Like that of the law of identity, the law of contradiction, (otherwise called the law of non ­contradiction) admits various formulations in different contexts of its use. It states that two contradictory qualities or predicates cannot be asserted with regard to anything at one and the same time.

In other words, for anything, it is not the case that it possesses a property and doe not possess that property at the same time. Aristotle says, “The same cannot belong and not belong together to the same under same respect”.

For example let a stand for “to be honest” and B stands for “not to be honest”. Then A and B will never belong to the same thing. In other word; it is not possible to assert and deny the same. In its propositional formulation, it asserts that two contradictory statements are not true together. It also suggests that no proposition is both true and false.

Symbolically, the law of contradiction is represented by the formula – (p~p) when p stands for any proposition (Read~(p ~p) as ‘not both p and not p’). This law, like the law of identity, also suggests the method of assigning truth values to propositions. It says that while assigning truth values to the propositions, we should not assign both truth and falsehood to the same proposition.

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This law is one of the minimum conditions of any good argument. It says that if something is a table, and then it is not the case that it is not a table. A thing cannot both be a table and not a ‘table at the same time.

Any argument violating this law would be inconsistent and thereby would become pointless as it would claim nothing. When we say that a good argument must conform to this law, it implies that it should be consistent.