Symbolic Arguments

• An argument is valid when its conclusion follows from a given set of permises.
• given: a set of premises: p₁, p₂ ...p_n and a conclusion: C
• if [p₁ ∧ p₂ ∧ ... ∧ p_n ] → C is a tautology, the the argument is valid.
• Our book presents four standard valid arguments
  • The law of Detachment:

    p → q
    p
    -----
    ∴ q
    	

  • The law of Contraposition

    p → q
    ~q
    -----
    ∴ ~p
            

  • The Law of Syllogism

    p → q
    q → r
    -------
    ∴  p → r
            

  • Disjunctive Syllogism

    p ∨ q
    ~p
    -------
    ∴ q 
    	

• And there are two well known invalid arguments
  • Fallacy of Converse

    p → q
    q
    -----
    ∴ p
    	

  • Fallacy of Inverse

    p → q
    ~p
    -----
    ∴ ~q