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

[DontTalkDT]

This isn't a point of information, but I wanna say that it is obviously necessary to give some sort of basis for tier 0 if it lacks one. People assume that it just refers to Mahlo cardinals and up, despite that we technically have never officially declared such, and so people form conceptions of tier 0 that may not be true, but which we cannot disprove because not even we seem to know what it truly is. Using the reflection principle/the universe of sets to define tier 0, on the other hand, works wonderfully. It fits a tier called "Boundless" far better than a random large cardinal without prohibiting further scaling (there is such a thing as a multiverse of sets!) or leading to anything being downgraded from tier 0, as far as I am aware.

Which feat that isn't explicitely that would justify being equal to that, though? I feel like, taken seriously, that would be unreachable for anything besides maybe some mathematics based verses. (as far as I'm aware even the mathematics based Tier 0's wouldn't really have the feats for this, though. Even the Downstreamers are technically only ranked Woodin Cardinal level currently)

 

[Ultima_Reality]

So is the notion that like an infinite series of Low 1-A structures need to be inferior to you?

Not exactly, just something that shows you're superior to the Low 1-A structure entirely, without being, like the example said, just "infinity+1" in relation to it. So, for example, if you have some infinite hierarchy, and a space of infinite dimensions is just the lowest step of that hierarchy (i.e the "floors" aren't exactly equivalent to +1 dimensions but some larger difference than just that), then the step immediately succeeding that one would be Low 1-A.

Can you exemplify this?

Most theological concepts that you see popping up in fiction can be seen as examples of that, although more inclined towards philosophy than math, I admit. I guess a verse with that would be World of Darkness, where the supreme being/state is just completely above any description, name, or identity that you might extrapolate for it, to the extent that, by assigning any of those three to it, you're automatically forming something lesser instead (That is in relation to High 1-A realms, for the matter)

Ah, I recognise now that Ultima didn't apecify what said objects are to be considered in his post.

To clarify this point: They can be whatever, really. Once you hit a large enough cardinality, a set of whatever is at that tier, regardless of what its elements are. So, say, a set of 0-dimensional points with cardinality aleph-2 is Low 1-A, and so is a set of universes, or whatever else you can think of.

I always felt like using the large cardinal here doesn't work well here. Like, just transcending the prior 1-A hierarchy system in most verses really shouldn't approach getting to large cardinals, seeing how ridiculously large regular cardinals can get already.

But transcending a 1-A hierarchy (system) is usually how characters get there, no?

I don't think anything less than a large cardinal would satisfy High 1-A's premise, which is, as said, exceeding the capability of the system defining what a "1-A" is. In the standard universe of ZFC, any given cardinal can be obtained and proved to exist, so the framework they operate in is very much the same. That doesn't seem very appropriate when High 1-A characters often have to showcase some difference in size/ontology/whatever that's fundamentally superior to the one that is in-between two lower points of a cosmology (Just like the gap between dimensions is bigger than any finite gap in energy, and the gap between alephs is bigger than the gaps between finite numbers of dimensions)

What do you mean with that? One can define a class of all sets, which would be the collection of all possible sets.

You can define it as the class of all sets, yes, but making anymore statements that characterize it beyond that is not really possible to do, as far as I am aware, which is what forms the basis of the Reflection Principle: Every property held by V (or ORD) is ultimately trivial, because it is also held by some segment of it. For instance, with the right order of logic, you might say V is technically strongly inaccessible, since it is not able to be obtained by any power set (Strong limit), nor through the unions of classes smaller than itself (Regular), but then that just means there is some stage Vκ that holds this property, and therefore by saying that, you didn't really describe V so much as you just described a subset of it.

I think your confusion is probably off of thinking that "description" meant any informal statement whatsoever. I'm talking in terms of specific formulas definable in some set theory, instead.

Which feat that isn't explicitely that would justify being equal to that, though? I feel like, taken seriously, that would be unreachable for anything besides maybe some mathematics based verses. (as far as I'm aware even the mathematics based Tier 0's wouldn't really have the feats for this, though. Even the Downstreamers are technically only ranked Woodin Cardinal level currently)

Which is why I admitted that this definition may or may not be under consideration in my post. I suppose the answer to your question depends on what exactly we assume exists by default in the context of a verse.

