Critical Thinking

[Pages:225]Critical Thinking

Mark Storey Bellevue College

Copyright (c) 2013 Mark Storey Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is found at .

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Contents

Part 1

Chapter 1: Thinking Critically about the Logic of Arguments .. 3 Chapter 2: Deduction and Induction ............ ................... 10 Chapter 3: Evaluating Deductive Arguments ...................... 16 Chapter 4: Evaluating Inductive Arguments ....................... 24 Chapter 5: Deductive Soundness and Inductive Cogency ........ 29 Chapter 6: The Counterexample Method ........................... 33

Part 2

Chapter 7: Fallacies ................................................... 43 Chapter 8: Arguments from Analogy .............................. 75

Part 3

Chapter 9: Categorical Patterns....................................... 86 Chapter 10: Propositional Patterns.................................... 116

Part 4

Chapter 11: Causal Arguments.......................................... 143 Chapter 12: Hypotheses................................................ 159 Chapter 13: Definitions and Analyses................................. 179 Chapter 14: Probability.................................................199

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Chapter 1: Thinking Critically about the Logic of Arguments

Logic and critical thinking together make up the systematic study of reasoning, and reasoning is what we do when we draw a conclusion on the basis of other claims. In other words, reasoning is used when you infer one claim on the basis of another. For example, if you see a great deal of snow falling from the sky outside your bedroom window one morning, you can reasonably conclude that it's probably cold outside. Or, if you see a man smiling broadly, you can reasonably conclude that he is at least somewhat happy. In both cases, you are reasoning from evidence to a conclusion.

We use reasoning all the time, but sometimes we make a mess out of it. Whether a line of reasoning is good or not is definitely more than "just a matter of opinion." Surely the reasoning in the following arguments is not compelling:

* My four-year-old niece says that the planet Mars is smaller than Jupiter. It must thereby be the case that Mars is smaller than Jupiter. * Some women are baseball fans. And some mothers are baseball fans. Thus, all women are mothers. * An earthquake occurred in San Francisco five minutes after the senator's speech there. Thus that senator's voice causes natural disasters.

But the reasoning in the next set of arguments is better, yes?

* All bears are mammals. Grizzlies are bears. Thus grizzlies are mammals. * If Jimmy Carter was the U.S. President, then he was a politician. Carter was indeed the U.S. President. Thus, Carter was a politician. * It has rained in Seattle, Washington every year for the past 100 years. Thus it will probably rain there next year.

Some examples of reasoning are clearly better than others. The study of logic and critical thinking are designed to make us better at recognizing good from bad lines of argumentation.

An argument consists of one or more statements, called premises, offered as reason to believe that a further statement, called the conclusion, is true. Technically speaking, premises and conclusions should be made up of statements. A statement is a sentence that declares something to be true or false. They are thus sometimes called declarative sentences. A sentence is a grammatically correct string of words, and there are many kinds of sentences other than statements. Questions (e.g., "What is your name?"), commands (e.g., "Turn to page three"), and exclamations (e.g., "Ouch!") are all grammatically correct sentences that are not statements. They are not statements because it makes no sense to say they are true or false. ("What is your name?" "That's true!" This would be a ridiculous mini-conversation.) Statements will always be true or false, never both, and never neither. We may disagree on whether a given statement is true (e.g., "God exists"), or we may not be able to determine whether a statement is true or false

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(e.g., "There is a mountain on Pluto exactly 1000 meters tall, plus or minus 2 centimeters"), yet the statement is objectively true or false (but not both) nonetheless.

In this course, the words "statement" and "sentence" can--in many contexts--be used interchangeably. This is so because all statements are sentences (although not all sentences are statements). So we can refer to "Bellevue is in Washington" as both a statement (because it declares something to be true) and a sentence (because it is a grammatically correct sequence of words conveying a meaning).

An argument can have any number of premises, but technically speaking there is one conclusion per argument. Thus, an argument splits into two distinct parts:

1. One or more premises offer evidence for the truth of the conclusion. 2. The conclusion is supported by the premise or premises.

Here is an argument:

All dogs are mammals. No mammals are birds. Thus, no dogs are birds.

The conclusion seems well supported by the two premises. However, things are not so good in the following argument:

Some cats are animals. Some animals are fish. Hence, some cats are not fish.

In both examples above, the arguments contained two premises and one conclusion, but in the second argument immediately above, the premises by themselves do not offer good reason to believe the conclusion--even if though the premises are true!

Sometimes the conclusion of an argument can be used as a premise of a following argument, making a chain of arguments. Still, to be precise, each argument or specific line of inference contains one and only one conclusion, although each may contain varying number of premises. For instance:

1. All dogs are mammals. 2. All mammals are animals. 3. Thus, all dogs are animals. 4. Scooby-Doo is a dog. 5. Thus, Scooby-Doo is an animal. 6. No animals are plants. 7. All trees are plants. 8. Thus, Scooby-Doo is not a tree.

