional dollar bill. Demand from banks for the coins has been so low that US$1.2 billion worth – which cost US$300 million to manufacture – are sitting in storage… According to The Telegraph, opinion polls show that three-quarters of the American public say they

E because C:Conclusion I:Reason

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would prefer to carry on using the paper dollar bill, affectionately known as the “greenback”, which celebrates its 150th birthday next year.

Here the thing being explained (E) is a mountain of unused dollar coins; the cause (C) is the public’s attachment to the dollar bill. The explanatory judgement (E because C) is expressed in the claim. A mountain of coins is sitting unused because the public is so attached to dollar bills.

But why should we believe this? What evidence is there that the public’s attachment to dollar bills is in fact the cause of the mountain of unused coins?

The passage does provide some evidence, in the form of some opinion-poll based information about what the public says it prefers. We can diagram this relationship as follows:

In other words we have an argument with a casual explanation as the conclusion.

8.4 Pitfall: Hasty Explanation Hasty generalization. ... Hasty generalization is an informal fallacy of faulty generalization by reaching an inductive generalization based on insufficient evidence—essentially making a rushed conclusion without considering all of the variables.

(also known as: argument from small numbers, statistics of small numbers, insufficient statistics, argument by generalization, faulty generalization, hasty induction, inductive generalization, insufficient sample, lonely fact fallacy, over generality, overgeneralization, unrepresentative sample)

Description: Drawing a conclusion based on a small sample size, rather than looking at statistics that are much more in line with the typical or average situation.

Logical Form:

Sample S is taken from population P.

Sample S is a very small part of population P.

Conclusion C is drawn from sample S and applied to population P.

Example #1:

My father smoked four packs of cigarettes a day since age fourteen and lived until age ninety-nine.  Therefore, smoking really can’t be that bad for you.

Explanation: It is extremely unreasonable (and dangerous) to draw a universal conclusion about the health risks of smoking by the case study of one man.

Example #2:

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Four out of five dentists recommend Happy Glossy Smiley toothpaste brand.  Therefore, it must be great.

Explanation: It turns out that only five dentists were actually asked.  When a random sampling of 1000 dentist was polled, only 20% actually recommended the brand.  The four out of five result was not necessarily a biased sample or a dishonest survey; it just happened to be a statistical anomaly common among small samples.

Exception: When statistics of a larger population are not available, and a decision must be made or opinion formed if the small sample size is all you have to work with, then it is better than nothing.  For example, if you are strolling in the desert with a friend, and he goes to pet a cute snake, gets bitten, then dies instantly, it would not be fallacious to assume the snake is poisonous.

Tip: Don’t base decisions on small sample sizes when much more reliable data exists.

The simplest and most common pitfall is essentially just jumping to a conclusion. It is judging that C caused E with little or no evidence, and without seriously considering any alternatives.

Consider this example:

Joost Juice is a chain of fresh-squeezed juice bars. Joost Juice has plenty of customers, but the business always seems to be on the verge of collapse. Millie Joost, the founder and CEO, noticed that their Punch brand juicing machines were breaking down quite often. She decided to replace them all with machines of a prestigious European brand, Judy, taking a bank loan to cover the cost. After a year, she found that machines were still breaking down. Doing some more research, she found out that Punch and Judy machines were essentially the same, made in the same Chinese factory, but branded differently for different markets.

Millie Joost seems to have made a number of simple business mistakes here, but the first was a hasty explanation: she judged that the Punch machines were breaking down because they were of inferior quality.

Notice that Millie jumped to this “obvious” conclusion without stopping to consider any alternatives, i.e. what else might have been causing the machines to break down. It can sometimes take a bit of thought to come up with plausible alternatives, but here are a few possibilities:

• Staff were abusing the machines, e.g. overloading them. • Machines were installed poorly. • Some staff may have been vandalising machines.

Notice also that Millie had no evidence that the inferior quality of the machines was causing them to break down. Perhaps the quality, though inferior to some other brands, was quite adequate for the task.

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Indeed she had no real evidence that the Punch machines were in fact of inferior quality, other than that they were breaking down.

Millie’s judgement may seem so rash that you find it implausible that such stupidity would rarely happen in real business situations. The truth unfortunately is that we make hasty explanations very often, and we are usually totally unaware that is what we are doing.

8.5 Tool: AVOID HASTY EXPLANATIONS Here is a simple tool for avoiding the pitfall of hasty explanation. It is in part just a specific version of the AS COMPARED WITH WHAT? tool introduced in Unit 1.

TOOL: AVOID HASTY EXPLANATIONS Having noticed that you are explaining, i.e. making a judgement of the form E because C:

1. Clearly articulate the explanatory judgement. Preferably, spell it out in writing. This will force you to clarify exactly what E and C are. 2. Ask yourself these simple questions:

a. What alternative explanations could there be? i.e. what, other than C, could have caused E? List plausible alternatives. b. What evidence do you have that C is the cause? List the evidence. c. Does the evidence clearly show that C, rather than any alternative, was the cause of E?

The hardest part of using a tool like this is usually the very first step – i.e. noticing that you’re making an explanatory judgement, and pausing to think about it.

8.6 Summary

1. A Causal Explanation is a judgement that one event E happened because of another event C (the cause).

2. Causal Explanations are common in business, because to succeed businesses need to know why things are happening and how to influence them.

3. Causal explanatory judgements are often based on inferences from other information.

4. The pitfall of Hasty Explanation is making a causal explanatory judgement on the basis of little or no evidence.

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Unit 9 “Post Hoc” Explanations

This unit continues the examination of Causal Explanations. It introduces another common pitfall, known as the “Post Hoc” fallacy, and a tool to guard against that pitfall. In the design and analysis of experiments, post hoc analysis (from Latin post hoc, "after this") consists of looking at the data—after the experiment has concluded—for patterns that were not specified a priori. ... More subtly, each time a pattern in the data is considered, a statistical test is effectively performed.

