# Principle of Explosion

ex contradictione (sequitur) quodlibet

from contradiction, anything (follows)

The principle of explosion is an observation that anything can be proven from a contradiction (and hence, an **explosion** of proofs).

That's easy to construct:

| :-----: | :------------: | :----------------------------------: |
| 1 | P **AND** ~P | Premise |
| 2 | P | Conjunction elimination and 1 |
| 3 | P **OR** A | Disjunction introduction and 2 |
| 4 | ~P | Conjunction elimination and 1 |
| 4 | A | Disjunction syllogism from 3 and 4 |

That is, if we start from a contradiction (namely, "P **and** ~P") we can derive any other proposition that we'd like (namely, "A").

It is interesting to think that we live with a massive amount of contradictions in our heads, so perfectly easy to derive logical conclusions but that aren't correct at all.

Question your premises, because **from contradiction, anything follows**.