Non-scientific, non-linguistic magic system?
I don't see a forum for worldbuilding questions that aren't about geography, so...
For several years, I've developed some strong goals for a magic system. I don't know what sort of world I want to put it in yet. Well, I suppose the world will develop based on how its magic works.
Most importantly, magic is not science. It does not look or feel like science. Not just real science, but any conceivable science.
This suggests that it should not be possible to discover or learn magic by trial and error. The obvious way is for magic to be non-reproducible. But than how can anyone learn to use it?
Also, I don't want "cast from mana pool" magic. There should be nothing like conservation of energy; magic should not be based on resource consumption. However, I don't want a skilled magician to have do-anything Power of Plot.
I don't want linguistic magic. That's always felt too much like something a writer would come up with rather than something that might "actually" exist. It's boring. I don't want the related concept of "like produces like". Why? Because the world was made by the gods, who do not classify things as humans do.
I'm reminded of an example I once saw concerning believable languages. An example satisfying at least some of my requirements is a world where a certain spell needs either a red bird or a blue flower as a spell component. Things grouped bizarrely. But how to do this without seeming just silly? And how to convince the reader that there is a method to it?
I don't want elemental magic. Like linguistic magic, it's based on human categorization of objects. Also, it's too easy to become arbitrarily powerful. I tend to refer to this as "Green Lantern powers". The power ring can make anything so long as it's green. Aside from this being too broad of a concept, he can make anything at all, because he's not even limited to making things that are naturally green. On a similar note, I once saw a mention on an RPG forum of a mage with fire powers. He could make anything burn, whether or not it was flammable. This sort of use defeats the concept of elemental powers.