The post hoc ergo propter hoc (after this therefore because of this) fallacy is based upon the mistaken notion that simply because one thing happens after another, the first event was a cause of the second event. Post hoc reasoning is the basis for many superstitions and erroneous beliefs.

Many events follow sequential patterns without being causally related. For example, you have a cold, so you drink fluids and two weeks later your cold goes away. You have a headache so you stand on your head and six hours later your headache goes away. You put acne medication on a pimple and three weeks later the pimple goes away. You perform some task exceptionally well after forgetting to bathe, so the next time you have to perform the same task you don't bathe. A solar eclipse occurs so you beat your drums to make the gods spit back the sun. The sun returns, proving to you the efficacy of your action.

You use your dowsing stick and then you find water. You imagine heads coming up on a coin toss and heads comes up. You rub your lucky charm and what you wish for comes true. You lose your lucky charm and you strike out six times. You have a "vision" that a body is going to be found near water or in a field and later a body is found near water or in a field. You have a dream that an airplane crashes and an airplane crashes the next day or crashed the night before.However, sequences don't establish a probability of causality any more than correlations do. Coincidences happen. Occurring after an event is not sufficient to establish that the prior event caused the later one. To establish the probability of a causal connection between two events, controls must be established to rule out other factors such as chance or some unknown causal factor. Anecdotes aren't sufficient because they rely on intuition and subjective interpretation. A controlled study is necessary to reduce the chance of error from self-deception.

9.1 Pitfall: “Post Hoc” reasoning One of the fundamental rules of causal explanation is that causes happen before effects. First you step on the brake, then the car stops. First, you pull the trigger, then the gun fires. First the earthquake, then the tsunami. If C caused E, then C must have happened before E.

Sometimes we fall into the trap of reversing this pattern. Something happened before E, and we infer it must have caused E. For example,

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Chair of the Board: Mackenzie Consultants are expensive but they’re worth every cent. The StarStruck motivation program they designed and ran for our company really turned its fortunes around. Within a year, revenues were up 21%.

But this argument is of course quite weak. A great many things happened within a year of the StarStruck motivation program; very few of those were caused by the program. Being closely related in time, on its own, is poor evidence of being causally connected.

This mistake is so common it has a Latin name: post hoc ergo propter hoc, which translates as after this, therefore because of this. The general form is:

As with most pitfalls covered in this module, the error is obvious when stated in such simple terms, but it can be less easy to spot when happening in real life.

9.2 An example

The tweeter is inviting you to infer that the government changed its mining policy because of the meeting with Rio Tinto bosses. No evidence is provided, other than that the meeting preceded the change in policy. The tweet is implicitly making this argument:

9.3 Tool: AVOID POST HOC EXPLANATIONS TOOL: AVOID POST HOC EXPLANATIONS Having noticed that you are explaining, i.e. making a judgement of the form E because C:

1. Carefully consider what evidence you have that C caused E. List it. 2. If all you have is that C happened before E, then do not accept the explanation. Seek further evidence of a genuine causal connection between C and E.

9.4 Summary

1. We often make the mistake of inferring that one thing caused another because it happened before it. This is known as the “post hoc” fallacy. 2. Use the simple Avoid Post Hoc Explanations tool to avoid making this mistake.

This tweet is another relatively simple example:

Conclusion: A caused BReason: A happened before B

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Unit 10 Correlation and Cause

This unit continues the examination of Causal Explanations. It introduces another common pitfall, and a tool to guard against that pitfall.

What are correlation and causation and how are they different?

Two or more variables considered to be related, in a statistical context, if their values change so that as the value of one variable increases or decreases so does the value of the other variable (although it may be in the opposite direction). For example, for the two variables "hours worked" and "income earned" there is a relationship between the two if the increase in hours worked is associated with an increase in income earned.

Correlation is a statistical measure (expressed as a number) that describes the size and direction of a relationship between two or more variables. A correlation between variables, however, does not automatically mean that the change in one variable is the cause of the change in the values of the other variable. Causation indicates that one event is the result of the occurrence of the other event; i.e. there is a causal relationship between the two events. This is also referred to as cause and effect. 

Theoretically, the difference between the two types of relationships are easy to identify — an action or occurrence can cause another (e.g. smoking causes an increase in the risk of developing lung cancer), or it can correlate with another (e.g. smoking is correlated with alcoholism, but it does not cause alcoholism). In practice, however, it remains difficult to clearly establish cause and effect, compared with establishing correlation.

Why are correlation and causation important?

The objective of much research or scientific analysis is to identify the extent to which one variable relates to another variable. For example:

Is there a relationship between a person's education level and their health? Is pet ownership associated with living longer? Did a company's marketing campaign increase their product sales?

These and other questions are exploring whether a correlation exists between the two variables, and if there is a correlation then this may guide further research into investigating whether one action causes the other. By understanding correlation and causality, it allows for policies and programs that aim to bring about a desired outcome to be better targeted. 

How is correlation measured?

For two variables, a statistical correlation is measured by the use of a Correlation

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Coefficient, represented by the symbol (r), which is a single number that describes the degree of relationship between two variables. 

The coefficient's numerical value ranges from +1.0 to –1.0, which provides an indication of the strength and direction of the relationship.

If the correlation coefficient has a negative value (below 0) it indicates a negative relationship between the variables. This means that the variables move in opposite directions (ie when one increases the other decreases, or when one decreases the other increases).If the correlation coefficient has a positive value (above 0) it indicates a positive relationship between the variables meaning that both variables move in tandem, i.e. as one variable decreases the other also decreases, or when one variable increases the other also increases.

Where the correlation coefficient is 0 this indicates there is no relationship between the variables (one variable can remain constant while the other increases or decreases).

The correlation coefficient should not be used to say anything about cause and effect relationship. By examining the value of 'r', we may conclude that two variables are related, but that 'r' value does not tell us if one variable was the cause of the change in the other. 

