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Inductive, Deductive, and Fallacies

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Inductive, Deductive, and Fallacies

  1. 1. Deductive and Inductive Reasoning and fallacies Darnell Kemp Adapted from westmwires website
  2. 2. An Argument  Claim – the writer’s main idea or point (not just opinion, arguable)  Evidence – to support the claim  Refutation –discussion of opposing viewpoint  Conclusion – a restatement of claim or call to action
  3. 3. Deductive vs. Inductive Reasoning The difference:  Inductive reasoning uses patterns to arrive at a conclusion (conjecture)  Deductive reasoning uses facts, rules, definitions or properties to arrive at a conclusion.
  4. 4. Examples of Inductive Reasoning  Every quiz has been easy. Therefore, the test will be easy.  The teacher used PowerPoint in the last few classes. Therefore, the teacher will use PowerPoint tomorrow.  Every fall there have been hurricanes in the tropics. Therefore, there will be hurricanes in the tropics this coming fall.
  5. 5. Example of Deductive Reasoning An Example: The catalog states that all entering freshmen must take a mathematics placement test. You are an entering freshman. Conclusion: You will have to take a mathematics placement test.
  6. 6. 1. Inductive or Deductive Reasoning? Geometry example… 60◦ x Triangle sum property - the sum of the angles of any triangle is always 180 degrees. Therefore, angle x = 30°
  7. 7. 2. Inductive or Deductive Reasoning? Geometry example…
  8. 8. 3.
  9. 9. Deductive Reasoning  Deductive Reasoning – A type of logic in which one goes from a general statement to a specific instance.  The classic example All men are mortal. (major premise) Socrates is a man. (minor premise) Therefore, Socrates is mortal. (conclusion) The above is an example of a syllogism.
  10. 10. Deductive Reasoning  Syllogism: An argument composed of two statements or premises (the major and minor premises), followed by a conclusion. Premise A:Governments that fail to ensure people the God given rights of life, liberty, and the pursuit of happiness should be abolished. Premise B: The King has been destructive of the colonists’ rights. Conclusion: “We, therefore” are absolved from the British Crown, have no political connections, and are now “free and independent states.” The Declaration of Independence. The most famous syllogistic argument
  11. 11. Deductive Reasoning Examples: All students eat pizza. Emily is a student at Fullerton College. Therefore, Emily eats pizza. All athletes work out in the gym. Colin Kapernik is an athlete. Therefore, Colin Kapernik works out in the gym.
  12. 12. Valid and Sound  A deductive argument is valid if the premises logically lead to the conclusion  A deductive argument is sound if the premises are actually true  So it is possible for an argument to be valid but not true
  13. 13. Example of valid but not sound All math teachers are over 7 feet tall. Mr. P is a math teacher. Therefore, Mr. P is over 7 feet tall.  This argument is valid, but is certainly not true.  The above examples are of the form If p, then q. (major premise) x is p. (minor premise) Therefore, x is q. (conclusion)
  14. 14. Examples  No one who can afford health insurance is unemployed. All politicians can afford health insurance. Therefore, no politician is unemployed. 4. VALID OR INVALID????? Valid = the premises logically lead to the conclusion Sound = the premises are actually true
  15. 15. Example  Some professors wear glasses. Mr. Einstein wears glasses. Therefore, Mr. Einstein is a professor. 5. VALID OR INVALID?????
  16. 16. Inductive Reasoning Inductive Reasoning, involves going from a series of specific cases to a general statement. The conclusion in an inductive argument is never guaranteed. 6. What is the next number in the sequence 6, 13, 20, 27,…? There is more than one correct answer.
  17. 17. Inductive Reasoning  Here’s the sequence again 6, 13, 20, 27,…  Look at the difference of each term.  13 – 6 = 7, 20 – 13 = 7, 27 – 20 = 7  Thus the next term is 34, because 34 – 27 = 7.  However what if the sequence represents the dates. Then the next number could be 3 (31 days in a month).  The next number could be 4 (30 day month)  Or it could be 5 (29 day month – Feb. Leap year)  Or even 6 (28 day month – Feb.)
  18. 18. All bats are mammals. All mammals are warm-blooded. So, all bats are warm-blooded. All arguments are deductive or inductive. Deductive arguments are arguments in which the conclusion is claimed or intended to follow necessarily from the premises. Inductive arguments are arguments in which the conclusion is claimed or intended to follow probably from the premises. 7. Is the argument above deductive or inductive?
  19. 19. All bats are mammals. All mammals are warm-blooded. So, all bats are warm-blooded. Deductive. If the premises are true, the conclusion, logically, must also be true.
  20. 20. Kristin is a law student. Most law students own laptops. So, probably Kristin owns a laptop. In the example above, the word probably shows that the argument is inductive. Arguments by elimination are arguments that seek to logically rule out various possibilities until only a single possibility remains. Arguments of this type are always deductive. Either Kurt voted in the last election, or he didn't. Only citizens can vote. Kurt is not, and has never been, a citizen. So, Kurt didn't vote in the last election.
  21. 21. Tess: Are there any good Italian restaurants in town? Don: Yeah, Luigi's is pretty good. I've had their Neapolitan rigatoni, their lasagna col pesto, and their mushroom ravioli. I don't think you can go wrong with any of their pasta dishes. 8. Based on what you've learned, is this argument deductive or inductive? How can you tell?
