I understand trivialism is the position that everything is true, but I don't understand how it arrives there conceptually. The trivialist realizes that our natural (L)anguage (combined with our classical logic) is inconsistent because you can formulate the liar sentence that is contradictory either way. So by principle of explosion he gets
L, p & ~p |- q and L, p & ~p |= q (we assume our linguistic-logical system to be sound).
But by semantic definition p & ~p is false, so if q = p & ~p then it yields a false conclusion, so not everything becomes true! In classical logic it is just true that any q follows from a contradiction (p & ~p |- q), if the inference system is sound it is even true that if the contradiction was true then the conclusion were true (p & ~p |= q), but it is not true that q becomes always true because contradicitons are defined to be false and q can always stand for such a contradiction.
So it seems the trivialist must first and foremost manipulate the semantic definitions of truth (p, ~p, &, v, ->), but then he has no argument, he basically just defines his position.
