This question was inspired (at least in my head) by this wish question.
So part of the reason wishes for levels are perverted is because there is so much wiggle room for interpretation. Most DM's say that a player is meta-gaming if they talk about "levels". Because of this, there is nothing to point to as a marker of being a "higher level" than another.
But I wonder if levels are truly a abstract concept.
We all accept that "hit points" must be an abstract concept. A sword blow, a magic missile, acid, falling 10 feet, and being crushed by a falling rock are all tracked via the same method.
But levels have very specific traits attached to to them. The player gains more hit points, so yes, that part is still abstract and reflects the ability to withstand more punishment. But there are skills that are determined (or even defined) by level such as extra attacks, new feats, ability to learn and use new spells. The list goes on. There is a direct correlation between abilities and level.
I know some DM's have rules that the players do not actually level up just because they have the XP, but instead must seek out a tutor.
To these points, XP is still an abstract of knowledge gained, but "level" is a literal standard. I would put it akin to gaining a new belt in karate/kung-fu. So a 1st level Fighter is a white belt, and a 20th level Blade Master is a black belt and there would be stages in between.
So I'm asking, is "level" (not XP) an abstract or a literal?