Critical Thinking Chapter 3 Basic Logical Concepts Please

What We Are Concerned With: l In evaluating argument, one should ask: Are the premises true? l Do the premises provide good reasons to accept the conclusion? l l We will look at the latter question in this chapter. Lecture Notes © 2008 Mc. Graw Hill Higher Education 2

Example: l Take this argument: 1. 2. 3. l l Premise 1: If the moon is made of green cheese then you will score perfectly on the next exam. Premise 2: The moon is made of green cheese. Conclusion: Therefore, you will score perfectly on the next exam. Even though premises 1 & 2 are false, they still provide good reason to accept the conclusion. We’ll see “truth evaluation” in chapter 8. Lecture Notes © 2008 Mc. Graw Hill Higher Education 3

Deduction vs. Induction l Deductive Arguments - inescapable logic: 1. 2. 3. l All humans are mortal. Socrates is a human. Therefore, Socrates is mortal. Inductive Arguments conclusion is plausible (likely or probable), given the premises: 1. 2. So far, for every class, the professor has worn a tie. Therefore, next class, the professor will wear a tie. Lecture Notes © 2008 Mc. Graw Hill Higher Education 4

Telling the difference between Deductive and Inductive Arguments l Indicator Words: Deductive: certainly, definitely, this entails that, conclusively l Inductive: probably, likely, one would expect, odds are, reasonable to assume l Lecture Notes © 2008 Mc. Graw Hill Higher Education 5

Common Patterns of Deductive Reasoning 1. 2. 3. 4. 5. Hypothetical Syllogism Categorical Syllogism Argument by Elimination Argument Based on Mathematics. Argument from Definition Lecture Notes © 2008 Mc. Graw Hill Higher Education 6

Common Patterns of Deductive Reasoning 1 Hypothetical Syllogism: l l If A then B. A. Therefore B. (Modus Ponens) If P then Q. if Q then R. Therefore if P then R. (chain argument) If only A then B. Not B. Therefore not A. (Modus Tollens) Deductive but invalid versions: l If A then B. Not A. Therefore not B. (denying the antecedent) l l If I am female then I am a person. I am not female. Therefore I am not a person. If A then B. B. Therefore A. (affirming the consequent). l If we’re on Krypton then we are in the solar system. We are in the solar system. Therefore, we’re on Krypton. Lecture Notes © 2008 Mc. Graw Hill Higher Education 7

Common Patterns of Deductive Reasoning 2 Categorical Syllogism: l Example Forms: l l All a’s are b’s. All b’s are c’s. Therefore, all a’s are c’s. Example: l l l All oaks are trees All trees are plants. So all oaks are plants. Lecture Notes © 2008 Mc. Graw Hill Higher Education 8

Common Patterns of Deductive Reasoning 3 Argument by Elimination: rule out various possibilities until only a single possibility remains. l Example forms: l l A or B. Not B. Therefore A. P or Q. if A then not P. A. Therefore Q. Lecture Notes © 2008 Mc. Graw Hill Higher Education 9

Common Patterns of Deductive Reasoning 4 Argument based on Mathematics: l Example forms: l l There are four a’s and two b’s. Therefore there are six things all together. Example: 1. 2. 3. Eight is greater than four. Four is greater than two. Therefore, eight is greater than two. Lecture Notes © 2008 Mc. Graw Hill Higher Education 10

Common Patterns of Deductive Reasoning 5 Argument from definition: the conclusion is true in virtue of the definition of some keyword or phrase. l Example: l Quah is a bachelor. Therefore Quah is unmarried. Lecture Notes © 2008 Mc. Graw Hill Higher Education 11

Common Patterns of Inductive Reasoning 1. 2. 3. 4. 5. 6. Inductive generalization Predictive argument Augment from authority Causal Argument Statistical Argument from Analogy Lecture Notes © 2008 Mc. Graw Hill Higher Education 12

Common Patterns of Inductive Reasoning 1 Inductive generalization: drawing a generalization as a likely conclusion from observations. l Example: 1. 2. All dinosaur bones found so far have been over 65 million years old. Therefore all dinosaur bones found will be over 65 million years old. Lecture Notes © 2008 Mc. Graw Hill Higher Education 13

Common Patterns of Inductive Reasoning 2 Predictive argument: l l l Prediction: a statement about what will happen in the future. Predictive argument: an argument that has, as a conclusion, a prediction. Example: l l Most U. S. presidents have been tall. Therefore, the next president will be tall. Lecture Notes © 2008 Mc. Graw Hill Higher Education 14

Common Patterns of Inductive Reasoning 3 Augment from authority: citing some presumed authority or witness. l Example: l The Encyclopedia says that bats eat bugs; therefore it is likely that bats eat bugs. Lecture Notes © 2008 Mc. Graw Hill Higher Education 15

Common Patterns of Inductive Reasoning 4 Causal Argument: asserts something is the cause of something else. l Example: l There are some dinosaur footprints. A dinosaur must have been here. Lecture Notes © 2008 Mc. Graw Hill Higher Education 16

Common Patterns of Inductive Reasoning 5 Statistical Argument: l Example: 1. 2. 3. 83% of Notre Dame students are Catholic. Bob is a Notre Dame student. Therefore Bob is probably Catholic. Lecture Notes © 2008 Mc. Graw Hill Higher Education 17

Common Patterns of Inductive Reasoning 6 Arguing from Analogy: 1. 2. 3. Victoria Park is a great amusement park and it has a great roller coaster. Beckham Park is a great amusement park. Beckham Park probably has a great roller coaster. Lecture Notes © 2008 Mc. Graw Hill Higher Education 18

Deductive Validity l. A valid deductive argument is an argument in which it is impossible for all the premises to be true and the conclusion false. Lecture Notes © 2008 Mc. Graw Hill Higher Education 19

Deductive Validity l Valid arguments: The validity of an argument has nothing to do with the truth of its premises. If the premises would guarantee the conclusion if the premises were true, then the argument is valid. l Valid argument: 1. 2. 3. All squares are circles. All circles are triangles. Therefore, all squares are triangles. Lecture Notes © 2008 Mc. Graw Hill Higher Education 20

Deductive Invalidity l Invalid deductive arguments: deductive arguments whose premises do not guarantee their conclusion. (i. e. , they have bad deductive form. ) 1. 2. 3. All dogs are animals. Snoopy is an animal. Therefore, Snoopy is a dog. Lecture Notes © 2008 Mc. Graw Hill Higher Education 21