How can causation be established?

Causality is the area of statistics that is commonly misunderstood and misused by people in the mistaken belief that because the data shows a correlation that there is necessarily an underlying causal relationship. The use of a controlled study is the most effective way of establishing causality between variables. In a controlled study, the sample or population is split in two, with both groups being comparable in almost every way. The two groups then receive different treatments, and the outcomes of each group are assessed.

For example, in medical research, one group may receive a placebo while the other group is given a new type of medication. If the two groups have noticeably different outcomes, the different experiences may have caused the different outcomes. Due to ethical reasons, there are limits to the use of controlled studies; it would not be appropriate to use two comparable groups and have one of them undergo a harmful activity while the other does not. To overcome this situation, observational studies are often used to investigate correlation and causation for the population of interest. The studies can look at the groups' behaviours and outcomes and observe any changes over time.

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The objective of these studies is to provide statistical information to add to the other sources of information that would be required for the process of establishing whether or not causality exists between two variables.

10.1 Pitfall: Confusing Correlation with Causation Consider this passage, by a social affairs editor of a major Australian paper:

Does being happy make you better off financially? After years of studying the influence money has on happiness, one Australian economist set out to examine the reverse. Using research from the Household, Income and Labour Dynamics in Australia (HILDA) survey, Professor Paul studied the self-rated happiness levels of 9300 people between 2001 and 2005. He found happier people get more done at work and are paid more. ''We found happy people are more active, more productive and get less upset by the work,'' he said. Professor Paul found that when other income factors such as age, education and geographic location were the same, Australians who were most satisfied with their life earned about $1766.70 a year more than people at the bottom of a happiness scale of zero to 10. For every one point rise in happiness on this scale, he found, a person's income rose by $176.67.

The editor seems to be claiming that being happy does indeed make you better paid. The evidence is that happier people get paid more. Diagrammatically:

So if think you are not being paid enough, then perhaps you should try being happier.

You can probably see the problem here already. If you were paid more, you would probably be happier. Which is more plausible: that being happy causes better pay, or that better pay causes happiness? Perhaps the latter?

The statistical evidence the editor is relying on is what is known as a correlation. This is where one thing is associated with, or varies with, another. But A can be correlated with B without causing B. Indeed A and B might have no connection whatsoever. Both crime and ice-cream sales go up in summer and down in winter, but there is no direct connection between them.

Reason: In general, happy people are paid more than unhappy people.

Conclusion: Being a happy person causes you to be paid more.

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The common pitfall of confusing correlation follows this pattern:

Like the post hoc pitfall, this one can be understood as wrongly reversing a valid pattern. If A does cause B, then A and B would be correlated. But A and B can be correlated for other reasons:

B causes A (e.g. being paid better making you happier) • Both A and B are caused by something else (e.g. being happier and being better paid both caused by extroversion) • A and B may be correlated purely by chance.

10.2 An example Here is a very serious example from macroeconomic policy (bold added):

In housing policy, politicians left, right, and center made the classic mistake of confusing correlation with causation. There's a difference between merely having property you've gotten easily and disciplining yourself so that you can acquire and keep it, just as there's a difference between earning a million dollars from hard work and winning a million dollars in the lottery. Since homeownership had correlated with fiscally virtuous behavior, policymakers imagined that they could boost such behavior by boosting homeownership.

10.3 Tool: DISTINGUISH CORRELATION FROM CAUSATION

TOOL: DISTINGUISH CORRELATION FROM CAUSATION Having noticed that you are explaining, i.e. making a judgement of the form E because C:

1. Carefully consider what evidence you have that C caused E. List it. 2. If all you have is a correlation, i.e. that Cs and Es are associated, then do not accept the explanation without further evidence that there is a genuine causal connection running from C to E.

As with so many of the simple tools we have covered in these units, the hardest part is stopping and remembering to apply the tool.

10.4 More Advanced Tools for Causal Explanations Because causal explanations are so important, and we are so prone to get them wrong, many tools have been developed to help improve such judgements.

Reason: Es and Csare correlated Conclusion: E because C

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In these units we have only covered three of the most basic pitfalls and corresponding simple tools.

To further develop your critical thinking skills in this area, you should look into some of the following:

• Mill’s Methods Five powerful general methods for identifying causal relationships. • Root Cause Analysis A general approach to identifying “root” or most significant underlying cause of some problem. • Five Whys A simple, handy version of root cause analysis.

You should also be aware that to properly identifying causal relationships often requires careful scientific research. This is a very large and quite technical field. The Wikipedia page on design of experiments is a useful introduction, but for deeper understanding you should go to a proper research methods textbook, or take a research methods subject.

10.5 Summary

1. A common pitfall in causal explanatory judgement is jumping to the conclusion that a causal relationship exists between two things based on observing a correlation between them.

2. To avoid this pitfall, using the simple DISTINGUISH CORRELATION FROM CAUSATION tool.

3. Rigorously determining when one thing causes another can require the use of sophisticated research methods; there are many advanced tools available.

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SECTION C:

LOGICAL FALLACIESIn reasoning to argue a claim, a fallacy is reasoning that is evaluated as logically incorrect and that undermines the logical validity of the argument and permits its recognition as unsound. ... Faulty inferences in deductive reasoning are common formal or logical fallacies.

A fallacy is a mistake in reasoning. It is a mistake to think that something is wrong simply because it makes us angry.

The common fallacies are usefully divided into three categories:

Fallacies of Relevance, Fallacies of Unacceptable Premises, and Formal Fallacies1.

A. Fallacies of RelevanceFallacies of relevance offer reasons to believe a claim or conclusion that, on examination, turn out to not in fact be reasons to do any such thing.

1. The ‘Who are you to talk?’, or ‘You Too’, or Tu Quoque Fallacy

When an argument is put forth as a charge of hypocrisy.

Rejecting an argument because the person advancing it fails to practice what he or she preaches.

