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<blockquote data-quote="clearstream" data-source="post: 9045106" data-attributes="member: 71699">I can restate it this wayFor a particular person on any actual day on Earth, is the whole of E accessible?Does the total set of sources on any actual day on Earth represent the whole of E?The answer to both of those questions is very clearly &quot;No&quot;. Therefore a particular person on an actual day on Earth can benefit from a game text (source) with rules constitutive of TTRPG possibilities novel and interesting to them.Hilbert's Paradox* shows that even though E is a logically infinite set, on any actual day on Earth more possibilities can be added to it. &quot;The statements &quot;there is a guest to every room&quot; and &quot;no more guests can be accommodated&quot; are not equivalent when there are infinitely many rooms.&quot; On any actual day on Earth a particular game designer can add to the possibilities by devising the rules constituting those possibilities.There's a bit of stuff to unpack around constitutive rules, norms, and dispositions or whatever is taken for a particular person to know to do whatever amounts to some possibility. I've tried to explain it above and believe it plays out to the same ends. Essentially, you need to decide if you are rejecting the notion of constitutive rules, so that rules would not be able to extend pre-existing norms. That would run counter to mainstream thought on game rules, but there's probably an interesting debate to be had if you do!*HB only applies to countable infinities, and whether or not E itself is countable (which honestly, I don't know) I believe there is a set matching E that can be made countable by assigning distinct non-modal identities to each possibility. E' then being the set of such identities. I've no idea how things work out if that's wrong and E isn't countable or we want to take modal possibilities into account.</blockquote>

[QUOTE="clearstream, post: 9045106, member: 71699"] I can restate it this way For a particular person on any actual day on Earth, is the whole of E accessible? Does the total set of sources on any actual day on Earth represent the whole of E? The answer to both of those questions is very clearly "No". Therefore a particular person on an actual day on Earth can benefit from a game text (source) with rules constitutive of TTRPG possibilities novel and interesting to them. Hilbert's Paradox* shows that even though E is a logically infinite set, on any actual day on Earth more possibilities can be added to it. "The statements "there is a guest to every room" and "no more guests can be accommodated" are not equivalent when there are infinitely many rooms." On any actual day on Earth a particular game designer can add to the possibilities by devising the rules constituting those possibilities. There's a bit of stuff to unpack around constitutive rules, norms, and dispositions or whatever is taken for a particular person to know to do whatever amounts to some possibility. I've tried to explain it above and believe it plays out to the same ends. Essentially, you need to decide if you are rejecting the notion of constitutive rules, so that rules would not be able to extend pre-existing norms. That would run counter to mainstream thought on game rules, but there's probably an interesting debate to be had if you do! *HB only applies to countable infinities, and whether or not E itself is countable (which honestly, I don't know) I believe there is a set matching E that can be made countable by assigning distinct non-modal identities to each possibility. E' then being the set of such identities. I've no idea how things work out if that's wrong and E isn't countable or we want to take modal possibilities into account. [/QUOTE]

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