Your claim about independence is contentious - Wittgenstein, for instance, takes a very different view on that from Plato. But could nevertheless set maths exams.What makes that possible in mathematics is that you have posed a question that is about things independent of your conception thereof.
What makes possible what I described is not independence but canonical inference rules.
I am not talking about portrayal. That's a red herring. Basil Rathbone portrayed someone solving mysteries. But all he was doing was following a script.Then I still don't understand how this produces I am solving a mystery myself. I fully agree that it can produce I am portraying a character who solves mysteries.
And I don't know why you use the first person - I am solving a mystery - when the techniques that I pointed to are expressly oriented around multiple participants with defined roles that involve both permissions and constraints, which are themselves dynamic in nature.
Is that true of an RPG where someone can--regardless of whether they follow rules for doing so--declare facts about the world? I would argue no. If you can, even while following strict and well-structured rules, still declare new facts, even if those facts must be consistent with what is already known, those new declarations decide the mystery. They don't solve it.
Your insistence on prior authorship is refuted by the mathematics example, where solution is possible without prior authorship.I just don't see how the things you've described do not result in, as an actual matter of fact to the players at the table, someone at some point made a decision which fixed who the "whodunnit" points at. Whether they knew they were doing so or not is irrelevant to me. Someone, at some point, created a truth that was not true before. I don't see how that truth-creation can be compatible with me as a player solving a mystery.
It's fundamentally declarative. Someone declared what the solution would be. There is a difference between declaring (even if you do not realize it) a solution, and finding out a solution. The former is incompatible with solving. The latter is precisely what "solving a mystery" is.
What enables us to make the jump from "we have declared facts, and those facts made a particular result be true, thus removing the mystery" to "there simply are facts, and we discovered what those facts were, thus solving the mystery"?
So the actual question becomes, can a RPG emulate the canonical inference rules of mathematics? Of course we are talking about a different domain - genre fiction - and hence the nature of the inference rules is very different - they are concerned with what is compelling, given the established fiction and the constraints under which some new bit of fiction is required to be articulated?
There does not need to be a unique solution across the whole space of possible fictions and RPGers, either. There only needs to be a uniquely salient solution for this group of RPGers, here and now in their play.
Perhaps you've never experienced that. I have.
EDIT: Not any old set of RPG techniques can do this. If all someone was familiar with was, say the DL modules and a CoC module from the same period, then I don't know if they would work out how to do this.
But RPG design has moved on from that era. Other techniques have been discovered - for instance, ways of integrating player-authored priorities into GM authority over scene-framing and consequence.
Vincent Baker points to it here: anyway: Rules vs Vigorous Creative Agreement (I'm eliding a footnote; italics original):
As far as I'm concerned, the purpose of an rpg's rules is to create the unwelcome and the unwanted in the game's fiction. The reason to play by rules is because you want the unwelcome and the unwanted - you want things that no vigorous creative agreement would ever create. And it's not that you want one person's wanted, welcome vision to win out over another's - that's weak sauce. No, what you want are outcomes that upset every single person at the table. You want things that if you hadn't agreed to abide by the rules' results, you would reject.