GM fiat - an illustration

What makes that possible in mathematics is that you have posed a question that is about things independent of your conception thereof.
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 possible what I described is not independence but canonical inference rules.

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.
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.

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.
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"?
Your insistence on prior authorship is refuted by the mathematics example, where solution is possible without prior authorship.

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.​
 

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Here's a mystery or two: what is the smallest prime number greater than 1,000,111,222,333,444? And how many factors does the natural number that immediately precedes it have?

I'd understand calling that a "mystery" in the colloquial sense of it being unknown, but as both a mathematician and avid reader, I reject calling it a "mystery" in the sense used in Hercule Poirot stories or Gumshoe games.
 

I think that MHRP, HeroWars/Quest, a 4e D&D skill challenge or Burning Wheel could all handle this - in BW, though, the GM might have to do a little bit of mechanical ad libbing, perhaps building on the rules for Circles and Relationships together with the rules for chases to create an extended resolution framework.

I don’t think I’d find mapping a 4e skill challenge to what I’m talking about quite appropriate. I don’t have the familiarity with the mechanics of the rest of the games to say. It’s more structuring the conversation around openness, vulnerability, etc. To quote Baker, drawing a line between AW's conflict-centric design and UHH:

"In Under Hollow Hills, your character isn’t a bundle of vision, self-interest, and survival instincts, armored up and armed to the teeth. Instead, your character is a bundle of what do I want? and what do I have to give?"

I've just been percolating on how to wrap that back into the games that I play that are primarily about conflict creation/clarification/escalation (occasional resolution), and how I can reduce feeling like I'm either sustaining relationships via fiat or always falling back on conflict moves (poor @niklinna 's Ranger and his boyfriend). AW actually makes it pretty easy, you see some of their thoughts bleeding into the playbooks and design for AW: Burned Over and its Sword and Sorcery spin.
 

I'd understand calling that a "mystery" in the colloquial sense of it being unknown, but as both a mathematician and avid reader, I reject calling it a "mystery" in the sense used in Hercule Poirot stories or Gumshoe games.
Sure. A sudoku is different from a crossword puzzle is different from charades is different from Pictionary is different from a whodunnit story.
 


I don’t think I’d find mapping a 4e skill challenge to what I’m talking about quite appropriate. I don’t have the familiarity with the mechanics of the rest of the games to say. It’s more structuring the conversation around openness, vulnerability, etc. To quote Baker, drawing a line between AW's conflict-centric design and UHH:

"In Under Hollow Hills, your character isn’t a bundle of vision, self-interest, and survival instincts, armored up and armed to the teeth. Instead, your character is a bundle of what do I want? and what do I have to give?"
I don't know Under Hollow Hills in any detail, but know that it is different from AW - and the quote shows that.

I think a skill challenge can be used where what is at stake is the reception of sincerity.
 

I don’t think I’d find mapping a 4e skill challenge to what I’m talking about quite appropriate. I don’t have the familiarity with the mechanics of the rest of the games to say. It’s more structuring the conversation around openness, vulnerability, etc. To quote Baker, drawing a line between AW's conflict-centric design and UHH:

"In Under Hollow Hills, your character isn’t a bundle of vision, self-interest, and survival instincts, armored up and armed to the teeth. Instead, your character is a bundle of what do I want? and what do I have to give?"

I've just been percolating on how to wrap that back into the games that I play that are primarily about conflict creation/clarification/escalation (occasional resolution), and how I can reduce feeling like I'm either sustaining relationships via fiat or always falling back on conflict moves (poor @niklinna 's Ranger and his boyfriend). AW actually makes it pretty easy, you see some of their thoughts bleeding into the playbooks and design for AW: Burned Over and its Sword and Sorcery spin.


What's the issue with fiat?

Do you just want to add a dice roll or are you not sure what you'd be rolling for?
 


I'd understand calling that a "mystery" in the colloquial sense of it being unknown, but as both a mathematician and avid reader, I reject calling it a "mystery" in the sense used in Hercule Poirot stories or Gumshoe games.
Is there really a material difference though? Each one involves moving from a question to an answer via some sort of set of rules of inference. I think I would probably agree that the rules of inference in relation to solving a murder mystery are perhaps somewhat looser, they apply to more complex and somewhat less clear cut things at times, but particularly when games and novels are in question it is a bad idea to get too fuzzy.
 


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