by M Storey · 2013 · Cited by 4 — Note the use of the conclusion indicator, “We can conclude that.” dozens that have been analyzed and named over the centuries.

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1 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 vers ion 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 .

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2 Contents Part 1 Chapter 1: Thinking Critically abou t t he Logic of Arguments .. 3 Chapter 2 : Deduction and Inducti 10 Chapter 3: Evaluating Deductive Arguments 16 Chapter 4: Evaluating Inductive .. 24 Chapter 5: Deductive Soundness and Inductive Cogency . 2 9 Chapter 6: The Coun 33 Part 2 Chapter 7: 43 Chapter 8: Argu 7 5 Part 3 Chapter 9: Catego 8 6 Chapter 10: Proposi . 116 Part 4 . 14 3 Cha 1 5 9 Chapter 13: D .. . 17 9 19 9

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3 Chapter 1: Thinking Cri tically about t he 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 c laim 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 s probably cold outside. Or, if you see a man smiling broadly, you can reasonably c onclude that he is at least somewhat happy. In both cases, you are reasoning from evidence to a conclusion. We use reasoning all the time, b ut sometimes we make a mess out of it. Whether a line of reasoning is good or not is 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 fa ns. And some mothers are baseball fans. Thus , all women are mothers. * But the reasoning in the next set of argument s is better, yes? * All bears are mammals. Grizzlies are bears. Thus grizzlies are mam m als . * 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 lin es of argumentation. An argument consist s 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., true – conversation.) Statements will always be true or false, never both, and never neither. We may disagree on whether a given statement is er a statement is true or false

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4 the statement is objectively true or false (but not both) nonetheless. an in many contexts be used interchangeably. This is so because all statements are sentences (although not all sentences are declares something to be true) and a se ntence (because it is a grammatically correct sequence of words conveying a meaning). A n 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 th e 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 arg ument immediately above , the premises by themselves do not offer good reason to be lieve the conclusion even if though the premises a re true! Sometimes the conclusion of an argument can be used as a premise of a following argument, making a chain of argume nts. 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 ani mals. 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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5 Whew! Here the first argument in the chain has lines 1 and 2 as premises, and has line 3 as its conclusio n. 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 Stat e 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. 20. Go deliver a dare, vile dog. Answers: 1. statement 6. s tat ement 11. not a statement 16. not a statement 2. statement 7. not a statement 12. s tatement 17. statement 3. not a statement 8. s tatement 13. not a statement 18. statement 4. statement 9. s tatement 14. not a statement 19. statement 5. statement 10. s tatement 15. s tatement 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 w ords 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

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6 dicators 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 co nclude 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 tha t 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 indic ator 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. careful in recognizing how they function in a sentence. **Practice Problems: Indicator Wo rds 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, a nd all mammals are animals; thus all dogs are animals. fact that all presidents of countries are politicians. 5. The ground is wet during a heavy rain. Conseque 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. Simón Bolívar was born in Vene zuela. Bolívar 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 ves 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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8 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 th e 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 comment aries on the Bhagavad Gita . Gandhi fought against British occupation of India. Thus probably Aurobindo did, too. 8. Rene Descartes had trouble see ing the relations between things in Nature , focused on breaking ing systems holistically. Thus he has been 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. Su nzi must therefore be a Chinese philosopher. Answers: 1. Non – 2. Non – 3. Non – on 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 5. Non – 6.

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9 7. Argument. This is an argument from analogy. 8. Non – pointing to the effect of a causal relation. That is, the final statement is explained by the previous ones, but there is no inference intended here. 9. Non – 10. Argument. The two claims in the first sentence offer reason to believe the c laim in the final sentence.

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10 Chapter 2: Deduction and Induction L ogicians divide all argu ments into two broad categories: deductive arguments and inductive arguments. Every argu ment falls into on e of these two categories. Of course people offering arguments often do not fully understand what they are doing. That is, they may be unclear how powerful their arguments could be, assuming they are arguing well. Still, once we understand what their argum deductive or inductive. Deductive Arguments A deductive argument claims (e xplicitly or implicitly) that if the premises all are true, then the conclusion must be true. Deduc tive arguments thus aim to establish their conclusions with complete certainty in such a way that the conclusion is guaranteed to be true if the premises all are true. Note that the argument may fail in its aim; what makes the argument deductive is that it is the kind of argument that if it were successful would have the premises absolutely guarantee the conclusion to be true. The following four arguments are all deductive: * All bats are cute animals . No cute animals are mean. So, certainly, no bats are mean. * * Nobody knows Ned. Therefore, it must be that Ned does not know himself. * Some cats are pets. Thus, some pets must be cats. Inductive Arguments An inductive argument claims (e xplicitly or implicitly) that if the premises all ar e true, the conclusion is thereby probably, or likely, true , although not absolutely guaranteed . Inductive arguments thus aim to establish their conclusions with probability, or likelihood, but not with c omplete certainty. An inductive argument does not attempt to guarantee that its conclusion is true ; however, it aims to show that we have good reasons to accept the conclusion as true chance. Admittedly, better than a 50 makes the argument inductive is that it is the kind of argument that done well can give good but less than 100 percent conclusive reason to believe the conclusion. Examples of induction are found in everyday life, where people use less than guaranteed reasoning to go about their daily business. Y cafeteria, so you feel safe eating there later today. Your past experiences do not absolutely perfectly rat following four arguments are also inductive:

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11 * * It has been sunny for ten days in a row, and there a re no clouds in the sky. So probably it will be sunny tomorrow. * * Most dogs are loving animals. Fido is a dog. Therefor e Fido is probably a loving animal. Deduct ive or Inductive? the reasoning is not clearly stated. When trying to decide whether an argument is deductive or inductive, a good rule of thumb is to ask your self: Is the arguer aiming to show that the conclusion is guaranteed to be true, or is he or she aiming only to show that the conclusion is likely to be true, i.e., is probably true but less than certain? clearly, the n there will often be words or other clues indicating which type of argument (deductive or inductive) is intended. If a deductive argument is intended, then the conclusion may be introduced with words or phrases indicating necessity or certainty, such as: It is certain that Absolutely Undeniably, it must be that For sure It is necessarily true that However, if an inductive argument is intended, then the conclusion may be introduced with words or phrases indicating probability, such as: The most reasonab le conclusion is Probably It is likely that It is reasonable to suppose that Some common phrases are found in both deductive and inductive arguments, and thus do not must be the case premises and the conclusion, of both deductive and inductive arguments. Notice, though, that whereas deductive arguments have an air of certainty, confidence, and conclusiven ess, inductive arguments have an air of uncertainty and incompleteness. While a deductive argument claims its conclusion must be true, and with certainty, an inductive argument claims only that if its premises all are true then its conclusion is probable a lthough not completely certain.

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