Classical Bad Idea

• Classical conditional connective
  • (φ → ψ) =_def (¬φ ∨ ψ)

• Modus Ponens fails
  • If ⟦φ⟧ = B and ⟦ψ⟧ = N
  • Then ⟦φ → ψ⟧ = ⟦¬φ ∨ ψ⟧ = B ∨ N = T
  • But ⟦φ⟧ (B) and ⟦φ → ψ⟧ (T) are designated, ⟦ψ⟧ (N) is not

• Modus Ponens is required!
  • The classical definition is a "Bad Idea"