 

[KingTempest]

Yeah above 3-A I'm not qualified enough to talk about anything on the tiering system. 2-B's the max I'd go. Tier 1 and 0 is out of my expertise

 

[KingPin0422]

Re: reflection principle talk - it certainly would require a slight change to our standards that nonetheless carry potentially great consequences, yeah. Right now, we limit fancy via negativa-type stuff to only being beyond what can be reasoned to exist in the 'verse. Making it so that, with the right context, such things are an automatic jump to tier 0 is bound to be a controversial decision, but it wouldn't necessarily be an unprecedented one: we currently do allow 'verses to skip ahead all the way to 1-A or even High 1-A from significantly lower tiers, for instance.

 

[DontTalkDT]

I don't think anything less than a large cardinal would satisfy High 1-A's premise, which is, as said, exceeding the capability of the system defining what a "1-A" is. In the standard universe of ZFC, any given cardinal can be obtained and proved to exist, so the framework they operate in is very much the same. That doesn't seem very appropriate when High 1-A characters often have to showcase some difference in size/ontology/whatever that's fundamentally superior to the one that is in-between two lower points of a cosmology (Just like the gap between dimensions is bigger than any finite gap in energy, and the gap between alephs is bigger than the gaps between finite numbers of dimensions)

Thing is, extrapolating this fundamental superiority to this extent seems like an extremely hasty generalization to me.

We are not talking about being infinite levels of infinity bigger anymore. Not about being infinite hierarchies of infinite levels of infinity each bigger either.
Even infinite hierarchies of infinite hierarchies of infinite hierarchies of infinite hierarchies (continue this infinite times) of infinite hierarchies of infinite levels of infinity bigger is even remotely large enough.
Not even if the amount of infinite hierarchies of transcending infinite hierarchies of levels of infinity is so large that it is described by the biggest infinity of the infinite hierarchies stack mentioned above it would approach large cardinal level.
And even infinite steps, with the gap between each gap being bigger than that, would be there yet.

Like, yeah, the Law of Identity for example would be bigger than the whole story hierarchy system. But extrapolating being bigger than the entire system to be bigger to this extent, when the entire known system just has one or two infinite hierarchies here and there, is an immense quantitative jump.

It just seems crazy to me that transcending some framework that has no showings of remotely approaching the size of all regular cardinals would be ranked as larger than it, just because some being is of a fundamentally greater nature than that smaller framework in its verse.

You can define it as the class of all sets, yes, but making anymore statements that characterize it beyond that is not really possible to do, as far as I am aware, which is what forms the basis of the Reflection Principle: Every property held by V (or ORD) is ultimately trivial, because it is also held by some segment of it. For instance, with the right order of logic, you might say V is technically strongly inaccessible, since it is not able to be obtained by any power set (Strong limit), nor through the unions of classes smaller than itself (Regular), but then that just means there is some stage Vκ that holds this property, and therefore by saying that, you didn't really describe V so much as you just described a subset of it.

I think your confusion is probably off of thinking that "description" meant any informal statement whatsoever. I'm talking in terms of specific formulas definable in some set theory, instead.

Nah, I think my problem comes with you speaking of "mathematical statements and formula" which would permit any kind of formal meta-language and pretty much any system of axioms, in which case you can no doubt make statements about it. In fact, even in ZFC you can write down the class without problem in some sense.
As the article you linked on the reflection principle states "A naive version of the reflection principle states that "for any property of the universe of all sets we can find a set with the same property". This leads to an immediate contradiction: the universe of all sets contains all sets, but there is no set with the property that it contains all sets. To get useful (and non-contradictory) reflection principles we need to be more careful about what we mean by "property" and what properties we allow."
I.e. the reflection principle is about restricted similarity and certain properties, not all properties. It is not saying that some set is the same as the class of all sets.

