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Deductive and Inductive Arguments

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Slides from the lecture on deductive and inductive arguments, Phil 57 ("Logic and Critical Reasoning") section 3, San Jose State University.

Slides from the lecture on deductive and inductive arguments, Phil 57 ("Logic and Critical Reasoning") section 3, San Jose State University.

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  • 1. Homework from last time:
    • 2. Another old SNL skit featured a newscaster saying, “In this country, a woman gives birth every 12 minutes. She must be found and stopped.” Explain the ambiguity in the newscaster’s first sentence.
  • 2. Homework from last time:
    • 4. At the movie theater, the ushers try to make sure that no children attend movies with R ratings unless accompanied by an adult parent or guardian. Children ages 2-12 pay one ticket price, and everyone older than 12 pays the adult ticket price. Discuss what is vague about “children” and “adult” here (at least as far as the ushers are concerned). How could a 14-year-old use this vagueness to argue that he should be admitted to an R-rated movie?
  • 3. Homework from last time:
    • 5. Explain what’s wrong with each of these lexical definitions:
    • “ Hamster” means “a small animal.”
    • e. “Overture” means “the orchestral opening to the symphony.”
  • 4. Homework from last time:
    • 6. Discuss the persuasive force of “natural medicines” and of “evidence-based medicine.” Describe the categories these terms pick out. (Are they completely distinct categories?)
  • 5. Homework from last time:
    • 7. Give a verbal extensional definition for “the five senses”. Discuss the limits of this definition (e.g., in conveying information to someone who doesn’t already have a clear understanding of what sense are).
  • 6. Homework from last time:
    • 8. For each of the following pairs of terms, identify whether there is a difference in emotive force between the members of the pair, and whether both members of each pair have the same intensional meaning (i.e., whether they refer to the same things):
    • i. House – home
    • Estate tax – death tax
  • 7. Homework from last time:
    • 8. For each of the following pairs of terms, identify whether there is a difference in emotive force between the members of the pair, and whether both members of each pair have the same intensional meaning (i.e., whether they refer to the same things):
    • k. College – university
    • l. Psychiatrist – shrink
  • 8. Homework from last time:
    • 8. For each of the following pairs of terms, identify whether there is a difference in emotive force between the members of the pair, and whether both members of each pair have the same intensional meaning (i.e., whether they refer to the same things):
    • m. Woman – lady
    • Tolerance – “anything goes”
  • 9. Homework from last time:
    • 8. For each of the following pairs of terms, identify whether there is a difference in emotive force between the members of the pair, and whether both members of each pair have the same intensional meaning (i.e., whether they refer to the same things):
    • o. Undocumented immigrant – illegal immigrant
    • p. Tuition payer -- student
  • 10. Homework from last time:
    • 9. Formulate an operational definition for “hot” in “This jalapeño is hot.”
  • 11. Deductive and Inductive Arguments Phil 57 section 3 San Jose State University Fall 2010
  • 12. Arguments:
    • Include at least one claim that is a conclusion , plus one or more other claims ( premises ) that offer support for the conclusion.
    • Arguments make a factual claim (that the premises are true) and an inferential claim (that the premises support the conclusion)
  • 13. Arguments: form vs. content.
    • To assess the inferential claim (the premises lead logically to the conclusion), need to look at the form of the argument, not the content.
  • 14. Arguments: form vs. content.
    • (a) If taxes increase, them inflation will increase.
    • Taxes will increase.
    • Thus, inflation will increase.
    • (b) If I drink coffee after 8 PM, I have a hard time getting to sleep.
    • I drank coffee after 8 PM.
    • So, I had a hard time getting to sleep.
  • 15. Arguments: form vs. content.
    • If P, then Q.
    • P
    • Therefore, Q.
    • (Same pattern of reasoning, even though the specific claims P and Q are different.)
  • 16. Arguments: form vs. content.
    • (c) All beans are legumes.
