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.