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I suppose that we will have to wait until @Ultima_Reality and @DontTalkDT have the time to help us out here.
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Wanted to ideally finish the other staff threads first... not to do too many things at the same time.So, bumping this thread.
And pinging @DontTalkDT too, for the matter, since the above discussion can't make much progress without his input.
Well, that's the thing. The mathematical metaphor is secondary to me. IMO we should choose it to fit our practices, as "transcending an infinite 1-A hierarchy" is a much more practical criteria for us than "corresponds in some way to a large cardinal." Given the way we are currently evaluating those feats something like aleph_omega would probably be a better match to reflect what we are requiring.With all due respect, your logic in both of these parts boils down to "we shouldn't allow things to be rated X unless they explicitly mention Y," which I feel is quite disingenuous and inconsistent with the fact that we do, in fact, allow things to be 1-A without requiring uncountably infinite dimensions to be present in the setting, for instance. I might also add that, were we to implement what you described in the first couple of paragraphs, we would be left with almost nothing going beyond 1-A+.
That just sounds like a NLF to me.It's not even accurate, anyway, since something that exceeds the system defining 1-A levels logically would exceed those levels regardless of if there were one, two, fifty, infinity, or infinity^infinity^infinity^(ad infinitum), much in the same way that "how many alephs can you count" is immaterial to the existence of an inaccessible cardinal.
Ehhhh... I don't quite understand. Do you want to say any property describing a certain cardinal number that is met by the class of all sets is also met by a set of lesser cardinality? That's tautological. Quite frankly, I don't think the reflection principle states something that can be used to claim a tiering relevant property, as it doesn't make a claim regarding the class of all sets or statements in general. It needs to be restricted to be non-contradictory in a fashion that makes the analogy meaningless for our purposes.True enough. I should've probably been more specific with that description, so, that's my bad. I guess "any sentence describing a certain cardinal number" would work better as a definition.
Still wonder about this idea btw.Btw. a small suggestion I thought of a while ago: Should we perhaps test whatever explanations we make for the system and possibly whatever different versions we come up with?
Like, we could write a few test scenarios, recruit some users that feel uncertain with the current system, make them judge the test scenarios based on the new version and that way get some feedback on how well it works in practice.
Think it's fine, I can try gathering groups of 3 staff members/trusted members, and we can organize this via wiki group DMs.Still wonder about this idea btw.
Personally, I would assume nothing but ZFC and I believe you know why ZFC isn't an arbitrary choice.I feel KingPin already tackled your points in regards to the first response well enough, so, I'll just give my thoughts on another aspect of this one.
Anyway: Even outside of the point he made, this kind of argument hits a wall when you take into account the fact some things naturally segue into others, meaning we are thus forced to consider them lest we start cherry-picking what parts of math we want to exist in a verse, for what is next to no good reason, in my view.
Like, for example, in ZFC, proper classes like ORD, V, ON, and etc don't exist as actual objects that we can refer to (As sets are), in much the same way infinite sets like N technically aren't "real" in a finitist formal system, but if we switch to a theory where we are allowed to quantify over them, then a lot of large cardinal axioms naturally emerge without having to be directly posited, by means of the Reflection Principle, something which I talked about in my above response to you. That example being something I specifically use because we do have characters who are identified with some Universal Set in their verses (Unsong's God, and in the future, the White Light, too), or have the ability to control such a structure (The Downstreamers), with said Universe being obviously something very real in those cases.
We can reduce that same argument to a smaller scale, too: Surely, we assume a set as simple as the real numbers exists by default in a verse, and so it naturally follows from there that the set of all subsets of the real numbers exists, too, and so does the set of all subsets of that, and so on. Things like that just emerge as a natural result of the basic assumptions we have to make for indexing's sake, and so arbitrary cutting them off doesn't seem very appropriate here.
You might say that this would allow any "beyond math" statements to qualify for ultra-high tiers, but that doesn't come off as very convincing to me, especially since even under the current kind of assumptions we make, some space with a countably infinite number of dimensions would have to exist at least as an idea, in pretty much any verse, and yet we still don't slap Low 1-A or 1-A onto any character stated to transcend mathematics. We'd just have to be careful and require very proper context in regards to this kind of statement, in my opinion, especially if it's throaway and/or not at all something that elaborated upon.
