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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.



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