    • All legumes are high in dietary fiber.
    • Thus, all beans are high in dietary fiber.
    • (d) All birds are animals.
    • All animals are mammals.
    • So, all birds are mammals.
  • 17. Arguments: form vs. content.
    • All A are B.
    • All B are C
    • Therefore, all A are C.
    • (Same pattern of reasoning, even though the specific claims A, B, and C are different.)
  • 18. Arguments: form vs. content.
    • To work out the logical form of the argument, assign letters for the specific claims, leaving just the logical phrases.
    • If the logical form of an argument is good (i.e., premises really do support conclusion), it’s good no matter what the content of the argument.
  • 19. Validity
    • An argument is valid when, if its premises are true, it is impossible for its conclusion to be false.
    • (Arguments (a), (b), (c), and (d) are all valid.)
    • Validity is a formal property of the argument.
    • (Depends on form, not content)
  • 20. Soundness
    • An argument is sound when it is valid and when all of its premises are true.
    • (Arguments (b) and (c) are sound; (a) might be sound, (d) is not sound.)
    • Soundness depends on both the form (because the argument must be valid) and the content (because the premises must be true).
  • 21. Validity and soundness
    • If whales are insects, then humans are reptiles.
    • Whales are insects.
    • Thus, humans are reptiles.
  • 22. Validity and soundness
    • If whales are insects, then humans are reptiles.
    • Whales are insects.
    • Thus, humans are reptiles.
    • If P, then Q
    • P
    • Thus, Q
  • 23. Validity and soundness
    • If whales are insects, then humans are reptiles.
    • Whales are insects.
    • Thus, humans are reptiles.
    • If P, then Q
    • P
    • Thus, Q (valid)
  • 24. Validity and soundness
    • If whales are insects, then humans are reptiles.
    • Whales are insects.
    • Thus, humans are reptiles.
    • If P, then Q
    • P
    • Thus, Q (valid)
    • But premises are false (not sound)
  • 25. Validity and soundness
    • If humans are mammals, then whales are mammals.
    • Whales are mammals.
    • Thus, humans are mammals.
  • 26. Validity and soundness
    • If humans are mammals, then whales are mammals.
    • Whales are mammals.
    • Thus, humans are mammals.
    • If P, then Q
    • Q
    • Thus, P
  • 27. Validity and soundness
    • If humans are mammals, then whales are mammals.
    • Whales are mammals.
    • Thus, humans are mammals.
    • If P, then Q
    • Q
    • Thus, P (not a valid pattern!)
  • 28. Validity and soundness
    • If humans are mammals, then whales are mammals.
    • Whales are mammals.
    • Thus, humans are mammals.
    • If P, then Q
    • Q
    • Thus, P (not a valid pattern!)
    • If invalid, can’t be sound.
  • 29. Is a sound argument always a good argument?
    • All mammals are animals.
    • Thus, all mammals are animals.
  • 30. Is a sound argument always a good argument?
    • All mammals are animals.
    • Thus, all mammals are animals.
    • Premise clearly supports conclusion. (valid)
  • 31. Is a sound argument always a good argument?
    • All mammals are animals.
    • Thus, all mammals are animals.
    • Premise clearly supports conclusion. (valid)
    • Premise is true. (sound)
  • 32. Is a sound argument always a good argument?
    • All mammals are animals.
    • Thus, all mammals are animals.
    • Premise clearly supports conclusion. (valid)
    • Premise is true. (sound)
    • But, it’s a circular argument .
    • (Premise is the same as the conclusion)
  • 33. Because validity is a formal property of an argument:
    • Can have valid argument with false premises and a false conclusion.
    • All squares are triangles.
    • All triangles are circles.
    • Thus, all squares are circles.
  • 34. Because validity is a formal property of an argument:
    • Can have valid argument with false premises and a false conclusion.
    • All squares are triangles.
    • All triangles are circles.