Doctor: You should quit smoking. It’s a serious health risk. Patient: Look who’s talking! I’ll quit when you quit.2

1 Many of these fallacies have Latin names, perhaps because medieval philosophers were particularly interested in informal logic. You don’t need to know the Latin names: what’s important is being able to recognize the fallacies.

2 Responses like that probably sound familiar. But the doctor’s failure to look after her own health is irrelevant to the argument, resting on a concern for the patient’s health, that the patient should quit smoking.

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2. The Red Herring Fallacy.

A red herring fallacy is caused when a person brings a topic into a conversation that distracts from the original point, especially if the new topic is introduced in order to distract.

An arguer tries to side-track his or her audience by raising an irrelevant issue and then claims that the original issue has effectively been settled by the irrelevant diversion.

There is a good deal of talk these days about the need to eliminate pesticides from our fruits and vegetables. But many of these foods are essential to our health. Carrots are an excellent source of vitamin A, broccoli is rich in iron, and oranges and grapefruits have lots of Vitamin C.

Plans to eliminate or reduce pesticides probably don’t entail stopping the production of common vegetables: the suggestion that they do is an irrelevant red herring.

3. The Strawman Fallacy.The straw man fallacy is committed when an arguer distorts an opponent’s argument or claim to make it easier to attack. The straw man fallacy happens when you refute a position or claim by distorting or oversimplifying or misrepresenting it, all the while ignoring the person’s actual position.

Someone distorts or caricatures an opponent’s arguments or views, and then attacks the weakened version rather than the real argument. Involves distorting, weakening, or oversimplifying someone’s position so that it can be more easily attacked or refuted.

Showing that a strawman version of a position we oppose may win a debate, but it is unlikely to move us toward the truth. If we can show that even the strongest version of a position we oppose is flawed, we may make progress.

So good logical and critical thinking leads to the principle of charity: When representing an argument that you do not agree with and are attempting to evaluate, it is important to represent that argument in a way that is reasonably faithful to the argument as it is made by the originators, and as strong as possible. We cover the principle of charity in greater details in week 3.

4. The Ad Hominem or ‘At the Person’ Fallacy.

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We commit the fallacy of personal attack when we reject someone’s argument or claim by attacking the person rather than the person’s argument or claim. The ad hominem fallacy rests on a confusion between the qualities of the person making a claim and the qualities of the claim itself. It is a rhetorical device that attacks the arguer instead of the argument.

Rejecting someone’s argument by attacking the person rather than evaluating their argument on its merits.

5. Fallacious Appeal to Authority.When a claim comes from someone falsely deemed to be an expert. Is the Source Not an Authority on the Subject at Issue? An authority is a person who possesses special knowledge, competence, or expertise in a particular field. The most obvious way to commit the fallacy of inappropriate appeal to authority is to appeal to a person who is not a genuine authority on the subject at issue. For example:

My barber told me that Einstein’s general theory of relativity is a lot of hogwash. I guess Einstein wasn’t as smart as everybody thinks he was.

Because the arguer’s barber presumably is not an authority on Einstein’s general theory of relativity, this argument commits the fallacy of inappropriate appeal to authority.

Fallacies of this sort are particularly common in advertising. Consider this example:

Hi, I’m heavyweight boxing champ Buster Brawler. After a tough night in the ring, my face needs some tender loving care. Lather-X Sensitive Skin Shaving Gel. You can’t get a smoother, closer shave.

The arguer may be an expert on knocking out opponents in the boxing ring, but because he is no expert on the comparative virtues of shaving products, the argument is fallacious.

Is the Source Biased? Common sense tells us that we should be cautious about accepting a claim when the person making the claim is biased or has some other obvious motive to lie or mislead. Here are two examples:

Ned Bumpley has been paid $100,000 by the Sensational Enquirer tabloid for his story that he is Bill Gates’s illegitimate son. Given Mr. Bumpley’s reputation for honesty, I think we should believe him, even though he has produced no corroborating evidence and DNA tests fail to support his claim.

Mrs. Cox has testified that her son Willie was home with her at the time when Willie is alleged to have shot Steve Wilson. Even though Willie’s fingerprints were found on the murder weapon and six witnesses have identified Willie as the assailant, I can’t believe that a good woman like Mrs. Cox would lie to protect her son. I think Willy is innocent.

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In both of these examples, the testifier has an obvious motive to lie (financial gain in the fi rst example, maternal love in the second). Given these motivations, together with other information contained in the examples, these appeals to authority are fallacious.2

Is the Accuracy of the Source’s Observations Questionable? A source may also be unreliable if we have reason to doubt the accuracy of his or her observations or experiences. Here are two examples:

Jerry [who was listening to heavy metal music on his iPod] claims he heard the victim whisper his name from more than 100 feet away. Jerry has always struck me as a straight shooter. So, I have to believe that Jerry really did hear the victim whisper his name.

After taking LSD and drinking seven beers, Jill claims she had a conversation with Elvis’s ghost in the alley behind McDearmon’s Bar. I’ve never known Jill to lie. So, I think we should believe her.

In these examples there are obvious reasons for doubting the reliability of the witnesses’ observations or experiences. Consequently, these appeals to authority are fallacious.

Is the Source Known to Be Generally Unreliable? Generally speaking, it is reasonable to accept claims made in reputable newspapers, magazines, encyclopedias, radio and television news programs, and Internet Web sites. But we must be cautious about accepting claims found in sources that we have reason to believe are generally unreliable. Here is an example from the Weekly World News, a once-popular supermarket tabloid.

Relying upon the view of apparent (as opposed to genuine) authorities to settle the truth of a statement or argument.

Richard Long, a respected retired New Zealand newsreader featured in advertising campaigns for Hanover Finance. Long had no financial expertise.

Newsreaders look well informed, but they are essentially presenters. They are well known because they’re on the news: not because they know about investments. If we rely upon a newsreader’s endorsement to settle which investment fund we should trust, we would be accepting a claim without adequate evidence. That would be a fallacious appeal to authority.

