  shows that either \(p \rightarrow q\) or \(p\) must hold. This is classically valid (if \(p\) fails, \(p\) is false, and conditionals with false antecedents are true), but invalid in intuitionistic logic. The difference between classical and intuitionistic logic, then, can be understood formally as a difference between the kinds of structural rules permitted, and the kinds of structures appropriate to use in the analysis of logical consequence. 