  22. 22. Don: Yeah, Luigi's is pretty good. I've had their Neapolitan rigatoni, their lasagna col pesto, and their mushroom ravioli. I don't think you can go wrong with any of their pasta dishes. Inductive.
  23. 23. I wonder if I have enough cash to buy my psychology textbook as well as my biology and history textbooks. Let's see, I have $200. My biology textbook costs $65 and my history textbook costs $52. My psychology textbook costs $60. With taxes, that should come to about $190. Yep, I have enough. 9. Is this argument deductive or inductive? How can you tell?
  24. 24. Mother: Don't give Billy that brownie. It contains walnuts, and I think Billy is allergic to walnuts. Last week he ate some oatmeal cookies with walnuts and he broke out in a severe rash. Father: Billy isn't allergic to walnuts. Don't you remember he ate some walnut fudge ice cream at Melissa's birthday party last spring? He didn't have any allergic reaction then. 10. Is the father's argument deductive or inductive? How can you tell?
  25. 25. What is a fallacy?  A FALLACY is an argument in which the premises do not justify the conclusion as a matter of logic. An argument can be fallacious for many reasons. The argument might mis-apply a legitimate rule of logic. Or it might omit a crucial premise or misconstrue a premise. Or it might misconstrue the conclusion.
  26. 26. Fallacies in action  Watch the video below titled:  “She’s a witch”  11. Write down any parts of an argument you hear.  Now, on the next slide, look how it breaks down.
  27. 27. The argument  First, inductive – the mob attempts to arrive at conclusion by using evidence ◦ Witch’s nose, clothing, hat, and wart ◦ All false premises except wart ◦ Non-witches have warts 1. The failed inductive argument: The woman has a witch's nose, (false premise) 2. and [she is wearing] witch's clothing, (false premise) 3. and [she is wearing] a witch's hat. (false premise) 4. She has a wart (insufficient for the conclusion) 5. Only witches have witches' noses, clothing, hats, and warts. 6. Therefore, she's a witch!
  28. 28. Sir Bedevere's Deductive Argument 1. If she weighs the same as a duck, she'll float. (false, confuses weight with density) 2. she does weigh the same as a duck; (true in this case, if the scales are to be trusted) 3. [conclusion #1] Therefore, she'll float. (valid but unsound) 4. If she floats, she is made of wood. (false, many other things float) 5. She does float; (false/based on conclusion #1) 6. [conclusion #2] Therefore, she's made of wood. (valid but unsound) 7. If she's made of wood, she's a witch. (assumed by all in the scene to be true) 8. She is made of wood; (false/based on conclusion #2) 9. [conclusion #3] Therefore, she's a witch! (valid but unsound) Valid = the premises logically lead to the conclusion Sound = the premises are actually true Slides 35 and 36 from Mooney’s Theology Blog
  29. 29. 11. Argument can fail for two reasons:  Factual Error  Error in logic ◦ Deductive argument premises fail to provide conclusive support for the conclusion. ◦ Inductive argument premises fail to provide even probable support for the conclusion.
  30. 30. Fallacies of Relevance – reason or conclusion is irrelevant to the argument  Straw man – a misrepresentation of opponents argument  Ad Hominem  Red Herring – the example is this one  Two wrong  False authority  Appeal to popular opinion  Begging the question  Non sequitur (claims cause & effect but there really is none)  Evasion See Fallacies of Relevance Example below and write on chart (just the name of the commercial)
  31. 31. Causal reasoning fallacies – cause doesn’t make sense  Post hoc, ergo propter hoc – example for this one  Slippery slope  Rationalization  False cause  See Example below and add to chart
  32. 32. False generalization – not enough info for conclusion  Hasty generalization – This is a conclusion based on insufficient or biased evidence (example page 360 textbook)  False analogy  Either or  Over simplification  See example below and add as example for hasty generalization “You Hate Children”
  33. 33. Fallacies of Ambiguity  Equivocation - It is the misleading use of a term with more than one meaning or sense (by glossing over which meaning is intended at a particular time). ◦ Example - Noisy children are a real headache. Two aspirin will make a headache go away. Therefore, two aspirin will make noisy children go away.  Example of numerous fallacies  Take some notes on what you hear?
  34. 34. Some quotes from ad (add to fallacy chart)  “Americans are under attack from Islamic extremists in every corner of the world”  “…lesbians and feminists are attacking everything sacred”  What does every or everything tell you? Which fallacy?  “…Jackson and Sharpton claim the answer is racial quotas”  Does this sound like an extreme representation of their position?  “The aliens are here but they didn't come in a spaceship they came across our unguarded Mexican border.”  How is aliens doubly used? Which fallacy?
  35. 35. Some quotes from ad (add to fallacy chart)  “Americans are under attack from Islamic extremists in every corner of the world”  “…lesbians and feminists are attacking everything sacred”  Hasty Generalization (write these examples on chart)  “…Jackson and Sharpton claim the answer is racial quotas”  Strawman (write this example on your chart)  “The aliens are here but they didn't come in a spaceship they came across our unguarded Mexican border.”  Equivocation (write this example on your chart)
  36. 36. An explanation of my personal pet peeve and just a really cute one  Begs the Question (see below)  Fallacies in Mean Girls (see below)

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