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10a chaptertenpowerpoint new

  1. 1. Second Thoughts, 4 th ed. Wanda Teays McGraw-Hill Higher Ed. ©2010. Wanda Teays All rights reserved. CHAPTER TEN Patterns of Deductive Reasoning: Rules of Inference
  2. 2. The Rules of Inference <ul><li>The rules of inference are valid argument forms. </li></ul><ul><li>A familiarity with the rules of inference give us the tools to evaluate arguments and draw inferences. </li></ul><ul><li>This allows us to greatly expand our reasoning capacity. Once we learn the rules of inference, we can spot poorly reasoned arguments, as well as strong ones! </li></ul><ul><li>Having a facility with logic gives us the techniques to examine and evaluate the many kinds of arguments we confront. </li></ul><ul><li>This does not help us develop moral fiber, but it does help us develop mental dexterity . </li></ul>
  3. 3. Validity <ul><li>An argument is valid if the conclusion follows directly from the premises and could not be false if the premises were assumed true. </li></ul><ul><li>This does not mean the premises have to be true! Repeat: A valid argument does not have to have true premises, even if that seems counterintuitive. </li></ul><ul><li>But it does mean that, if we assume they were true, the conclusion would necessarily be true as well. </li></ul><ul><li>FOR EXAMPLE: Rattlesnakes love to stretch out in the sun. </li></ul><ul><li>All creatures that like to stretch out in the sun are lazy lumps. </li></ul><ul><li>Therefore, rattlesnakes are lazy lumps. </li></ul>
  4. 4. Modus Ponens & Modus Tollens <ul><li>Modus ponens is the name of any argument in the following form: </li></ul><ul><li>If A then B. </li></ul><ul><li>A is true. </li></ul><ul><li>Thus, B is also true. </li></ul><ul><li>  </li></ul><ul><li>FOR EXAMPLE:   </li></ul><ul><li>If you buy the jumbo popcorn, then you will need a large drink. </li></ul><ul><li>Y ou bought the jumbo popcorn. </li></ul><ul><li>So you will need a large drink. </li></ul><ul><li>Modus tollens is the name of any argument in the following form: </li></ul><ul><li>If A then B. </li></ul><ul><li>B is not the case. </li></ul><ul><li>Therefore, A is not the case either. </li></ul><ul><li>FOR EXAMPLE: </li></ul><ul><li>If you get the bon bons, you won’t need popcorn. </li></ul><ul><li>Charlie needed popcorn. </li></ul><ul><li>So he did not get the bon bons. </li></ul>
  5. 5. More Valid Argument Forms: Hypothetical Syllogism & the Disjunctive Syllogism <ul><li>The hypothetical syllogism consists of three “if.. .then” claims, where the middle term links the first term to the third. The form is: </li></ul><ul><li>If A then B. If B then C. So, if A then C . </li></ul><ul><li>FOR EXAMPLE: </li></ul><ul><li>If you sing while driving, you’ll be more attentive. </li></ul><ul><li>If you are more attentive, you’ll be a better driver. </li></ul><ul><li>Therefore, if you sing while driving, you’ll be a better driver. </li></ul><ul><li>The disjunctive syllogism starts with an “either..or” claim and one of the disjuncts falls out, so you are left with the other one. The form is: </li></ul><ul><li>Either A or B.| A is not the case. (or B is not the case) So, B is the case. (or A is the case) </li></ul><ul><li>FOR EXAMPLE: </li></ul><ul><li>Either Jamal will get rid of his clunker or he’ll fix it up. </li></ul><ul><li>Jamal did not fix up his clunker. </li></ul><ul><li>So he got rid of it. </li></ul>
  6. 6. More Rules of Inference: Conjunction and Simplification <ul><li>Conjunction is the rule that two claims that are each true are true in combination. The form is this: </li></ul><ul><li>A is true. B is also true. </li></ul><ul><li>So, both A and B are true. </li></ul><ul><li>FOR EXAMPLE: </li></ul><ul><li>Ice is tricky to walk on. </li></ul><ul><li>Mud sticks to your shoes. So, ice is tricky to walk on and mud sticks to your shoes. </li></ul><ul><li>Simplification is the opposite of conjunction. If you know two things together are true, you know each one is true. The form is this: </li></ul><ul><li>A and B are true. </li></ul><ul><li>So, A [or B] is true. </li></ul><ul><li>FOR EXAMPLE: </li></ul><ul><li>Angie likes both skiing and jazz dancing. </li></ul><ul><li>Therefore, Angie likes skiing [ also: Angie likes jazz dancing.] </li></ul>
