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Introductory Logic PHI 120

Presentation: "Truth Tables – Validity vs. Soundness". Introductory Logic PHI 120. This PowerPoint Presentation contains a large number of slides, a good many of which are nearly identical. If you print this Presentation, I recommend six or nine slides per page. Homework.

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Introductory Logic PHI 120

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  1. Presentation: "Truth Tables – Validity vs. Soundness" Introductory LogicPHI 120 This PowerPoint Presentation contains a large number of slides, a good many of which are nearly identical. If you print this Presentation, I recommend six or nine slides per page.

  2. Homework • Study Allen/Hand Logic Primer • Sec. 1.1, p. 2: “soundness” • Sec. 2.2, p. 45, “incompatible premises” • Ex. 2.2: i-xii

  3. Validity: An argument is valid if and only if: • if all of its premises are true • its conclusion is true. • Corollary: It is impossible for a valid argument to have: • all true premises • false conclusion P & Q, ~P ⊢ R Validity vs. soundness

  4. Validity vs. Soundness Valid Argument • No invalidating assignment Criteria of a Sound Argument • argument is valid and • all premises are True. Valid but Unsound • no invalidating assignment • not all premises true Invalidating Assignment (1) conclusion is False (2) all premises are True

  5. Incompatible Premises

  6. Incompatible Premises Atomic statements MUST be written in alphabetical order

  7. Incompatible Premises

  8. Incompatible Premises

  9. Incompatible Premises

  10. Incompatible Premises

  11. Incompatible Premises

  12. Incompatible Premises

  13. Incompatible Premises

  14. Incompatible Premises

  15. Incompatible Premises

  16. Incompatible Premises

  17. Incompatible Premises

  18. Incompatible Premises

  19. Incompatible Premises

  20. Incompatible Premises

  21. Incompatible Premises

  22. Incompatible Premises Testing for Validity: Find the Invalidating Assignment

  23. Incompatible Premises

  24. Incompatible Premises

  25. Incompatible Premises

  26. Incompatible Premises

  27. Incompatible Premises

  28. Incompatible Premises No Invalidating Assignment So the argument is valid

  29. p. 45 Incompatible Premises

  30. Validity vs. Soundness Valid Argument • Impossible for conclusion to be False and all premises True Sound Argument • An argument is sound if and only if it is valid and all its premises are true. Valid but Unsound • No invalidating assignment • Not all premises true

  31. Determine truth-values of: • atomic statements • negations of atomics • inside parentheses • negation of the parentheses • any remaining connectives Truth Tables Sequents

  32. Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency. ~P, R v ~P <-> P v Q ⊢ ~Q First, identify the governing connectives.

  33. Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency. ~P, R v ~P <-> P v Q ⊢ ~Q First, identify the governing connectives.

  34. Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency. ~P, R v ~P <-> P v Q ⊢ ~Q First, identify the governing connectives.

  35. Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency. ~P, (R v ~P)<->(P v Q)⊢ ~Q The second premise is a complex binary: Φ <-> Ψ

  36. Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency. ~P, R v ~P <-> P v Q ⊢ ~Q The conclusion is a negation.

  37. Truth Tables – Sequents construct the truth table

  38. ~P, R v ~P <-> P v Q ⊢ ~Q Determine the number of rows for the sequent 23 simple statements = 8 rows

  39. Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency. _ __ Valid ____ Invalid

  40. Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency. _ __ Valid ____ Invalid

  41. Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency. _ __ Valid ____ Invalid Alphabetical Sequence!

  42. Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency. _ __ Valid ____ Invalid

  43. Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency. _ __ Valid ____ Invalid

  44. Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency. _ __ Valid ____ Invalid

  45. Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency. _ __ Valid ____ Invalid

  46. Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency. _ __ Valid ____ Invalid

  47. Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency. _ __ Valid ____ Invalid

  48. Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency. (R v ~P)<->(P v Q) _ __ Valid ____ Invalid

  49. Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency. (R v ~P)<->(P v Q) _ __ Valid ____ Invalid

  50. Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency. _ __ Valid ____ Invalid

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