Makes me think about how mathematicians at times say something is true "almost everywhere" if it is true on an uncountably infinite set with the same cardinality of exceptions to that rule.

Which is why I admitted that this definition may or may not be under consideration in my post. I suppose the answer to your question depends on what exactly we assume exists by default in the context of a verse.

Honestly, I feel like using statements like "above all mathematics" as actual Tier 0 evidence isn't better than using Omnipotence as evidence.

Like, I get it, it's tempting to say that if the character is already 1-A and depicted as practically omnipotent we might as well start to take statements we would usually discard as No-Limit Fallacies literally.
But we shouldn't give in to that. Ultra high-tier characters should be held up to higher standards of scrutiny, not to lower ones. Statements like "above mathematics", "above logic", "transcending everything at all levels" etc. should still remain in the realms of just things that were very explicitly addressed in the verse and not stretched beyond that.

 

[Antvasima]

Like, I get it, it's tempting to say that if the character is already 1-A and depicted as practically omnipotent we might as well start to take statements we would usually discard as No-Limit Fallacies literally.
But we shouldn't give in to that. Ultra high-tier characters should be held up to higher standards of scrutiny, not to lower ones. Statements like "above mathematics", "above logic", "transcending everything at all levels" etc. should still remain in the realms of just things that were very explicitly addressed in the verse and not stretched beyond that.

This makes sense to me. Thank you for helping out.

 

[Qawsedf234]

Anyways my attempt

Low 1-A | Low Outerverse level: Characters who can universally affect, create and/or destroy structures and expanses of uncountably infinite dimensions, or which have a size roughly analogous to them, such as uncountably infinite sets of hierarchical layers or planes of existence, most specifically ones whose amount of layers is comparable to the set of all real numbers, and are thus equated to the first uncountably infinite cardinal, ℵ1, for simplicity's sake.

Alternatively, this tier can also be assigned to characters who transcend High 1-B structures when no further context regarding the nature of such transcendence is given.

I would go with something like

Low 1-A | Low Outerverse level: Characters who can significantly affect, create and/or destroy realms or states of uncountably infinite dimensions, or which have a size roughly analogous to them: Such as uncountably infinite sets of hierarchical layers or planes of existence that equate to the first uncountably infinite cardinal, ℵ1.

Alternatively, this tier can also be assigned to characters who exceed High 1-B structures when no further context regarding the nature of such superiority is given.

For 1-A

1-A | Outerverse level: Characters who can significantly affect, create and/or destroy realms or states that fully transcend infinitely-layered hierarchies and/or dimensional levels on a conceptual or existential level, normally being portrayed as entirely external abstractions that lie outside of the applications of spatiotemporal dimensionality as a constant defined by physics on any level, even compared to infinite or uncountably infinite dimensions, usually by perceiving them as akin to fiction or something similarly insignificant.

However, do note that a character can qualify for this rating even if their verse does not have an infinitely-layered or equivalent cosmology, as long as it is either stated, shown or left very obvious that the character in question already bypasses the very nature of such structures altogether, in a way that simply "stacking" more of them logically would not allow one to reach their level of power / size.[3]

Mathematically, 1-A has its size represented by further uncountably infinite cardinals beyond useful applications of certain measures (ℵ2 and onwards, most specifically) and can be extended unto greater levels of infinity, representing different complexities or qualitative "steps" on an Outerversal scale, in the same way 1-B and 1-C are divided. Characters who stand an infinite number of steps above "Baseline" Outerversal realms and structures are to have a + modifier in their Attack Potency section (Outerverse level+)

I would probably go with something like

1-A | Outerverse level: Characters who can significantly affect, create and/or destroy realms or states that are shown to transcend infinitely-layered hierarchies and/or dimensional levels on a conceptual or existential level, normally being portrayed as external or outside of the applications of dimensionality as a constant defined by physics on any level. A typical portrayal of this level is the being perceiving the hierarchy/dimensional levels as akin to fiction or something similarly insignificant.

