An Introduction to Critical Thinking and Creativity - always yours

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80 VALID AND SOUND ARGUMENTS 9.2.5 Constructive dilemma A pattern of valid argument with three premises: PorQ. If P then R. If Q then S. ROTS. Either the president is lying, or he is telling the truth. If the president is lying, then he is wicked. If the president is telling the truth, then he is mad. Either the president is wicked, or he is mad. When R is the same as S, this is an equally valid pattern: PorQ. If P then R. If Q then R. R. Either our actions are random, or our actions are determined. If our actions are random, we do not have free will. If our actions are determined, we do not have free will. We do not have free will. 9.2.6 Destructive dilemma See if you can come up with your own example of this pattern of valid argument: Not-Pornot-S. IfPthenP. If Q then S. Not-P or not-Q. 9.2.7 Reductio ad absurdum Reductio ad absurdum is Latin for "reduced to absurdity." It is a method for showing that a certain statement S is false:
PATTERNS OF VALID ARGUMENTS 81 1. First assume that S is true. 2. From the assumption that S is true, show that it leads to a contradiction, or a claim that is false or absurd. 3. Conclude that S must be false. If you can spot connections quickly you might notice that this is none other than an application of modus tollens. As an example, suppose someone claims that a human being's right to life is absolute and so we should never kill or destroy human life. But is this acceptable? If it is, then it follows that when you are being attacked, it will be wrong for you to kill your attacker if this is the only way to prevent yourself from being harmed. But surely this is not correct. Most people would agree that in some situations when your life is threatened you can respond by deadly force, and this is recognized by our legal system. Since the original assumption leads to an absurd conclusion, this entails that the right to life is not absolute. In mathematics, reductio proofs are also known as proofs by contradiction, or indirect proofs. Many well-known proofs, such as the proof that the square root of two is an irrational number, and Euclid's proof that there are infinitely many prime numbers, employ this reductio method. They are beautiful proofs that are easy to understand. If you are interested you can look them up on the Internet quite easily. Self-refuting claims Many self-refuting claims can be shown to be false claims to themselves. Some examples: by applying the • There are only perspectives and there is no such thing as truth. (But then it is a truth that perspectives exist!) • Nothing can be known. (And how do we know that?) • Nothing exists. (Does the sentence exist and whose idea is it?) • All new ideas come from other people. (Where does the first idea come from?) 9.2.8 Combining patterns to form more complex arguments The patterns of valid arguments we have looked at are all rather simple. But they can be combined to form more complex arguments. This valid argument involves three applications of modus tollens:
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Copyright © 2011 by John Wiley & S
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VIII CONTENTS 9 Valid and sound arg
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X PREFACE • This book has a compa
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2 INTRODUCTION Which is more import
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4 INTRODUCTION knowing the rules of
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6 INTRODUCTION 1. The first questio
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8 INTRODUCTION • Open-mindedness:
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12 THINKING AND WRITING CLEARLY Con
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14 THINKING AND WRITING CLEARLY own
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16 THINKING AND WRITING CLEARLY •
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18 THINKING AND WRITING CLEARLY Tip
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20 THINKING AND WRITING CLEARLY g)
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22 DEFINITIONS • The referent of
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24 DEFINITIONS is too wide because
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26 DEFINITIONS sophisticated sense.