  7. 7. Logical Addition <ul><li>Logical Addition is NOT a move using mathematics! Logical Addition allows us to expand by going from one thing we know to saying either that OR anything else. The form is this: </li></ul><ul><li>A is true. </li></ul><ul><li>Therefore, either A or B. </li></ul><ul><li>FOR EXAMPLE: </li></ul><ul><li>Randy found it hard to drive in the blizzard. </li></ul><ul><li>Therefore, either Randy found it hard to drive in the blizzard or he was fooling me about how he got the dent in his fender. </li></ul>
  8. 8. The Two Dilemmas <ul><li>CONSTRUCTIVE DILEMMA </li></ul><ul><li>DESTRUCTIVE DILEMMA </li></ul><ul><li>The constructive dilemma is a valid argument with this form: </li></ul><ul><li>If A then B, and, if C then D. </li></ul><ul><li>Either A or B. </li></ul><ul><li>Therefore, either C or D . </li></ul><ul><li>FOR EXAMPLE: </li></ul><ul><li>If I eat the popcorn, I’ll feel guilty, but if I eat carrots, I’ll want popcorn. </li></ul><ul><li>Either I ate popcorn or I ate carrots. </li></ul><ul><li>Therefore, either I felt guilty or I wanted popcorn. </li></ul><ul><li>The destructive dilemma is a valid argument with this form: </li></ul><ul><li>If A then B, and, if C then D. </li></ul><ul><li>Either not B or not D. </li></ul><ul><li>Thus, either not A or not C. </li></ul><ul><li>FOR EXAMPLE: </li></ul><ul><li>If I eat the pretzel, I’ll need a drink, but if I eat ice cream, I’ll want chocolates. </li></ul><ul><li>Either I won’t need a drink or I’ll not want chocolates. </li></ul><ul><li>Thus, either I didn’t eat the pretzel or I didn’t eat the ice cream. </li></ul>
  9. 9. Did you notice? <ul><li>Did you notice anything when you were staring at the two dilemmas? Did little bells ring in your brain? </li></ul><ul><li>Hopefully, yes! </li></ul><ul><li>The constructive dilemma is like a compound modus ponens! </li></ul><ul><li>The destructive dilemma is like a compound modus tollens! </li></ul><ul><li>Remember: </li></ul><ul><li>All these rules of inference are valid argument forms. </li></ul><ul><li>That means any argument in these various forms is a VALID argument! </li></ul>
  10. 10. Our last Rule of Inference: Absorption <ul><li>Absorption is the “sponge rule” —It goes like this: If you have a conditional (“if..then”) claim, you can repeat the antecedent in the consequent for extra emphasis. The form is this: </li></ul><ul><li>If A then B </li></ul><ul><li>Therefore, if A then, A and B. </li></ul><ul><li>FOR EXAMPLE: </li></ul><ul><li>If Carlos stays out in the sun, he’ll need a hat. </li></ul><ul><li>Therefore, if Carlos stays out in the sun, he’ll stay out in the sun and need a hat. </li></ul>
  11. 11. Modus Ponens vs. The Fallacy of Affirming the Consequent <ul><li>Modus Ponens is a valid argument form: </li></ul><ul><li>If A then B. </li></ul><ul><li>A is true. Therefore B is true. </li></ul><ul><li>FOR EXAMPLE: </li></ul><ul><li>If Jasper eats his corn, he’ll want some peas. </li></ul><ul><li>Jasper ate his corn; therefore, he’ll want some peas . </li></ul><ul><li>The Fallacy of Affirming the Consequent is one of the formal fallacies. The form is: </li></ul><ul><li>If A then B. </li></ul><ul><li>B is true. </li></ul><ul><li>Therefore, A is true. </li></ul><ul><li>FOR EXAMPLE: </li></ul><ul><li>If Dan runs out of gas, his car won’t start. </li></ul><ul><li>Dan’s car didn’t start. </li></ul><ul><li>Therefore, he ran out of gas. </li></ul>
  12. 12. Modus Tollens vs. The Fallacy of Denying the Antecedent <ul><li>Modus Tollens is a valid argument form: </li></ul><ul><li>If A then B. </li></ul><ul><li>B is not true. So, A is not true. </li></ul><ul><li>FOR EXAMPLE: </li></ul><ul><li>If the traffic is bad, Jim will be late to the movie. </li></ul><ul><li>Jim wasn’t late to the movie. </li></ul><ul><li>Therefore, the traffic wasn’t bad. </li></ul><ul><li>The Fallacy of Denying the Antecedent is one of the formal fallacies. The form is: </li></ul><ul><li>If A then B. </li></ul><ul><li>A is not true. So, B is not true. </li></ul><ul><li>FOR EXAMPLE: </li></ul><ul><li>If she goes snorkling, Anita will wear sun lotion. </li></ul><ul><li>Anita didn’t go snorkling. </li></ul><ul><li>So, she didn’t wear sun lotion. </li></ul>

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