However, do note that a character can qualify for this rating even if their verse does not have an infinitely-layered or equivalent cosmology, as long as it is either stated or shown that the character in question already bypasses the very nature of such structures altogether in a conceptual manner, so that simply "stacking" more of them logically would not allow one to reach their level of power / size.

Mathematically, 1-A has its size represented by further uncountably infinite cardinals beyond useful applications of certain measures (ℵ2 and onwards, most specifically) and can be extended unto greater levels of infinity, representing different complexities or qualitative "steps" on an Outerversal scale, in the same way 1-B and 1-C are divided. Characters who stand on these higher steps above "Baseline" Outerversal realms and structures are to have a + modifier in their Attack Potency section (Outerverse level+)

High 1-A

High 1-A | High Outerverse level: Characters who can affect and create/destroy states or realms which are completely transcendent over infinitely-layered Outerversal hierarchies and any extensions thereof, as well as the framework in which such entities are defined in the first place. Note that simply adding more "layers" to an already infinite 1-A hierarchy (or some structure of equivalent size) is not enough to reach this tier, and one must be completely external and unreachable by it in any form.

I would just simplify it to

High 1-A | High Outerverse level: Characters who can affect and create/destroy realms or states which are completely transcendent over Outerversal hierarchies and any extensions thereof, as well as the framework in which such entities are defined in the first place. Note that simply adding more "layers" to an already infinite 1-A hierarchy (or some structure of equivalent size) is not enough to reach this tier, as to get the rating one must be completely external to the 1-A hierarchy as that 1-A is external to a High 1-B hierarchy.

Tier 0 doesn't need much of a change besides a note imo

0 | Boundless: Characters who demonstrate an equivalence to, or can create/destroy/affect, transcendental abstract levels of existence which conceptually stand superior to even High 1-A levels. Being “omnipotent” or any similar reasoning[4] is not nearly enough to reach this tier; characters at this level must transcend High 1-A characters as High 1-A characters would transcend 1-A ones. This tier has no true endpoint, and can be extended unto any higher level, spiraling infinitely upwards.

To

0 | Boundless: Characters who demonstrate an equivalence to or exist in a transcendental abstract levels of existence which stand conceptually superior to High 1-A levels. Characters at this level must transcend High 1-A characters as High 1-A characters would transcend 1-A ones. This tier has no true endpoint, and can be extended unto any higher level, spiraling infinitely upwards[4].

Being “omnipotent” or any similar reasoning is not enough reasoning to reach this tier on its own. Such statements can be used as supporting evidence of transcending the state of High 1-A

That's the best I got after like, ten minutes of looking at it

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[Qawsedf234]

As a separate comment with my rewrites

Low 1-A | Low Outerverse level: Characters who can significantly affect, create and/or destroy realms or states of uncountably infinite dimensions, or which have a size roughly analogous to them: Such as uncountably infinite sets of hierarchical layers or planes of existence that equate to the first uncountably infinite cardinal, ℵ1.

Alternatively, this tier can also be assigned to characters who exceed High 1-B structures when no further context regarding the nature of such superiority is given.

1-A | Outerverse level: Characters who can significantly affect, create and/or destroy realms or states that are shown to transcend infinitely-layered hierarchies and/or dimensional levels on a conceptual or existential level, normally being portrayed as external or outside of the applications of dimensionality as a constant defined by physics on any level. A typical portrayal of this level is the being perceiving the hierarchy/dimensional levels as akin to fiction or something similarly insignificant.

However, do note that a character can qualify for this rating even if their verse does not have an infinitely-layered or equivalent cosmology, as long as it is either stated or shown that the character in question already bypasses the very nature of such structures altogether in a conceptual manner, so that simply "stacking" more of them logically would not allow one to reach their level of power / size.