Okay. Never mind then.Personally, I don't think we need/should keep the feedback to staff. It's just feedback after all, in the end it's up to us what we make of the feedback.
If we think it's bad we can just ignore it.
Hmm. I would personally prefer if our standards for tier 0 remain very strict. I think that we already have over a dozen characters that qualify for this tier currently, so it likely shouldn't be an unreasonable demand.Personally, I would assume nothing but ZFC and I believe you know why ZFC isn't an arbitrary choice.
And IMO we don't need a tier just for verses that mention mathematics. Just put them higher into Tier 0 and leave the lower border of tier 0 in the realms of what can be reached without using mathematical terminology.
Since I generally don't see how a verse can proof being above mathematics in a not NLF way other than maybe introducing complex mathematical subjects that border wouldn't be in those realms.
As for a mathematical presentation of Tier 0: Why not just say it's infinite cardinals greater than whatever cardinal is High 1-A? Isn't transcending an infinite hierarchy above High 1-A how non-mathematical characters typically reach Tier 0?
I'm not saying we should lower the demands of Tier 0... at least not in total. I just think that other mathematical objects represent our standards for Tier 0 better, as the mathematical jump in power is more proportional to the jump in power we expect non-mathematical verses to show in order to reach the tier.Hmm. I would personally prefer if our standards for tier 0 remain very strict. I think that we already have over a dozen characters that qualify for this tier currently, so it likely shouldn't be an unreasonable demand.
That's a bit of a bad equivalence to make. "Framework of space" is a descriptor that's so vague we may very well just default to assuming it would refer to the whole of a verse's space, something which a -logical- framework (i.e what the description of High 1-A refers to) is not so easily reducible to, like I explained in my previous post, and which you seemed to take no issue with given the remark you made ("And IMO we don't need a tier just for verses that mention mathematics. Just put them higher into Tier 0 and leave the lower border of tier 0 in the realms of what can be reached without using mathematical terminology.")That just sounds like a NLF to me.
Like, in most cases when a character completely transcends the framework of space, we would just rank it however many dimensions the verse has actually shown. In rarer cases we extend that to 1-A, but still stop it at some reasonable point. But for 1-A hierarchies we tend to extrapolate any transcendence statement of a hierarchy to the greatest imaginable level.
As you can see, I have a few disagreements with what DontTalk proposed, even outside of the one post I addressed. But frankly given how needlessly extended this thread has been getting, and how we settled for my drafts for Low 1-A through High 1-A already, I'd say we should just apply those already and leave discussions regarding the clockwork behind Tier 0 for a later time. In which case, I remove the talk about the Reflection Principle from my draft for it and leave only the first tidbit.What do you think, @Ultima_Reality ?
Low 1-A | Low Outerverse level: Characters who can affect objects with a number of dimensions greater than the set of natural numbers, meaning in simple terms that the number of dimensions is aleph-1 (An uncountably infinite number, assumed to be the cardinality of the real numbers themselves), and therefore that such objects fully exceed High 1-B structures, which have only a countably infinite number of dimensions. More information on the concept is available on this page.
Note that, if the High 1-B structure in question is a hierarchy of levels of existence, then simply being at the top of such a hierarchy does not qualify a character for this tier without more context, and an additional layer added on top of the "infinity-th" level of this hierarchy is likewise not enough. To qualify, they need to surpass the hierarchy as a whole, and not simply be on another level within it.
1-A | Outerverse level: Characters who can affect objects with a number of dimensions equal to the cardinal aleph-2, which in practical terms translates to a level that completely exceeds Low 1-A structures to the same degree that they exceed High 1-B and below. This can be extrapolated to larger cardinal numbers as well, such as aleph-3, aleph-4, and so on, and works in much the same way as 1-C and 1-B in that regard. Characters who stand an infinite number of steps above baseline 1-A are to have a + modifier in their Attack Potency section (Outerverse level+).
High 1-A | High Outerverse level: Characters who can affect objects that are larger than what the logical framework defining 1-A and below can allow, and as such exceed any possible number of levels contained in the previous tiers, including an infinite number. Practically speaking, this would be something completely unreachable to any 1-A hierarchies.
