The principle of explosion is a logical principle which states that if we accept that a certain statement is true at the same time it is not true, then any other statement, no matter the truth value, can be proven. In other words, from a contradiction, any imaginable conclusion can be reached.
The Principle
The principle comes from an argument containing a proposition and its negation. By way of simplification and addition, anything can be proved deductively.
- P1: A · ~A
- P2: A (1, simplification)
- P3: ~A (1, simplification)
- P4: A v B (2, addition)
- C: B, (3, 4 disjunctive syllogism)