Mathematically, 1-A has its size represented by further uncountably infinite cardinals beyond useful applications of certain measures (ℵ2 and onwards, most specifically) and can be extended unto greater levels of infinity, representing different complexities or qualitative "steps" on an Outerversal scale, in the same way 1-B and 1-C are divided. Characters who stand on these higher steps above "Baseline" Outerversal realms and structures are to have a + modifier in their Attack Potency section (Outerverse level+)

High 1-A | High Outerverse level: Characters who can affect and create/destroy realms or states which are completely transcendent over Outerversal hierarchies and any extensions thereof, as well as the framework in which such entities are defined in the first place. Note that simply adding more "layers" to an already infinite 1-A hierarchy (or some structure of equivalent size) is not enough to reach this tier, as to get the rating one must be completely external to the 1-A hierarchy as that 1-A hierarchy is external to a High 1-B hierarchy.

0 | Boundless: Characters who demonstrate an equivalence to or exist in a transcendental abstract levels of existence which stand conceptually superior to High 1-A levels. Characters at this level must transcend High 1-A characters as High 1-A characters would transcend 1-A ones. This tier has no true endpoint, and can be extended unto any higher level, spiraling infinitely upwards[4].

Being “omnipotent” or any similar reasoning is not enough reasoning to reach this tier on its own. Such statements can be used as supporting evidence of transcending the state of High 1-A

 

[KingPin0422]

Thing is, extrapolating this fundamental superiority to this extent seems like an extremely hasty generalization to me.

We are not talking about being infinite levels of infinity bigger anymore. Not about being infinite hierarchies of infinite levels of infinity each bigger either.
Even infinite hierarchies of infinite hierarchies of infinite hierarchies of infinite hierarchies (continue this infinite times) of infinite hierarchies of infinite levels of infinity bigger is even remotely large enough.
Not even if the amount of infinite hierarchies of transcending infinite hierarchies of levels of infinity is so large that it is described by the biggest infinity of the infinite hierarchies stack mentioned above it would approach large cardinal level.
And even infinite steps, with the gap between each gap being bigger than that, would be there yet.

Like, yeah, the Law of Identity for example would be bigger than the whole story hierarchy system. But extrapolating being bigger than the entire system to be bigger to this extent, when the entire known system just has one or two infinite hierarchies here and there, is an immense quantitative jump.

It just seems crazy to me that transcending some framework that has no showings of remotely approaching the size of all regular cardinals would be ranked as larger than it, just because some being is of a fundamentally greater nature than that smaller framework in its verse.

[...]

Honestly, I feel like using statements like "above all mathematics" as actual Tier 0 evidence isn't better than using Omnipotence as evidence.

Like, I get it, it's tempting to say that if the character is already 1-A and depicted as practically omnipotent we might as well start to take statements we would usually discard as No-Limit Fallacies literally.
But we shouldn't give in to that. Ultra high-tier characters should be held up to higher standards of scrutiny, not to lower ones. Statements like "above mathematics", "above logic", "transcending everything at all levels" etc. should still remain in the realms of just things that were very explicitly addressed in the verse and not stretched beyond that.

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+. 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.

 

[CloverDragon03]

Sorry but I'm pretty much useless for any tiers above High 1-C so I can't really help here

 

[The_Impress]

Not exactly, just something that shows you're superior to the Low 1-A structure entirely, without being, like the example said, just "infinity+1" in relation to it. So, for example, if you have some infinite hierarchy, and a space of infinite dimensions is just the lowest step of that hierarchy (i.e the "floors" aren't exactly equivalent to +1 dimensions but some larger difference than just that), then the step immediately succeeding that one would be Low 1-A.


Most theological concepts that you see popping up in fiction can be seen as examples of that, although more inclined towards philosophy than math, I admit. I guess a verse with that would be World of Darkness, where the supreme being/state is just completely above any description, name, or identity that you might extrapolate for it, to the extent that, by assigning any of those three to it, you're automatically forming something lesser instead (That is in relation to High 1-A realms, for the matter)


To clarify this point: They can be whatever, really. Once you hit a large enough cardinality, a set of whatever is at that tier, regardless of what its elements are. So, say, a set of 0-dimensional points with cardinality aleph-2 is Low 1-A, and so is a set of universes, or whatever else you can think of.

I feel like this needs to be worded in the draft :v

As a separate comment with my rewrites

I feel like it still retains alot of unnecessary bulk (Worded in the OP), it's less of a pain to read generally, but its still unelaborating very much so

 

[Antvasima]

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+. 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.

