# The Concept of Trivialism

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.

• You are not being bold enough, for a trivialist everything is also false, because "everything is false" is also true. Everything is both true and false. There is no need to manipulate anything, this is exactly the result one reaches in classical logic by adding a single true contradiction, like the Liar, which natural language supplies. Priest, a founder of dialetheism (where only some things are both true and false), called it "certifiable insanity", but Kabay recently wrote a long defense of trivialism. Commented Apr 26, 2020 at 9:52
• If everything is true, also p & ~p is. Commented Apr 26, 2020 at 10:10
• Is logic trivial? Or is the Liar paradox trivial? The latter gets my vote.
– user20253
Commented Apr 26, 2020 at 10:43
• Your understanding is incorrect. Defined to be false does not preclude something from also being true, and if all falsehoods are truths trivial logic produces "only truths". In particular, the trivial algebra with T=F is a model of Boolean algebra, i.e. satisfies all laws of classical logic. Commented Apr 29, 2020 at 21:49
• Classical logic is not semantics, it is defined in terms of laws, as you can see in SEP or Wikipedia. And trivialists "move" within the four corners of those laws. You can say that they pick non-classical semantics of classical logic, if that helps, but that happens after their argument from the laws. Commented May 8, 2020 at 19:15