Principle of explosion

The principle of explosion is the rule of classical logic that states that anything follows from a contradiction -

Here is the proof:

1) P v ~P By assumption (the law of noncontradiction which is axiomatic) 2) P By (1) and conjunction elimination 3) P v A By (2) and disjunction introduction (4) ~P By (1) and conjunction elimination (5) A By (3), (4), and disjunctive syllogism

Supporters of paraconsistent logic typically disagree with (3), holding that there are contradictory views (such as those found in quantum mechanics) that do not necessarily hold that contradictions must 'explode".