The law of excluded middle, like the other two above laws, is also a fundamental law in the sense that every good argument must conform to this law. It asserts that everything is either or not A, where A stands for any quality. A is not an exhaust the entire discourse.

In other words, a thing can be either A or not-A but it cannot be neither. Hence there cannot be an intermediary between contradictory properties. Let a stand for “to be good” and B stands for “not to be good”. Then ‘either A or B’ will belong to everything.

In the propositional interpretation the law of excluded middle asserts that every proposition is either true or false. Symbolical it can be formalized as (p V ~ p) is always true for any proposition P. (Read ‘p V ~ p’ as ‘p < not p’). For any proposition p, p admits either the truth value T (for truth) or F (for falsehood P cannot be neither i.e. there is nothing in between T and F. The third or intermediary value between T and F is excluded.

These three laws in their propositional interpretation are all tautologies and hence are logically true. Since they are all tautologies, they are equivalent to each other. For that matter they all are equivalent to any of the tautologies. But logicians consider these laws as having a very special status. They are basic or fundamental principles to which any good or correct argument conform.