Appeals to authority also conflict with the basic tenet of good logical and critical thinking which calls upon us to take responsibility for evaluating the grounds for our beliefs. Adopting a belief merely because someone else simply told us it was true is a way of avoiding good logical and critical thinking.

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To rely on a genuine authority, one should consider the following questions:

1. Is the authority a genuine authority: are they experts?

2. Are they giving advice in the areas within which they are a genuine authority? (We should listen to actors about acting; not so much about investing or medicine).

3. Is there a broad consensus among authorities in the area? If not, we should not decide to believe X solely because an authority says X is true, since other genuine authorities say that X isn’t true.

4. Is the authority speaking sincerely (they might be giving an endorsement because they’re paid to do so) and are they free of obvious bias?

Only if the answer to all four of these questions is “yes” should we accept a claim because an authority endorses it, and even then, we should only do so if we are not in a position to evaluate the evidence for the claim ourselves.

6. The Fallacy of Composition.

Arguing that what is true of the parts must be true of the whole. (All of the parts of the object O have the property P. Therefore, O has the property P.)

Rugby players Ma’a Nonu, Jerome Kaino and Charles Piatau are all great players. In 2012, they all played for the Auckland Blues. Therefore, the 2012 Auckland Blues were a great team.

Sadly, for Tim, a long-suffering Blues Fan, the conclusion of this argument was false even though the premises were true.

And, showing that famous philosophers are not immune:

“Should we not assume that just as the eye, hand, the foot, and in general each part of the body clearly has its own proper function, so man too has some function over and above the function of his parts?” Aristotle, Nichomachean Ethics

7. The Fallacy of Division.

Arguing that what is true of the whole must be true of the parts. (The opposite of the fallacy of composition: Object O has the property P. Therefore all the parts of the object O have the property P.)

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Men are, on average, taller than women. Therefore, Tim is taller than Maria Sharapova.

Tim would have to be taller than 188cm/6ft 2in to be taller than Sharapova: he’s not.

8. Equivocation.

A key word is used in two or more senses in the same argument and the apparent success of the argument depends on the shift in meaning.

Any law can be repealed by the proper legal authority. The law of gravity is a law. Therefore, the law of gravity can be repealed by the proper legal authority.

When the two senses of ‘law’ (laws regulating human conduct vs. uniformities of nature) are made explicit, it is apparent that the first premise is irrelevant, hence a fallacious argument.

And, showing that famous philosophers are not immune again, we see John Stuart Mill arguing that happiness is desirable:

“The only proof capable of being given that an object is visible, is that people actually see it. The only proof that a sound is audible, is that people hear it… In like manner, I apprehend, the sole evidence it is possible to produce that anything is desirable, is that people do actually desire it… [T]his being a fact, we have not only all the proof which the case admits of, but all which it is possible to require, that happiness is a good. ” John Stuart Mill, Utilitarianism.

But ‘desirable’ is used in two different ways in this passage, to mean ‘can be desired’ (just like ‘visible’ means ‘can be seen’) and ‘worthy of being desired’.

9. Appeal to Popularity.“Argument” from popularity is when we accept the conclusion of an argument because a lot of other people have accepted the same conclusion. The name of a rhetorical device that encourages the acceptance of a claim on the grounds that it is already accepted by some substantial number of others.

Arguing that a claim must be true because lots of people believe it.

Perhaps the Bible is true, but the fact lots of people believe it to be so is irrelevant to whether it is or not. We should investigate and evaluate their reasons for believing it, rather than taking the mere fact that they believe it as a reason to do so.

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But … sometimes a consensus among properly informed people may be a fairly good guide to the truth of a claim: see the circumstances in which an appeal to authority might not be fallacious.

10. Appeal to Tradition.

Like appeals to popularity except the appeal is to how long something has been believed, rather than to the number of people who have believed it

People have believed in astrology for a very long time, therefore, it must be true.

But all of the objections to arguments from majority belief apply here, too.

11. Appeal to Ignorance: Argumentum Ad Ignorantiam.

Arguing the lack of evidence proves something. When we lack evidence for or against a claim, it is usually best to suspend judgment—to admit that we just don’t know. When an arguer treats a lack of evidence as reason to think that a claim is true or false, he or she commits the fallacy of appeal to ignorance. More precisely, the fallacy of appeal to ignorance occurs when an arguer asserts that a claim must be true because no one has proven it false or, conversely, that a claim must be false because no one has proven it true.

The arguer asserts that a claim must be true because no one has proven it false, or that a claim must be false because no one has proven it to be true.

Note: When we describe someone as ignorant, we often mean it as an insult. Here we use it to describe the situation in which we do not know (are ignorant of) something. In this sense, the smartest of us are ignorant of quite a lot. (We don’t want any equivocation in our use of the term ‘ignorant’).

There must be intelligent life on other planets: No one has proven there isn’t.

There isn’t any intelligent life on other planets: No one has proven there is.

Both claims assume that the lack of evidence for (or against) a claim is good reason to believe that the claim is false (or true). Ignorance – in the sense of a lack of knowledge – features as part of the proof of the conclusion. But in general, the mere fact that a claim has not yet been proven is not enough reason to think that claim is false.

However, are there some non-fallacious appeals to ignorance?

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If qualified researchers have used well-designed methods to search for something for a long time, without success, and it’s the kind of thing people ought to be able to find, then the fact that they haven’t found it might constitute some evidence that it doesn’t exist.

12. Appeals to Emotion – e.g., pity, affection.Remember: When “arguments” evoke emotions that make us want to accept the conclusion without support, look for fallacies and rhetoric.

An arguer attempts to evoke feelings of pity or compassion, when such feelings are not logically relevant to the arguer’s conclusion.

Student to Lecturer: I know I missed most of the lectures and all of my tutorials. But my family will be really upset if I fail this course. Can’t you find a few more marks?

