"Symbolically the second form is expressed thus A ∨ ~A where ∨ means "or". The equivalence of the two forms is easily proved (p. 421)

Examples For example, if P is the proposition:

Socrates is mortal. then the law of excluded middle holds that the logical disjunction:

Either Socrates is mortal, or it is not the case that Socrates is mortal. is true by virtue of its form alone. That is, the "middle" position, that Socrates is neither mortal nor not-mortal, is excluded by logic, and therefore either the first possibility (Socrates is mortal) or its negation (it is not the case that Socrates is mortal) must be true."

But Socrates isn't mortal or not mortal. Socrates is isn't...