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Whew! Here the first argument in the chain has lines 1 and 2 as premises, and has line 3 as its conclusion. The second argument then uses line 3 as a premise and uses it with line 4 to conclude in line 5 that Scooby-Doo is a dog. The third argument then uses line 5 as a premise, hooks it up with lines 6 and 7, and uses the trio together to infer line 8 as the final conclusion.

**Practice Problems: Types of Sentences

Are the following statements or not?

1. George Carlin is presently president of the USA. 2. Chocolate is a popular flavor of ice cream in the USA. 3. Sally Brown, come on down! 4. Washington State is south of Oregon. 5. Bob believes that Washington State is south of Oregon. 6. College students are morally obliged to believe that Washington State is south of Oregon. 7. Who in Oregon is rooting for the Huskies? 8. It is prudent for Duck fans not to wear green when going to a Husky game in Seattle. 9. Green is an Oregon Ducks color, while purple is a Washington Huskies color. 10. The Huskies are my favorite college football team! 11. Go Cougars! 12. The Ducks will never win the Apple Cup. 13. Huskies 14. Ducks vs. Cougars 15. The Ducks will play the Cougars tonight. 16. Slap a ham on Omaha, pals! 17. Dennis and Edna sinned. 18. Rats live on no evil star. 19. Tarzan raised Desi Arnaz' rat. 20. Go deliver a dare, vile dog.

Answers: 1. statement 2. statement 3. not a statement 4. statement 5. statement

6. statement 7. not a statement 8. statement 9. statement 10. statement

11. not a statement 12. statement 13. not a statement 14. not a statement 15. statement

16. not a statement 17. statement 18. statement 19. statement 20. not a statement

Indicator Words

Before determining whether an argument is good or bad, we need to recognize its structure. We need, that is, to know which claims are premises and which one is the conclusion. Indicator words or phrases can help us out here.

A conclusion indicator is a word or phrase that, when used in the context of an argument, signals that a conclusion is about to be given or was just given. In the two examples above, "Thus" and

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"Hence" were used as indicators to signal the presence of the conclusion. The following are some of the commonly used conclusion indicator words and phrases:

Therefore Thus So

In conclusion Accordingly It follows that

Hence Ergo We can conclude that

entails that We may infer implies that

A premise indicator is a word or phrase that, when used in the context of an argument, signals

that a premise is about to be given or was just given. Here are some examples:

Because

Since

If

Provided that

For the reason that for

Given that

Assuming that

Due to the fact that may be inferred from

Inasmuch as

is evidence for

is reason to believe that

supports the claim that

If you want to make your reasoning as clear as possible when you present arguments, use indicator words to signal your premises and conclusions. Your audience (e.g., a teacher grading your essay) will appreciate it, and your reasoning will be easier to follow than it otherwise might be.

Note, though, that some indicator words have multiple uses. The premise indicator "if," for instance, is often used in other ways. For example, in the sentence, "If Yogi is a bear, then Yogi is an animal," the word "if" is used as part of a single complex statement called a conditional (i.e., an "if..., then..." statement). Also, the conclusion indicator "so" can be used in many ways, such as, "I am so happy I'm studying logic!" Indicator words can be helpful, but we must still be careful in recognizing how they function in a sentence.

**Practice Problems: Indicator Words

For each argument, (a) state any premise or conclusion indicators, and (b) state the conclusion.

1. Since Tuan is a student, it follows that he studies regularly. 2. Sarah is a mother, because she has given birth to a child. 3. All dogs are mammals, and all mammals are animals; thus all dogs are animals. 4. Given that Kim is the country's president, that Kim is a politician may be inferred from the fact that all presidents of countries are politicians. 5. The ground is wet during a heavy rain. Consequently, due to the fact that it's raining now, the ground now is wet. 6. Provided that two is greater than one, and three is greater than two, it follows that three is greater than one. 7. Tran is happy. Hence Tran is happy. 8. Sim?n Bol?var was born in Venezuela. Bol?var was a military hero in South America. This implies that a military hero was born in Venezuela. 9. According to Socrates, people will do what they believe is in their best interests. Thus, since the good is in people's best interest, it behooves philosophers to explain the good to people. 10. Given that all dogs are mammals, and because no mammals are birds, it must be concluded that no dogs are fish.

