The only numbers I'd get rid of are the Progression Points, and that would sure be anti-powerleveling. But we've been there already. Which sure as hell doesn't mean I won't take every chance I get to criticize it.

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Anyway, I think it'd be nice if someone with metallurgy that trains enough suddenly think "I might be able to attempt melting gold now, I think I got it." Rather than the player thinking "Yes, my character is level 20, let's get rich." Or in the example of cooking, a cook that suddenly realizes that there's a trick to mixing ingredients and so he can try it with that recipe he never got right. I also think that you should be able to attempt at any recipe, though your results would be dreadful if you didn't have the skill required. There are many games with that system. Want to melt gold ore without knowing how it's done? There you go, a fresh nice, useless lump of metal for you. Now get to working with less complex materials.
I also judge it better to have a character think "I can kill a Trepor with a hit!" rather than a player bragging that his character does 400 damage.
How could this be done? Just take out the numbers. What would it mean? That you'd have to try things out each time you believe your skill has evolved. "And what does that mean?" That people will be forced into the realistic attempt method rather than the "that player told me" method.
I don't see anything wrong with that. Good thinking Feline Prince.
In Martial Arts people that wear the same belt might have different skill levels. In PS people of the same rank have exactly the same skill. I don't think comparing these makes much sense.
Still, there's nothing too wrong with using numbers. Numbers are references for players to use while they're roleplaying their character, they're useful for you, so you know how your character is faring in a certain skill and if you should rise it more or keep it like that to have it be the way you want. He's right though, it would add to the "immersible environment" thingy, though it could make life for players a little harder.
Variables are there anyway, without numbers or not. I don't get it Quq Leque.