Daughter: Can we get a puppy? Father: No. Daughter: If you loved me, we’d get a puppy.

That would be an appeal to emotion, in this case love. Note that the persistent child might continue:

Daughter: A puppy would grow up and protect us. Can’t we get a puppy?Father: No.Daughter: If you wanted to keep us safe you’d get a puppy! You don’t care about us!

That would be a strawman, not contemplated by the father or entailed by his actual view, and attacking that. Being able to spot the common fallacies can be very useful in the home.

Remember, there are three species of fallacies. The Fallacies of Relevance sketched so far attempt to introduce premises that are irrelevant to the conclusion.

B. Fallacies of Unacceptable PremisesFallacies of Unacceptable Premises attempt to introduce premises that, while they may be relevant, don’t support the conclusion of the argument.

13. Begging the Question.The attempt to establish the conclusion of an argument by using that conclusion as a premise. (arguing in a circle)

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In philosophy, unlike in many other areas, ‘begging the question’ does not mean ‘raises a question which must be answered’. In philosophy, when someone begs the question, they state or assume as a premise the very thing they are trying to prove as a conclusion.

Arthur: God exists.Barbara: How do you know?Arthur: Because it says so in the Bible.Barbara: How to you know what the Bible says is true?Arthur: Because the Bible is divinely inspired. Everything it says is true.

The Bible could only be divinely inspired if God existed. So Arthur’s appeal to the Bible to prove the existence of God assumes the very thing he’s trying to prove.

14. False Dilemma or False Dichotomy.

Occurs when an argument presents two options and gives the impression that only one of them may be true, never both, and that there are no other possible options.

Either Shakespeare wrote all the plays attributed to him, or Bacon did. There’s good reason to think Shakespeare didn’t write all the plays attributed to him. Therefore, Bacon wrote all the plays attributed to Shakespeare.

It’s possible that Shakespeare didn’t write all of the plays attributed to him, but that doesn’t mean Bacon did: there are other possibilities.

In the Shakespeare/Bacon case the false dilemma was explicit (either Shakespeare wrote all the plays … or Bacon did), but often the dilemma is implicit.

If I spend all of the week partying, I won’t have time to study and I’ll fail.

If I spend all week studying, I’ll be over-prepared and stressed and I’ll fail.

So I’m going to fail either way. I might as well spend the week partying.

Here the dilemma is unstated – “The only options are to spend all week studying or to spend all week partying” – and once stated it surely isn’t plausible: the student could spend some of the week studying and some of the week partying?

15. Loaded Question

A loaded question is a question that contains an unfair or questionable assumption. For example, “Do you still steal from your boss?” is a loaded question if it presupposes,

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without justification, that you once did steal from your boss. The loaded question fallacy occurs when an arguer asks a question that contains an unfair or unwarranted presupposition. Here is a particularly blatant example:

Joe: Have you stopped cheating on exams?Pete: No!Joe: Oh, so you admit that you still cheat on exams?Pete: No, I meant to say yes!Joe: Oh, so you admit that you used to cheat on exams?Pete: No!

16. Questionable Cause

QUESTIONABLE CAUSE: We live in a complex and mysterious world. Often it’s hard to know what has caused some event to occur. When an arguer claims, without sufficient evidence, that one thing is the cause of something else, he commits the fallacy of questionable cause.

There are three common varieties of the questionable cause fallacy: the post hoc fallacy, the mere correlation fallacy, and the over simplified cause fallacy.

1. The post hoc fallacy (from the Latin post hoc ergo propter hoc [“after this,

therefore because of this”]) is committed when an arguer assumes, without adequate evidence, that because one event, A, occurred before another event, B, A is the cause of B.

2. Another common variety of the false cause fallacy is the mere correlation fallacy, which is committed when an arguer assumes, without sufficient evidence, that because A and B regularly occur together, A must be the cause of B or vice versa.

3. Perhaps the most common form of the questionable cause fallacy is the oversimplified cause fallacy. This fallacy is committed when we assume, without adequate evidence, that A is the sole cause of B when, in fact, there are several causes of B.

17. Decision Point Fallacy or the Sorites Paradox.

Sometimes the conditions that make the use of a term appropriate vary along a continuum and there is no sharp cut off between circumstances in which the term is correctly applied and those in which it is not.

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If an arguer claims that because we cannot identify a precise cut-off or decision point, we cannot distinguish between correct and incorrect uses of the term, they are arguing fallaciously.

One grain of wheat doesn’t make a heap. Suppose 1 million does. Take one away. Surely we still have a heap: if a million makes a heap, surely 999,999 does too. One grain can’t turn a heap into a non-heap. Take another away. Surely we still have a heap: if 999,999 does, surely 999,998 does too. One grain … etc. Take another away. Surely we still have a heap …. etc etc etc. But if one grain doesn’t make a difference, then it seems that we will be forced to conclude that 1 grain does make a heap. But that means we can’t talk about heaps of wheat at all: we don’t know when we can describe a collection of grains of wheat as a heap and when we can’t.

At conception an embryo is not a person. At birth, a baby is a person. There is no non-arbitrary way of determining exactly when the embryo became a person. Therefore, there is no moral difference between the embryo and the baby at birth.

But we can tell the difference between people who are bald and not bald, between heaps and non-heaps, and embryos and babies, even if we can’t tell exactly when something stopped being one thing and became the other.

18. The Slippery Slope Fallacy.

We commit the slippery-slope fallacy when we claim, without sufficient evidence, that a seemingly harmless action, if taken, will lead to a disastrous outcome.A form of fallacious reasoning in which it is assumed that some event must inevitably follow from some other, but in which no argument is made for the inevitability.

Arguers say that an innocent-looking first step should not be taken because once taken, it will be impossible not to take the next, and the next, and so on, until you end up in a position you don’t want to be in.