This is also a good point. I am neutral then.

 

[Antvasima]

Anyway, what do you think about Qawsedf's suggestions and KingPin's comments, @Ultima_Reality and @DontTalkDT ?

 

[Qawsedf234]

I feel like it still retains alot of unnecessary bulk (Worded in the OP), it's less of a pain to read generally, but its still unelaborating very much so

Yeah. I have ways to further simplify it I guess, but it's still going to be wordy to some degree if you don't want to make the tiers rather vague.

 

[Antvasima]

I would also prefer if the listed requirements are quite specific.

 

[Qawsedf234]

When I get off work I'll try to tweak it down to the bare essentials and try to avoid some of the more wordy parts.

 

[Antvasima]

Okay. Thank you for helping out. Just please remember to not simplify it to the point that the essential points/explanations are not left.

 

[Qawsedf234]

Anyways here's my best attempt.

Low 1-A | Low Outerverse level: Characters who can significantly affect, create and/or destroy realms or states of uncountably infinite dimensions, or which have a size roughly analogous to them: Such as uncountably infinite sets of hierarchical layers or planes of existence that equate to the first uncountably infinite cardinal, ℵ1.

Alternatively, this tier can also be assigned to characters who exceed High 1-B structures when no further context regarding the nature of such superiority is given.

1-A | Outerverse level: Characters who can significantly affect, create and/or destroy realms or states that are shown to transcend a High 1-B hierarchy on a conceptual or existential level, normally being portrayed as external or outside of the applications of dimensionality defined by physics on any level. A typical portrayal of this level is the being perceiving the High 1-B hierarchy as akin to fiction or something similarly insignificant.

However, do note that a character can qualify for this rating even if their verse does not have an infinitely-layered or equivalent cosmology, as long as it is either stated or shown that the character in question bypasses the very nature of such structure in a conceptual manner, so that simply "stacking" more of them logically would not allow one to reach their level of power / size.

Mathematically, 1-A has its size represented by further uncountably infinite cardinals (ℵ2 and onwards, most specifically) and can be extended unto greater levels of infinity, representing different complexities or qualitative "steps" on an Outerversal scale, in the same way 1-B and 1-C are divided. Characters who stand on these higher steps above "Baseline" Outerversal realms and structures are to have a + modifier in their Attack Potency section (Outerverse level+)

High 1-A | High Outerverse level: Characters who can affect and create/destroy realms or states which are completely transcendent over 1-A hierarchies and any extensions thereof, as well as the framework in which such entities are defined in the first place. Note that simply adding more "layers" to an already infinite 1-A hierarchy (or some structure of equivalent size) is not enough to reach this tier, as to get the rating one must be completely external to the 1-A hierarchy as that 1-A hierarchy is external to a High 1-B hierarchy.

0 | Boundless: Characters who demonstrate an equivalence to or exist in a transcendental abstract level of existence which stand conceptually superior to High 1-A levels. Characters at this level must transcend High 1-A characters as High 1-A characters would transcend 1-A ones. This tier has no true endpoint, and can be extended unto any higher level, spiraling infinitely upwards[4].

Being “omnipotent” or any similar reasoning is not enough reasoning to reach this tier on its own. However, such statements can be used as supporting evidence of transcending the state of High 1-A hierarchy.

 

[DontTalkDT]

"transcendental abstract level of existence which stand conceptually superior"
"conceptual or existential level"
I think the bolded parts would need a definition to be unambiguously understandable for everyone.
Perhaps conceptually superior could be exchanged for "qualitatively superior", a term for which we wanted to add a definition to the Tiering System FAQ a while ago. (which reminds me that I think we haven't finished that thread yet... I need to get to that sometime soon)

 

[KingPin0422]

I guess I'll throw my hat into the ring as well, only I'll be building on Ultima's draft:

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.

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 "levels" contained in the previous tiers, including an infinite number of them. Practically speaking, this would be something completely unreachable to any 1-A hierarchies.