    • Thus, all squares are circles.
    • All A are B
    • All B are C
    • Thus, all A are C.
  • 35. Because validity is a formal property of an argument:
    • Can have valid argument with false premises and a true conclusion.
    • All squares are circles.
    • All circles are rectangles.
    • Thus, all squares are rectangles.
  • 36. Because validity is a formal property of an argument:
    • Can have valid argument with false premises and a true conclusion.
    • All squares are circles.
    • All circles are rectangles.
    • Thus, all squares are rectangles.
    • All A are B
    • All B are C
    • Thus, all A are C.
  • 37. Because validity is a formal property of an argument:
    • But, when the logical form is valid, if premises are true, conclusion must be true!
  • 38. Consider this argument:
    • All squares are polygons.
    • All rectangles are polygons.
    • Thus, all squares are rectangles.
  • 39. Consider this argument:
    • All squares are polygons.
    • All rectangles are polygons.
    • Thus, all squares are rectangles.
    • Premises, conclusion are true.
  • 40. Consider this argument:
    • All squares are polygons.
    • All rectangles are polygons.
    • Thus, all squares are rectangles.
    • Premises, conclusion are true.
    • But not a valid argument.
  • 41. Consider this argument:
    • All squares are polygons.
    • All rectangles are polygons.
    • Thus, all squares are rectangles.
    • Premises, conclusion are true.
    • But not a valid argument.
    • All A are C
    • All B are C
    • Thus, all A are B (NOT a valid pattern!)
  • 42. How to recognize a bad pattern:
    • All A are C
    • All B are C
    • Thus, all A are B (NOT a valid pattern!)
  • 43. How to recognize a bad pattern:
    • All A are C
    • All B are C
    • Thus, all A are B (NOT a valid pattern!)
    • Find content (A, B, C) that makes premises true but conclusion false.
  • 44. How to recognize a bad pattern:
    • All A are C
    • All B are C
    • Thus, all A are B (NOT a valid pattern!)
    • Find content (A, B, C) that makes premises true but conclusion false.
    • All cats are animals.
    • All dogs are animals.
    • All cats are dogs.
  • 45. Deductive vs. inductive arguments:
    • The valid arguments we’ve been discussing are deductive arguments. ( If premises are true, conclusion must be true. )
    • There are some arguments where premises support conclusion but do not guarantee that it’s true. ( Inductive arguments.)
  • 46. An inductive argument:
    • Last time I went to the beach, I got a sunburn and an ear-ache.
    • The time before that when I went to the beach, I got a sunburn and an ear-ache.
    • Thus ( probably ) next time I go to the beach I will get a sunburn and an ear-ache.
  • 47. Homework:
    • 1. Explain the difference between the form of an argument and the content of an argument, using an example in your explanation.
  • 48. Homework:
    • 2. Define a valid argument . Is validity a formal property of an argument or a content based property of an argument?
  • 49. Homework:
    • 3. Define a sound argument . Is soundness a formal property of an argument or a content based property of an argument?
  • 50. Homework:
    • 4. Explain why a sound argument cannot have a false conclusion. (Your explanation can take the form of an argument involving the definitions of validity and soundness.)
  • 51. Homework:
    • 5. Give an example of a valid argument whose premises are actually false and whose conclusion is actually true.
  • 52. Homework:
    • 6. Define an invalid argument .
  • 53. Homework:
    • 7. Can a valid argument have all its premises be actually true and its conclusion be actually false?
  • 54. Homework:
    • 8. Give an example of an argument that is both valid and sound but is still not persuasive.
  • 55. Homework:
    • 9. Recall that arguments make both factual claims (that the premises are true) and inferential claims (that the premises support the conclusion). Which of these claims are false in an invalid argument? In a valid argument that is unsound?
  • 56. Homework:
    • 10. Define an inductive argument . Explain how the inferential claim made by an inductive argument differs from that of a deductive argument.