Modern Logic (Propositional Calculus)

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Created by
Margaux

Cards (7)

  • Difference between Aristotelian Logic and Propositional Calculus
    • Artisolean logic tends to use the words “all” and “some” in making generalizations in the first premise. 
    • However, propositional calculus uses more defined words such as “and”, “or”, if… then”, “not” and “therefore” in their more-formulaic ways of formatting arguments.
  • Simplification

    p.q
    —————
    ∴ p
    Example:
    Cats are yummy and dogs are yummy
    —————
    Therefore cats are yummy
  • Addition

    p
    —————
    ∴ p v q
    Example:
    Cats are weird
    —————
    Therefore cats are weird or dogs are weird (both may be true)
  • Conjunction

    p
    q
    —————
    ∴ p.q
    Example:
    Cats are yummy grilled
    Dogs are yummy grilled
    —————
    Cats and dogs are yummy grilled
  • Disjunction

    p v q
    ~ p
    —————
    ∴ q
    Example:
    Cats or dogs are tall
    Cats are not tall
    —————
    Dogs are tall
  • Given = A.B      Prove = A.D
    (AvC) ⊃ (D) 
    A.B 
    A [ use simplification ] 
    AvC [ use addition ] 
    D [ use modus ponens ]
    _______________
    ∴ A.D [ use conjunction ] 
  • Given = A      Prove = C
    (AvB) ⊃ (C.D) 
    A [ use simplification ] 
    AvB [ use addition ] 
    C.D [ use modus ponens ]
    _______________
    ∴ C [ use conjunction ]