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Critical Thinking 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 http://www.gnu.org/copyleft/fdl.txt. 1 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 2 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 3 (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. 4 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 6. statement 11. not a statement 16. not a statement 2. statement 7. not a statement 12. statement 17. statement 3. not a statement 8. statement 13. not a statement 18. statement 4. statement 9. statement 14. not a statement 19. statement 5. statement 10. statement 15. 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 5 “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 In conclusion Hence entails that Thus Accordingly Ergo We may infer So It follows that We can conclude that 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).
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