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28 DEFINITIONS 3.5.2 Definition by
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Page 46 and 47: 34 NECESSARY AND SUFFICIENT CONDITI
Page 54 and 55: 42 LINGUISTIC PITFALLS ambiguous. A
Page 56 and 57: 44 LINGUISTIC PITFALLS change of di
Page 58 and 59: 46 LINGUISTIC PITFALLS BILLY : All
Page 60 and 61: 48 LINGUISTIC PITFALLS absolve anyb
Page 62 and 63: 50 LINGUISTIC PITFALLS 5.4 GOBBLEDY
Page 64 and 65: 52 LINGUISTIC PITFALLS c) Our cooki
Page 66 and 67: 54 TRUTH false, but we would never
Page 68 and 69: 56 TRUTH matter of linguistic conve
Page 70 and 71: 58 TRUTH i) If Rebecca is Shannon's
Page 72 and 73: 60 BASIC LOGIC 7.1.1 Consistency A
Page 74 and 75: 62 BASIC LOGIC Q, or equivalently,
Page 76 and 77: 64 BASIC LOGIC "or both", or "but n
Page 78 and 79: 66 BASIC LOGIC • PiffQ. • P whe
Page 82 and 83: 70 IDENTIFYING ARGUMENTS of opinion
Page 84 and 85: 72 IDENTIFYING ARGUMENTS it easier
Page 88 and 89: 76 VALID AND SOUND ARGUMENTS This s
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Page 96 and 97: 84 VALID AND SOUND ARGUMENTS 9.4 SO
Page 100 and 101: 88 INDUCTIVE REASONING highly confi
Page 102 and 103: 90 INDUCTIVE REASONING elusion give
Page 104 and 105: 92 INDUCTIVE REASONING tive strengt
Page 108 and 109: 96 ARGUMENT MAPPING Every person is
Page 110 and 111: 98 ARGUMENT MAPPING of arguments ex
Page 112 and 113: 100 ARGUMENT MAPPING elusion. Separ
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Page 116 and 117: 104 ARGUMENT MAPPING a) High school
Page 120 and 121: 108 ARGUMENT ANALYSIS ing. It will
Page 122 and 123: 110 ARGUMENT ANALYSIS As an example
Page 124 and 125: 112 ARGUMENT ANALYSIS b) We should
Page 126 and 127: 114 SCIENTIFIC REASONING or perhaps
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Page 130 and 131: 118 SCIENTIFIC REASONING the planet
Page 132 and 133: 120 SCIENTIFIC REASONING dollars in
Page 134 and 135: 122 SCIENTIFIC REASONING report. Ho
Page 136 and 137: 124 SCIENTIFIC REASONING 13.3 Some
Page 138 and 139: 126 MILLS METHODS 14.1 THE METHOD O
Page 140 and 141: 128 MILLS METHODS 14.3 THE JOINT ME
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130 MILLS METHODS feet is not among
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132 MILLS METHODS d) Situation Cand
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134 REASONING ABOUT CAUSATION Simil
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136 REASONING ABOUT CAUSATION suffe
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138 REASONING ABOUT CAUSATION immor
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140 REASONING ABOUT CAUSATION i) Te
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142 DIAGRAMS OF CAUSAL PROCESSES an
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144 DIAGRAMS OF CAUSAL PROCESSES co
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146 STATISTICS AND PROBABILITY 17.1
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148 STATISTICS AND PROBABILITY •
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150 STATISTICS AND PROBABILITY A mi
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152 STATISTICS AND PROBABILITY On t
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154 STATISTICS AND PROBABILITY 17.4
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156 STATISTICS AND PROBABILITY 4,12
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160 THINKING ABOUT VALUES It is the
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162 THINKING ABOUT VALUES Once thes
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164 THINKING ABOUT VALUES is flat o
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166 THINKING ABOUT VALUES will be c
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168 THINKING ABOUT VALUES Similarly
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170 THINKING ABOUT VALUES 18.2 M Ou
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174 FALLACIES One further clarifica
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176 FALLACIES All circular argument
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178 FALLACIES 19.4.1 Irrelevant res
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180 FALLACIES the question. Murder,
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182 FALLACIES • Non sequitur: Non
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184 FALLACIES g) All my Facebook fr
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186 COGNITIVE BIASES These question
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188 COGNITIVE BIASES • Subjects w
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190 COGNITIVE BIASES more likely to
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192 COGNITIVE BIASES - Avoid framin
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196 ANALOGICAL REASONING a big appe
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198 ANALOGICAL REASONING Furthermor
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202 MAKING RATIONAL DECISIONS 22.1
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204 MAKING RATIONAL DECISIONS So if
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206 MAKING RATIONAL DECISIONS the s
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208 MAKING RATIONAL DECISIONS succe
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210 MAKING RATIONAL DECISIONS about
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212 MAKING RATIONAL DECISIONS EXERC
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216 WHAT IS CREATIVITY? The observa
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218 WHAT IS CREATIVITY? Step 1 : Pr
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220 WHAT IS CREATIVITY? remedy our
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224 CREATIVE THINKING HABITS made o
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226 CREATIVE THINKING HABITS materi
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228 CREATIVE THINKING HABITS orate
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230 CREATIVE THINKING HABITS Ellis
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234 SOLUTIONS TO EXERCISES any of t
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236 SOLUTIONS TO EXERCISES SOLUTION
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242 SOLUTIONS TO EXERCISES 1 l.l.h
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244 SOLUTIONS TO EXERCISES 12.1.f T
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246 SOLUTIONS TO EXERCISES 13.4 One
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250 SOLUTIONS TO EXERCISES 17.3.d T
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252 SOLUTIONS TO EXERCISES 19.2.e F
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Bibliography Ackerman, J., Nocera,
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258 BIBLIOGRAPHY McRae, C, Cherin,
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260 BIBLIOGRAPHY Wolf, G. (1996). S
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262 INDEX consequentialist reasonin
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