Don’t get a credit card. If you do, you’ll be tempted to spend money you don’t have. Then you’ll max out your card. Then you’ll be in real debt. You’ll have to start gambling in the hope of getting a big win. But you’ll normally lose. Then you’ll have to steal money to cover your losses. Then your partner will leave you. And you won’t be able to feed the dog, and it’ll die. And it would be bad if the dog died. So you mustn’t get a credit card.

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Slippery Slope arguments are fallacious if it is possible to stop at one of the steps: couldn’t I get a credit card with a maximum, or exercise a bit of control, or get the local animal protection society to help me feed the dog?

19. Hasty Generalisations.When a conclusion is made about a whole group based on an inadequate same of the group. A generalization is a statement that asserts that all or most things of a certain kind have a certain quality or characteristic

Arguer draws a general conclusion from a sample that is biased or too small.

The oldest woman in the world, Jeanne Calment (122 years, 164 days) smoked until her early 110s. Therefore, smoking isn’t really bad for you.

The claim that smoking carries significant health risks isn’t falsified by a single case and trials drawing population wide conclusions must recruit representative study-populations.

20. Faulty Analogies.

The conclusion of an argument depends upon a comparison between two (or more) things that are not actually similar in relevant respects, or without pointing out how the two differ and why it does or does not matter. (See reasoning by analogy in Week 6).

I need a new car. My last three cars have all been reliable, and they were blue. So I’m going to buy a blue car.

A letter to the editor following a report someone had been turned away from an after-hours medical clinic because she couldn’t pay for treatment for her feverish, vomiting child: “Why do people attend private clinics for medical treatment with insufficient funds to cover fees? Do these same people go to the petrol station, fill up, toss $5 out the window and say “I’ll be back with the rest later,” or perhaps after dining out one evening, pay for the meal and promise to return next week, month or year to pay for the wine? I think not. The answer is simple - don’t go to private clinics.”

Are visits to after-hours medical clinics with a sick child analogous to visits to a gas station or a restaurant?

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21. . And … the Fallacy Fallacy!

The fallacy of inferring that merely because an argument contains a fallacy, its conclusion must be false.

Bob told me that I shouldn’t steal because everyone knows that stealing is wrong, but I recognised immediately that argument contained the popularity fallacy, so I concluded that it was ok to steal the apple.

The conclusion of an argument may be true, even if the argument contains a fallacy. Finding a fallacy just means that the arguer needs to look for other, better reasons in support of their conclusion.

C. Formal FallaciesThe third species of fallacy are Formal Fallacies. Some arguments are fallacious not because of their content – because of what they say – but because of their form or structure. Any argument with these forms or structures will be invalid, no matter what content we put into them.

There are some common argument forms, however, which look quite like the valid versions, but which are not valid. Here we’re just going to identify two formal fallacies that will come up later in the course.

22. Affirming the consequent.Suppose I have a guard dog, Brutus, and I’m confident he will bark if an intruder comes into my house.

I might reason like this:

P1P2CIf there’s an intruder, then Brutus will bark. Brutus hasn’t barked. Therefore, There’s no intruder. P1If there’s an intruder, then Brutus will bark. P2Brutus hasn’t barked. Therefore, There’s no intruder.

That’s valid: If it’s true that Brutus will bark if there’s an intruder, and if Brutus hasn’t barked, then there can’t be an intruder.

If the premises are true, then the conclusion must be true too.

But what if I reason like this:

P1P2CIf there’s an intruder, then Brutus will bark. Brutus has barked. Therefore, There's an intruder. P1If there’s an intruder, then Brutus will bark. P2Brutus has barked. Therefore, C There's an intruder.

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That’s not valid. Why? Well the premises might be true, but the first premise doesn’t say that Brutus will bark if and only if there’s an intruder.

The first premise can be true – that is it can be the case that Brutus will bark if there’s an intruder – even if Brutus occasionally barks for other reasons as well.

Notice that you can’t respond here “Oh, the burglar might have fed Brutus tranquilized steak. That’s why he hasn’t barked. There is a burglar!” That rejects the first premise (If there’s an intruder, Brutus will bark), and we’re seeing what happens if the premises are true. So here, if the premises are true, the conclusion must follow.

23. Denying the Antecedent.Suppose I hear barking and reason like this:

P1P2CIf it barks, then it’s a dog. It’s barking. Therefore, It's a dog. P1If it barks, then it’s a dog. P2It's barking. Therefore, It’s a dog.

That’s valid. If the premises are true – if it’s true that if it barks it’s a dog and it barks – then the conclusion must be true too.

But what if I reason like this:

P1P2CIf it barks, then it’s a dog. It’s not barking. Therefore, It isn't a dog.P1If it barks, then it’s a dog.P2It's not barking. Therefore, C It isn't a dog.

That’s not valid. The first premise says that if something barks then it’s a dog (i.e., that only dogs bark), but it doesn’t say that every dog barks. So we can’t be sure that the conclusion of this second argument is true even if the premises are true.

It might be true that something doesn’t bark (i.e., the antecedent is false, or denied, as the second premise says), but is a dog.

MORE FALLACIES

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1. Appeal to General Belief: Arguing that a claim must be true merely because many people believe it.

2. Appeal to Popular Attitudes & Emotions: Peer pressure

3. The Gambler’s Fallacy: Thinking that previous events can influence the probabilities in the random event at hand

4. The False Cause Fallacy (Post Hoc): Confusing cause with temporal order (the rooster crowed, then the sun cam up. So the rooster made the sun come up)

5. The Fallacy of False Dilemma: Asserting that there are only 2 alternatives when in fact there are more.

6. The Fallacy of the Loaded Question: Consist of attempting to get an answer to a question that assumes the truth of an unproved assumption.

7. The Fallacy of Against the Person: Rejecting a claim based on the person who makes it, rather than the claim itself.

8. The Pooh-Pooh Fallacy: Involves a refusal to examine an argument seriously and evaluate it fairly.

9. The Loaded Words Fallacy: Using highly charged words to assume the truth of a conclusion.

10. The Definitional Dodge Fallacy: Consists of redefining a crucial term in a claim to avoid acknowledging a counter-example that would falsify the claim.

