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Message: <blockquote data-quote="pemerton" data-source="post: 9624658" data-attributes="member: 42582">First, the claim that mathematical facts are "pre-existing" is contentious in the philosophy of mathematics. Plato asserts it. Brouwer and Wittgenstein deny it. Fr(om my engagement with contemporary mathematicians, my understanding is that most default to Hilbert's formalism and so deny that there are mathematical facts at all.The whole point of formalism is that it allows for the operation of robust inference rules while remaining agnostic about what, if anything, underlies them.Second, when it comes to legal reasoning I take it to be obvious that there is no underlying reality in any straightforward sense - eg when the Parliament promulgates a statute, or a court makes a decision, do we really think that it also generates a whole Platonic universe of consequences and entailments?(I could say the same thing about [USER=6790260]@EzekielRaiden[/USER]'s example of Clue(do). When someone puts the cards in the envelope, it now becomes true that a series of inferences permits identification of the cards. But does that also mean that putting the cards in the envelope brought into being a whole host of abstract Platonic facts that explain those inferences? We can remain neutral on the metaphysical speculation without being especially puzzled by what the process of solving Clue(do) involves.)Third, even if one accepted the Platonic hypothesis about underlying facts that explain the soundness of the inferences, this wouldn't mean that those facts were pre-authored. No one would have chosen them, for instance - they come about "automatically" by dint of the entailments that are yielded by the inference rules.Thus, it is mere dogma to assert that the only way to achieve "objectivity" - that is, an outcome/"solution" that is not simply decided upon in the moment - is by way of pre-authorship.And as I said, this is a common-place in fiction already. When we read a story, all sorts of things about the imaginary "world" of the story are implied by what the author authors, although not themselves authored by the author. For instance, the author might have a character wandering around the streets, having perfectly conventional interactions on the streets of 1950s Melbourne. The author then tells us that the character reaches into his pocket. Even if nothing has been mentioned hitherto about the character's clothing, the pocket does not come from nowhere, like a rabbit from a hat: perfectly convention interactions imply that the character is clothed rather than naked, and being clothed, for a man on the streets of 1950s Melbourne, implies pockets.As I've also said upthread, the more that those who are engaging together with a fiction are on the same page, the more inferences of this sort will be generated. Successful RPGing begins with people being on the same page, but it also has techniques to bring them even more onto the same page in respect of the fiction, and to gradually build up more and more shared fiction, following rules for inference and extrapolation (both general and particular) of the sort set out in rulebooks like Burning Wheel and Apocalypse World.This is how, as Vincent Baker has said, rules in a RPG can do something different from mere "vigorous creative agreement": <a href="http://lumpley.com/index.php/anyway/thread/360" target="_blank">anyway: Rules vs Vigorous Creative Agreement</a></blockquote>

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