A concrete example of such an object would be an inaccessible cardinal, which in simple terms is a number so large that it cannot be reached ("accessed") by smaller numbers, and as such has to be "assumed" to exist in order to be made sense of or defined in a formal context (Unlike the standard aleph numbers, which can be straightforwardly put together using the building blocks of set theory). More information on the concept is available on this page.
0 | Boundless: Characters that can affect objects which completely exceed the logical foundations of High 1-A, much like it exceeds the ones defining 1-A and below, meaning that all possible levels of High 1-A are exceeded, even an infinite amount of such levels. This tier has no true endpoint, and can be extended unto any higher level, spiraling infinitely upwards.
Being "omnipotent" or any similar reasoning is not nearly enough to reach this tier on its own; however, such statements can be used as supporting evidence in conjunction with more substantial information.
I really don't see a difference here. If the verse didn't explicitely mention these levels, then it is just as much reduceable to the highest that was mention.That's a bit of a bad equivalence to make. "Framework of space" is a descriptor that's so vague we may very well just default to assuming it would refer to the whole of a verse's space, something which a -logical- framework (i.e what the description of High 1-A refers to) is not so easily reducible to, like I explained in my previous post, and which you seemed to take no issue with given the remark you made ("And IMO we don't need a tier just for verses that mention mathematics. Just put them higher into Tier 0 and leave the lower border of tier 0 in the realms of what can be reached without using mathematical terminology.")
"NLF," under those premises, is then not really the best shield to use because that fallacy is specifically used to prevent people from extrapolating higher tiers or whatever else based on there technically being no stated limit to a certain ability. It very much doesn't apply to cases where, by all accounts, something cannot be reasonably reduced to a certain point without stumbling on logical problems like those I mentioned before.
Personally, if we stay at inaccessible/large cardinal representation, I would add some more to High 1-A to give a better impression of how serious "any higher number" is, to make sure nobody thinks we are talking merely of transcending a single infinite 1-A hierarchy.Alright, here's a slightly updated version of my previous drafts to account for stuff that wasn't accounted for previously:
Basically, I added the 1-A+ line back (with some minor changes) because we still need it, and modified the second part of High 1-A's description in order to be clearer on what High 1-A and 0 currently represent (the latter of which may be reevaluated in the future, as Ultima said up there). If it's necessary to elaborate on the latter some more by including an example of a tier 0 object, that can be done.
Characters who can affect objects that are larger than what the logical framework defining 1-A and below can allow, and as such exceed any possible number of levels contained in the previous tiers, including an infinite number. Even an infinite amount of hierarchies, with infinite levels of infinity each and the lowest level of each hierarchy infinitely bigger the prior hierarchy altogether, wouldn't approach this. Practically speaking, this would be something completely unreachable to any 1-A hierarchies.
A concrete example of such an object would be an inaccessible cardinal, which in simple terms is a number so large that it cannot be reached ("accessed") by smaller numbers, and as such has to be "assumed" to exist in order to be made sense of or defined in a formal context (Unlike the standard aleph numbers, which can be straightforwardly put together using the building blocks of set theory). Even the amount of cardinals between such a cardinal and aleph-2, which defines 1-A, is larger than many (typically all) regular cardinals. More information on the concept is available on this page.
High 1-A | High Outerverse level: Characters who can affect objects that are larger than what the logical framework defining 1-A and below can allow, and as such exceed any possible number of levels contained in the previous tiers, including an infinite number. Practically speaking, this would be something completely unreachable to any 1-A hierarchies; even an infinite number of these hierarchies, each with infinite levels of infinity and with the lowest level of each hierarchy being infinitely bigger than the entire previous hierarchy, wouldn't approach this tier.
A concrete mathematical representation of this tier is an inaccessible cardinal, which in simple terms is a number so large that it cannot be reached ("accessed") by smaller numbers, and as such has to be "assumed" to exist in order to be made sense of or defined in a formal context (Unlike the standard aleph numbers, which can be straightforwardly put together using the building blocks of set theory). More information on the concept is available on this page.