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11. Assuming that Senator Sunny Shine likes to swim, and inasmuch as today is warm and the sun is out, it follows that Sunny Shine is swimming in her backyard pool. 12. Shine and her husband don't want to unduly offend their neighbors, and their neighbors are not fans of skinny-dipping. We may infer that Shine and her husband don't skinny-dip when their neighbors are watching. 13. Pastor Bustle is opposed to all skinny-dipping. Bustle is opposed to some of the Shines' activities, due to the fact that Bustle knows that the Shines like to skinny-dip. 14. If Bustle climbs a ladder to look over the fence at the Shines, then Bustle will probably fall and twist his ankle. Bustle does indeed climb a ladder to look over the fence at the Shines. This entails that Bustle will probably fall and twist his ankle. 15. Either Bustle gets away with voyeurism or the police fail to charge him with a misdemeanor. Since the police do fail to charge Bustle with a misdemeanor, Bustle accordingly gets away with voyeurism.

Answers: 1. (a) Since; it follows that; (b) he studies regularly 2. (a) because; (b) Sarah is a mother 3. (a) thus; (b) all dogs are animals 4. (a) Given that; may be inferred from; (b) Kim is a politician 5. (a) Consequently; due to the fact that; (b) the ground is now wet 6. (a) Provided that; it follows that; (b) three is greater than one. 7. (a) Hence; (b) Tran is happy (the second instance of the claim) 8. (a) This implies that; (b) a military hero was born in Venezuela 9. (a) Thus; since; (b) it behooves philosophers to explain the good to people 10. (a) Given that; because; it must be concluded that; (b) no dogs are fish 11. (a) Assuming that; inasmuch as; it follows that; (b) Sunny Shine is swimming in her backyard pool. 12. (a) We may infer that; (b) Shine and her husband don't skinny-dip when their neighbors are watching 13. (a) due to the fact that; (b) Bustle is opposed to some of the Shines' activities 14. (a) This entails that; (b) Bustle will probably fall and twist his ankle 15. (a) Since; accordingly; (b) Bustle accordingly gets away with voyeurism

Distinguishing Arguments from Non-arguments

We probably will not understand what an argument is unless we can tell the difference between an argument and a non-argument. This is why the ability to distinguish arguments from things that are not arguments is an important skill in logic.

An argument is someone's reasoning expressed in the format of a language. When an argument is given, one or more reasons are being offered for a conclusion. However, there are many things we do with language besides reason. We use language to describe things, to explain things, to express our feelings, to give orders, to ask questions, to tell stories, to give advice, to offer reports, to babble incoherently, and on and on. None of these activities involves logical argumentation; none constitutes giving an argument. Essentially, in the case of a non-argument,

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someone is not trying to prove a point--someone is not offering a reason to believe a claim that is being advanced, someone is not offering evidence for a conclusion, while in the case of an argument, someone is offering reasons in support of a conclusion, reasons to believe that a claim is true.

**Practice Problems: Arguments and Non-arguments

In each case, does the passage present an argument or a non-argument?

1. Elizabeth and Marty went together to school on Tuesday, got in a minor automobile accident, and were late for their biology class. Their teacher was giving a test that day, and the two students were not there to take it. 2. Elizabeth and Marty left their house to go to school on Tuesday, but on the way decided to spend the day at the movie theater instead. Their biology teacher was giving a test that day, and the two students were not there to take it. That is why they received a poor grade for their coursework that week. 3. Elizabeth and Marty, you two are crazy! You should not have gone to the movies Tuesday, especially when you had a test in your biology class. You should go to school each day classes are in session. 4. Elizabeth and Marty went together to school every day this week and studied the material covered in class. Students who attend class regularly and study regularly usually do well in class. Thus Elizabeth and Marty probably did well in class this week. 5. Some students do not attend class regularly. For instance, Elizabeth and Marty went together to school on Tuesday, but decided to return home to play Grand Theft Auto all day. Such behavior is indicative of poor study habits. 6. Maria studies every night for her chemistry class, and works very precisely in her chemistry lab work. She also attends class each day and takes complete notes. We can conclude that Maria will likely do well in her chemistry class. 7. Both Mahatma Gandhi and Sri Aurobindo were philosophically minded, both were male, both were from India, and both wrote commentaries on the Bhagavad Gita. Gandhi fought against British occupation of India. Thus probably Aurobindo did, too. 8. Rene Descartes had trouble seeing the relations between things in Nature, focused on breaking "problems" into smaller parts, and missed viewing systems holistically. Thus he has been deemed a "mechanistic" philosopher. 9. Fatima likes pizza. Julio likes football. Takashi likes reading The Tale of Genji. 10. Sunzi wrote The Art of War, and The Art of War was written by a Chinese philosopher. Sunzi must therefore be a Chinese philosopher.

Answers: 1. Non-argument. It's merely a report of the day's events with no inference. 2. Non-argument. It's a causal explanation of the students' poor grades with no inference. 3. Non-argument. It's a combination of opinion and advice, but with no inference. 4. Argument. There are a series of claims serving as premises leading to a conclusion (note the indicator word "thus"). 5. Non-argument. It's merely an illustration of the opening claim with no inference. 6. Argument. Note the use of the conclusion indicator, "We can conclude that."

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