A concrete example of such an object would be a large cardinal, which is most simply defined as a number too large to be constructed or even proven to exist using the tools provided by standard mathematics, and as such has to be "assumed" to exist in order to be made sense of or defined in formal ways (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.

And while we're talking about rewriting the tiering system's explanations, something else has been bothering me as well that I think is somewhat related to this discussion: do we still need 1-A+? As far as I am aware, we only have one 1-A+ character on the entire site as of this post; all the other ones have since left the tier, and now it feels very barren and... unnecessary. If the rest of you here would rather save it for a separate discussion, I understand, but I wanted to get this thought out there in case someone asks about it, since it was suspiciously absent from Ultima's draft.

 

[The_Impress]

And while we're talking about rewriting the tiering system's explanations, something else has been bothering me as well that I think is somewhat related to this discussion: do we still need 1-A+? As far as I am aware, we only have one 1-A+ character on the entire site as of this post; all the other ones have since left the tier, and now it feels very barren and... unnecessary. If the rest of you here would rather save it for a separate discussion, I understand, but I wanted to get this thought out there in case someone asks about it, since it was suspiciously absent from Ultima's draft.

This I feel is a separate discussion, yeah.

Anyways here's my best attempt.

I feel personally it still doesn’t fully address my issues with it completely, but I’ll probably let others state their judgement as well :V

 

[Antvasima]

@Ultima_Reality

What do you think about Qawsedf's and KingPin's suggested modifications to your draft?

 

[Ultima_Reality]

I feel like this needs to be worded in the draft :v

Sure thing. Would something like this work?:

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 (Although they don't necessarily need to transcend infinitely-many Low 1-A structures for this). 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.

Makes me think about how mathematicians at times say something is true "almost everywhere" if it is true on an uncountably infinite set with the same cardinality of exceptions to that rule

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.

Honestly, I feel like using statements like "above all mathematics" as actual Tier 0 evidence isn't better than using Omnipotence as evidence.

Like, I get it, it's tempting to say that if the character is already 1-A and depicted as practically omnipotent we might as well start to take statements we would usually discard as No-Limit Fallacies literally.
But we shouldn't give in to that. Ultra high-tier characters should be held up to higher standards of scrutiny, not to lower ones. Statements like "above mathematics", "above logic", "transcending everything at all levels" etc. should still remain in the realms of just things that were very explicitly addressed in the verse and not stretched beyond that.

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.

What do you think about Qawsedf's and KingPin's suggested modifications to your draft?

I like KingPin's suggestion more, if only because I'd want to simplify the descriptions as much as possible, which in my eyes means distancing them from the current ones. Although I admit I don't see how they're much different from mine. (Might be the tired brain speaking, though)

 

[The_Impress]

Sure thing. Would something like this work?:

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 (Although they don't necessarily need to transcend infinitely-many Low 1-A structures for this). 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.

Yeah this works well.

I'm fine with Ultima's draft for now, it's less layman-ey, but at the same time I feel it at least removes essentially all unnecessary bulk and contradictions, and I feel listing it alongside the Tiering Explanation Page (Which for the record should be renamed to "Cardinality for Wiki Purposes" or something) will help most people understand all crucial asepcts well.

Of course it can be improved, but if the thread goes dead I'll just suggest using that, is what I'm implying here.

 

[KingPin0422]

I like KingPin's suggestion more, if only because I'd want to simplify the descriptions as much as possible, which in my eyes means distancing them from the current ones. Although I admit I don't see how they're much different from mine. (Might be the tired brain speaking, though)

All I did was reword a few things and correct some typos, really. For one, I got rid of mentions of "transcend" because that's frankly a nebulous term that people on this site tend to throw around without understanding its nuances.

 

[Antvasima]

Big thanks to everybody who are helping out here. It is extremely appreciated.

