I'm sorry, but this isn't about what's on the PCs sheet. It is about whether the GM considers the use of some form of untrained task resolution.
In the largest example: D&D - if you aren't trained in appropriate tools, you can still make a check to fix your wagon. It is just less likely to succeed.
I think "untrained" is not accurate to Michael's OP... it's a narrow subset of...
I think "Previously undefined" is. That's a different liminal space, a broader one.
He is noting that a player adding defined truths in play isn't his space as a GM to inhibit/prohibit. I strongly disagree with that concept - the agreement to rules is what makes it a game instead of just play. His wain repair vs wainwright is a case where there are four widely accepted GM approaches to resolving that: Say yes, say no, make a roll against the most relevant defined element (Dex or Int, in that example), or make a penalized roll for lack of predefined competence. (I've used all of those over the years. I tend to use the last of those these days, as it's the default mode for most games I've run.)
And, as Snarf and I have noted in different ways, the liminal space of Previously Undefined is readily observed in the history of gaming.
There are games that have mechanics to cover for previously undefined. The strongest examples of this are John Wick's
Houses of the Blooded and
Blood & Honor. You can always make a Risk¹ to define the undefined in those two games. In fact, the story emerges from play both from explicitly changing things already established
in prior risks, and by defining previously undefined things.
WEG Star Wars has a definition-of-state action for one skill: Linguistics. Do you know a given language? The difficulty is based upon how rare the language is and whether you can make & perceive the signals - sounds, or visual cues, or kinetics. Once you've rolled, say, for Wookie, it's a known thing, and goes on the sheet...
Burning Wheel and
Burning Empires have a wises to define truths option. And Circles. In the case of circles, it's defining the unknown of "is ___ available"... while Wises, you make the statement you want to be true, the GM has you roll on the suitable wises. In the case of Wises, it's I know X, is X correct or erroneous?
My fundamental counter to Michael's core complaint as exemplified by the wainwright example is that anything in game is defining the previously undefined, and setting the line is axiomatically the GM's first and most important role... since all resolutions can be seen to be doing either define something previously undefined, or changing something's defined state. Like the Orc... my attack is changing his defined state (aggressive pigman with greenish skin, up in my character's grill, in good health...) to that of Corpse-of-Orc, but probably only getting to "wearing down"...
The classic line is: I control what my character's emotions and attempts at action are. The GM, often by using the rules, determines what the outcome is.
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¹ "Risk" in this context is game specific jargon for invoking the rolling mechanic.