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Insufficient Explanations on the Vs. Battles Tiering Pages (STAFF ONLY)

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Bump.

DontTalk should be (more-or-less) back in full swing in about two days, right? Since that's when the weekend starts.
 
I hope so at least, but he may need to recover a while after his exams are over.
 
What’s left to do here, actually? Isn’t Ultima’s proposal fine to apply?
 
Probably, yes, although I think that KingPin also made a suggestion, and it would be best if @DontTalkDT and @Ultima_Reality reach an agreement regarding what we should do here.
 
I am not sure. I think that his exams are over for now.
 
I will send a PM to DontTalk.
 
Thank you very much for helping out again Ultima.
 
Ultima_Reality said:
So, bumping this thread.

And pinging @DontTalkDT too, for the matter, since the above discussion can't make much progress without his input.
Click to expand...
Wanted to ideally finish the other staff threads first... not to do too many things at the same time.
But, alright then. I guess I will read through everything tomorrow, to not stall this any longer.

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.
 
Thank you for helping out DontTalk. My apologies if we stress you out too much.
 
KingPin0422 said:
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+.
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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.

KingPin0422 said:
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.
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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.
Ultima_Reality said:
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.
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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.
The fact that it's IMO general abstract nonsense that no reader will comprehend doesn't favour it as a mathematical metaphor for a tier either...


Will get to the rest tomorrow. Real-life sadly kept me busy and sleep-deprived today and the other half of counterpoints need more concentration to debate.
DontTalkDT said:
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.
Click to expand...
Still wonder about this idea btw.
The more I read, the more I think it's a good idea. Ultimately, we primarily want a functional system, after all.
 
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Thank you for helping out DontTalk. Please take your time to rest and recover properly.
 
DontTalkDT said:
Still wonder about this idea btw.
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Think it's fine, I can try gathering groups of 3 staff members/trusted members, and we can organize this via wiki group DMs.

Although I feel we'd need extremely active respondants, for the members I bring not to get discouraged
 
I think that it seems safest to only involve the administrators and maybe the thread moderators in the test groups, if we go with that option, given that this is such an important issue.
 
...I mean I don't think we should gatekeep input when the entire point of the thread is to stop gatekeeping tiering knowledge behind confusing wording.

It's important, but it doesn't have sitewide/tiering implications, the point is only to word our pages better.
 
The definitions in our tiering system definitely do have sitewide implications, so I would much prefer if some of the most trusted members handle evaluating it, for safety reasons.
 
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.
 
Ultima_Reality said:
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.
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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?
 
DontTalkDT said:
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.
Click to expand...
Okay. Never mind then.
 
DontTalkDT said:
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?
Click to expand...
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.
 
Antvasima said:
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.
Click to expand...
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.

It would make the standards stricter for some verses and less 'strict' for other verses.

Specifically, since it would use a lower cardinality as baseline, verses that specifically state that they deal with a certain cardinality for size would have an easier time getting in. In that sense, the standards become less strict. Although, I think we probably don't have a verse that would profit from it? Well, maybe Ultima knows one.

However, on the other hand, the suggestion carries with it that if a verse wants to enter "transcends an infinite hierarchy of infinite hierarchies" tier or greater level, they actually have to demonstrate that such hierarchies exist or, at least, have reliable statements that explicitly suggest that they could transcend such structures if they existed.
Currently, we seem to accept that, if a character transcends an infinite hierarchy in nature (i.e. qualitatively), then it could also transcend an infinite hierarchy of infinite hierarchies of that nature (and even bigger structures) even if the verse never brings such things up. By doing away with that reasoning the standard would become stricter, as the verses need to proof more.
 
DontTalkDT said:
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.
Click to expand...
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.

Antvasima said:
What do you think, @Ultima_Reality ?
Click to expand...
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.
 
Okay. Thank you for helping out.

It is hard for me to personally make qualified evaluations of this issue though, so it is best if you, DontTalk, and the other knowledgeable members here try to work out a good solution.
 
Alright, here's a slightly updated version of my previous drafts to account for stuff that wasn't accounted for previously:

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.
Click to expand...
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+).
Click to expand...
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.
Click to expand...
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.
Click to expand...

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.
 
Ultima_Reality said:
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.
Click to expand...
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.

When I single out mathematics I do so because these verses have an opportunity to specify their transcendence not just qualitatively, but quantitatively.
It is one thing to say that you absolutely, totally transcend the essence of some hierarchy and another thing to say that you transcend it specifically by Woodin cardinal man levels of infinity. One is a lot more explicit and doesn't require extrapolation to get the power.
Aside from that factor mathematical verses should be treated the same in my opinion. A verse has an infinite hierarchy of spaces with more and more dimensions, the third of which has Woodin cardinal many dimensions? Well, then a character that qualitatively transcends that hierarchy would be assumed to be more than infinite levels of infinity higher than Woodin cardinal space, but not greater than all cardinals if that wasn't brought up.

Anyways, the two of us debating this in a thread which purpose wasn't to debate this in the slightest won't lead to a good result. Best we do a separate thread in which we explain the practical effects on the tiering requirements and see what others prefer as well.
@Antvasima I would suggest the same in regards to adding a mathematical presentation for Tier 0. That's probably a decision the staff at large should be involved in, in a thread made for that purpose. It's something that is supposed to be of use for others, after all, so if only three people here even understand the implications and make the decision it would be no good.

KingPin0422 said:
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.
Click to expand...
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.
Maybe extend that part to:
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.
Click to expand...
 
Thank you for helping out @DontTalkDT. I personally do not mind your adjustments to KingPin0422's suggested definitions.

So do you suggest that we should close this thread, after you have first started a new staff forum thread in which you present our progress so far, after which I call for our other staff members to take a look and comment? That seems fine to me in that case.
 
I think we can leave this thread open for the time being, as the topic of improving the explanations is still on the table, independent of setting the mathematical representations.
I will send Ultima a private message in a while regarding making a thread on the representation. We each have our own proposal, so if I write the introduction on my own it would probably be one-sided. Hence we better coordinate on that.
 
Okay, but won't it be confusing for us to jump back and forth between two threads that cover largely the same things? Isn't it better to cover, and get more input for, our progress so far instead, as I suggested above?
 
I guess we could also keep it here, but then the title and OP of this thread should probably be edited. Wouldn't want people to miss that this isn't purely about extending explanations, but also about adding new mathematical metaphors for the tiers and by that about changing the system.
 
That is also fine of course. However, if you want more input, it is easier to get staff interested with a quicker to read continuation thread with a to the point summary in the beginning.
 
Alright, here's a (hopefully) finalized version of the new High 1-A description, using DontTalk's suggestion as a reference point:

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.
Click to expand...

I feel that "Even the amount of cardinals between such a cardinal and aleph-2 (which defines 1-A) is larger than many (typically all) regular cardinals." is unnecessary to include in the description because it's completely redundant. As in, "the amount of cardinals between [an inaccessible cardinal] and aleph-2" is... an inaccessible cardinal. Saying that it's "larger than many/all regular cardinals" wouldn't really be appropriate, either, given that an inaccessible cardinal is itself a regular cardinal. In fact, under ZFC, every finite-index aleph number is a regular cardinal, but every infinite-index aleph number is instead singular. The first regular cardinal you can encounter after the finite-index alephs is an inaccessible cardinal, which is unprovable within ZFC without adding another axiom to permit discussion of inaccessible cardinals. Therefore, in a certain sense, even 1-A+ is larger than all regular cardinals (in ZFC), and so the aforementioned detail is superfluous, in my opinion.
 
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