Why in an inconsistent axiom system every statement is true? (For Dummies) I would like to know if someone can explain in a somehow down to earth (almost logic free) way why is it true that in an axiom system where there is some statement $P$ such that $P$ and its negation $\lnot P$ are true, then every statement in the system is true?
I'm not sure if this can be done, but basically since I don't know any formal logic at all, I'm interested in seeing if at least the argument can be conveyed in an intuitive way, or if the idea can be explained without talking about first or second order logic and using symbols like $\top$, $\bot$, and $\vdash$.
This previous question is like the formal version (which I don't understand) so maybe my question can be thought of as a version for dummies of that question. 
Thanks a lot in advance.

In basic sentence logic: there is a sentence $P$ such that $P$ implies $S$ and $P$ implies $\lnot S$.
 Then, start assuming any statement $\lnot Q$ in your system. Then introduce the sentence $P$, from which $S$ and $\lnot S$ follow. Then the assumption of $Q$ leads to the conclusion $S \land \lnot S$, so by reduction, $\lnot Q$ follows. You can do this for any sentence $Q$ in your system.
