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6.6 Argument Forms

6.6 Argument Forms. A sound deductive argument is valid and has true premises. A deductive argument is one in which it is claimed that the conclusion necessarily follows from the premises. That is, it is claimed that it is valid. .

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6.6 Argument Forms

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  1. 6.6 Argument Forms

  2. A sound deductive argument is valid and has true premises. • A deductive argument is one in which it is claimed that the conclusion necessarily follows from the premises. That is, it is claimed that it is valid.

  3. A valid argument is one in which it is impossible for the premises to be true and the conclusion false. • Or, • If the premises are true, the conclusion must be true. • Or, • There is no line on the truth table (no possible world) where the premises are true and the conclusion is false.

  4. Valid • If James does well on the LSAT, then he will go to law school. James does well on the LSAT; therefore, he will go to law school.

  5. Valid • If James does well on the LSAT, then he will go to law school.James does well on the LSAT; therefore, he will go to law school. • P1. J  L • P2. J • C.  L

  6. Valid

  7. Invalid • If James does well on the LSAT, then he will go to law school. James will go to law school; so he does well on the LSAT.

  8. Invalid • If James does well on the LSAT, then he will go to law school. James will go to law school; so he does well on the LSAT. • P1. J  L • P2. L • C.  J

  9. Invalid

  10. Valid • P1. J  L • P2. J • C.  L Invalid P1. J  L P2. L C.  J

  11. Valid • P1. J L • P2. J • C.  L Invalid P1. J L P2. L C.  J

  12. P1. If Renée is from CA, then she runs marathons. • P2. Renée is from CA. • So, she runs marathons. • P1. If God exists, then life has meaning. • P2. God exists. • C. Therefore, life has meaning. • P1. Monkeys eat tulips. • P2. If monkeys eat tulips, then grape nuts are healthy. • C. So, grape nuts are healthy.

  13. P1. If Renée is from CA, then she runs marathons. • P2.Renée is from CA. • C. So, she runs marathons. • P1. If God exists, then life has meaning. • P2.God exists. • C. Therefore, life has meaning. • P1. Monkeys eat tulips. • P2. If monkeys eat tulips, then grape nuts are healthy. • C. So, grape nuts are healthy.

  14. Validity has to do with the form of the argument, not its content. • We can see the form by translating an argument into propositional logic. • Then, using a truth table we can see whether or not the argument is valid.

  15. Valid Argument Forms • Arguments with certain forms are always valid. • P  Q • P • Q

  16. Valid Argument Forms • Modus Ponens (MP) • P  Q • P • Q • VALID

  17. Valid Argument Forms • Arguments with certain forms are always invalid. • P  Q • Q • P

  18. Valid Argument Forms • Affirming the consequent (AC) • P  Q • Q • P • INVALID

  19. Valid Argument Forms • Modus Tollens (MT) • P  Q • ~Q • ~P • VALID

  20. Valid Argument Forms • Modus Tollens (MT) • P  Q / ~Q // ~P

  21. Valid Argument Forms • Denying the Antecedent (DA) • P  Q • ~P • ~Q • INVALID

  22. Valid Argument Forms • Denying the Antecedent (DA) • P  Q / ~P // ~Q

  23. Disjunctive Syllogism (DS) • P v Q P v Q • ~P ~Q • Q P • VALID

  24. Affirming a Disjunct (AD) • P v Q P v Q • P Q • Q (or ~Q) P (or ~P) • INVALID

  25. (Pure) Hypothetical Syllogism (HS) • P  Q • Q  R • P  R

  26. Constructive Dilemma (CD) • (P  Q) • (R  S) • P v R • Q v S • VALID

  27. Constructive Dilemma (CD) • (P  Q)• (R  S) • P v R • Q v S • VALID

  28. Constructive Dilemma (CD) • (P  Q) • (R  S) • P v R • Q v S • VALID

  29. Constructive Dilemma (CD) • (P  Q)• (R  S) • P v R • Q v S • VALID

  30. Destructive Dilemma (DD) • (P  Q) • (R  S) • ~Q v ~S • ~P v ~R • VALID

  31. Destructive Dilemma (DD) • (P  Q)• (R  S) • ~Q v ~S • ~P v ~R • VALID

  32. Destructive Dilemma (DD) • (P  Q) • (R  S) • ~Q v ~S • ~P v ~R • VALID

  33. Destructive Dilemma (DD) • (P  Q)• (R  S) • ~Q v ~S • ~P v ~R • VALID

  34. Recognize argument forms by recognizing types of statements, patterns   

  35. Recognize argument forms by recognizing types of statements (F v P)(G  O) (F v P) (G  O)

  36. Premises can be put in any order • D v (K • J) • (D  F) • [(K • J)  H] • F v H

  37. Premises can be put in any order • Dv(K • J) • (D  F)•[(K • J)  H] • FvH • Given a conjunction of 2 conditionals and the disjunction of each of their antecedents, one can validly derive the disjunction of each of their consequents.

  38. Think of negations as “opposite truth value” or the “denial of P” • ~A v B H  ~S • AS • B ~H

  39. 1. • N  C • ~C • ~N

  40. 1. MT • N  C • ~C • ~N

  41. 2. • S  F • F  ~L • S  ~L

  42. 2. HS • S  F • F  ~L • S  ~L

  43. 3. • A v ~Z • ~Z • A

  44. 3. Invalid (AD) • A v ~Z • ~Z • A

  45. 4. • (S  ~P) • (~S  D) • S v ~S • ~P v D

  46. 4. CD • (S  ~P) • (~S  D) • S v ~S • ~P v D

  47. 5. • ~N • ~N  T • T

  48. 5. MP • ~N • ~N  T • T

  49. 6. • M v ~B • ~M • ~B

  50. 6. DS • M v ~B • ~M • ~B

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