11. The Exception That Proves the Rule Fallacy: Allows someone defending a claim to dodge a counter-example

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Glossary causal claim A claim that asserts or denies the existence of a causal connection between two things, such as events, people, states, or between two types of things. A causal claim indicates that the connection is more than a mere accidental one. The standard form of a causal claim is: C causes E, where C is the cause and E is the effect. A causal claim is also called a cause-effect claim or a causal statement. causal generalization A generalization that makes a causal claim. Causal generalizations assert causal connections between kinds of things rather than between specific things. The standard form is: (All, most, many) events of kind C cause events of kind E. causal indicator A term that signals the presence of a causal claim. Examples: produces, cures, makes, triggers. cause-effect claim A causal claim. contributing cause One among many causes. The contributing cause that is most important for our present purposes we call the cause. A contributing cause is also called a contributing factor or partial cause. control group In a controlled experiment, the group that does not receive the cause that is suspected of leading to the effect of interest. correlation An association. Finding a correlation between two variables A and B is a clue that there may be some causal story to uncover, such as that A is causing B. Characteristics A and B are correlated if the percentages of A's among the B's is not the same as the percentages of A’s among the not-B's. determinate cause A cause that will make its effect happen every time under known proper conditions. directly proportional A perfect positive straight-line correlation between two variables. experimental group In a controlled experiment, the group that receives the suspected cause of the effect being studied. Sometimes called the “treatment group.” inversely proportional Characteristic of a perfect negative straight-line correlation between two variables.

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negative correlation A relationship that exists when variable A tends to increase when B decreases, and vice versa. Characteristic A is negatively correlated with characteristic B in a given population whenever the percentage As among the Bs is less than the percentage of As among the not-Bs. no correlation A lack of relation between two variables. Characteristics A and B are uncorrelated if the percentages of A's among the B's is the same as among the not-B's. perfect correlation A relationship that exists when two variables always change together. That is, both may increase together or both may decrease together. positive correlation A relationship between A and B that exists when variable A tends to increase when B increases and vice versa. Characteristic A is positively correlated with characteristic B in a given population whenever the percentage of A's among the B's is greater than the percentage A's among the not-B's. post hoc fallacy The mistake of supposing that A caused B when the only evidence is that A is followed by B a few times. probable cause A cause that will make the effect happen occasionally. When a probable cause occurs, the effect is probable but not certain. specific causal claim A causal claim that asserts a specific claim rather than a general claim. spurious association An association between A and B that results not because A is causing B or B is causing A but instead because some lurking factor C is causing A and B to be associated. strength of the correlation A measure of how well two things are correlated. As a rule of thumb, the strength of the correlation between characteristics A and B is proportional to the difference between the percentage of B's that are A and the percentage of B's that are not-A. treatment group The experimental group in an experiment involving treatment with a drug. uncorrelated A lack of correlation between two variables.

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Glossary II

The Problem:Everyone thinks; it is our nature to do so. But much of our thinking, left to itself, is biased, distorted, partial, uninformed or down-right prejudiced. Yet the quality of our life and that of what we produce, make, or build depends precisely on the quality of our thought. Shoddy thinking is costly, both in money and in quality of life. Excellence in thought, however, must be systematically cultivated.

A Definition:Critical thinking is the art of analysing and evaluating thinking with a view to improving it.

The Result:A well cultivated critical thinker:• raises vital questions and problems, formulating them clearly and precisely;• gathers and assesses relevant information, using abstract ideas to interpret it effectively;• comes to well-reasoned conclusions and solutions, testing them against relevant criteria and standards;

• thinks open-mindedly within alternative systems of thought, recognizing and assessing, as need be, their assumptions, implications, and practical consequences; and

• communicates effectively with others in figuring out solutions to complex problems.Critical thinking is, in short, self-directed, self-disciplined, self-monitored, and self-corrective thinking. It requires rigorous standards of excellence and mindful command of their use. It entails effective communication and problem solving abilities and a commitment to overcome our native egocentrism and sociocentric.

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Clarity Accuracy Depth Breadth Significance Precision Relevance

ConsequencesImplications and

taking for grantedpresupposition,

Assumptions

modelslaws, principles,

definitions, axioms, theories,

Concepts

solutionsconclusions,

and inferenceInterpretation

experiencesobservations,

data, facts,Information

problem, issueQuestion at issue

objectivegoal, Purpose

orientationperspective,

frame of reference,Point of View

The Elements of Thought

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The Miniature Guide to Critical Thinking Concepts and Tools

Traits or VirtuesIntellectual

Fairmindedness

EmpathyIntellectual

PerseveranceIntellectual

CourageIntellectual

HumilityIntellectual

AutonomyIntellectual

in ReasonConfidence

IntegrityIntellectual

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Critical thinkers routinely apply the intellectual standards to the elements of reasoning in order to develop intellectual traits

applied toMust be

to developAs we learn

raITS TnTellecTualI

FairmindednessIntellectual EmpathyConfidence in ReasonIntellectual Perseverance

Intellectual CourageIntellectual IntegrityIntellectual AutonomyIntellectual Humility

lemenTS eheT

AssumptionsImplicationsConceptsInferences

InformationPoints of viewQuestionsPurposes

TandardS SheT

DepthFairnessCompletenessSignificancePrecision

BreadthLogicalnessRelevanceAccuracyClarity

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References

1. Gregory Bassham, William Irwin, Henry Nardone, James M. Wallace (2011) Critical Thinking: A Student’s Introduction, 4th ed., New York: McGraw-Hill.

2. John Chaffe (2014) Think Critically, Wadsworth Publishing Co Inc; 11th Revised edition.

3. Hunter, David A. (2009) A Practical Guide to Critical Thinking: Deciding What to Do and What to Believe. Hoboken: Wiley & Sons