 

[First_Witch]

Well, if people dont mind then i will use this to ask questions regarding our standards then, maybe that helps making our explanations simpler. And, well, i apologize in advance if what im saying in following is super elementar, wrong and stupid. But i think i rather take the embarrasment of being wrong and have at least my basics covered and corrected

Currently, my biggest question is... What exactly IS Low-1A? I used to operate under the pretense that Low-1A was something akin to baseline 1-A, the first layer that trancends an High 1-B structure in its entirety. But considering that we align it with Aleph 1, is it its own hierachy? To make my thoughtprocess a bit more clearer, let me explain how i view and explain to myself mentally how the tiering system works;

Basically, i take a example structure and asign the corresponding numbers to it. Example: High 1-B, an infinite layered hierachy, a infinite dimensional structure, whatever it is. Such structure corresponds with Aleph 0, or the smallest infinity. The set of all natural numbers is called Aleph 0, so its easy to assign numbers to the corresponding structure. 3 Is anything from below human to an infinite universe, 4 is a infinite space time continuum, 5 is 5 dimensional, 6 is 6 dimensional etc etc, until you reach Aleph 0, which corresponds to the entirety of the infinite layered structure. So far so easy.

So Aleph 1, the last Aleph i still have a semblance of a grasp on. Aleph 1 is, continuing or number example, all real numbers right. Aleph 1 is uncountably, its a infinite bigger than the infinity that is Aleph 0, like how the set of all real numbers is literally bigger than the set of all natural numbers is. So its logical to say that a structure, that is Aleph 1 big to a smaller structure that is Aleph 0 big, to be superior by size or whatever superiority you want to assign it.

So ultimatly, how exactly does Aleph 1 correlate to Low 1-A. This is not a proof it question, that i dont doubt that it is correct, but rather a "how does it correlate", if that makes sense. Currently, i have 3 ideas of Low 1-A:

1. Low 1-A corresponds to Aleph 1 in its entirety, making it a single layer in a Outerversal Hierachy (Aleph infinity? Omega? I dont know the name)

2. Low 1-A corresponds to the numbers within Aleph 1, making it its own infinite layered hierachy. Seeing as by sheer amount of numbers between 0 to 1 in Aleph 1 already dwarves Aleph 0 in amounts, is this how we visualize the layers in a Low 1-A hierachy? Like R(Real number)0 to R1 is Layer 0 to Layer 1 in Low-A because they are literally bigger than Aleph 0 and could fit more than a infinite amount of such structures inbetween?

3. Or, now that i actually wrote down my thoughts, both? Which would make Low-1A compareable to our old 1-A pre Ultima and DT tiering system revision and our current 1-A compareable to our old High 1-A? Isnt our tiering system thus unfathomoably bigger than it used to be then?

I will ask more after i have my basics down, thanks in advance for your attention.

cough

 

[KingPin0422]

In practice, Low 1-A is almost always going to be a single layer in an outerversal hierarchy. To quote Ultima:

Not exactly, just something that shows you're superior to the Low 1-A structure entirely, without being, like the example said, just "infinity+1" in relation to it. So, for example, if you have some infinite hierarchy, and a space of infinite dimensions is just the lowest step of that hierarchy (i.e the "floors" aren't exactly equivalent to +1 dimensions but some larger difference than just that), then the step immediately succeeding that one would be Low 1-A.

Basically, as long as it's not a difference that can be considered as just "infinity+1," something that stands above any Low 1-A structure in scale should be 1-A. This also extends to High 1-B in that being completely external and superior to a structure of that tier, provided it isn't reducible to just another dimensional difference, is enough to qualify for Low 1-A. Whether it's baseline High 1-B or infinitely above baseline is irrelevant.

 

[First_Witch]

So it is basicaly just Layer 1 in a outerversal hierachy then?

 

[KingPin0422]

You can think of it as that in a general sense, yeah, but it obviously depends on the verse.

 

[First_Witch]

Now that sounds ominous. Do you perhaps have examples on how it might differ between verses?

 

[KingPin0422]

Let's see...

• Twin Peaks has a High 1-B multiverse with infinite levels of space and time, followed by a spiritual realm that stands beyond the entire structure, but nonetheless still beholds some level of spacetime. Above even that is a void in which space and time completely cease to be relevant concepts.
• Marvel Comics directly defines an uncountably infinite number of dimensions, and the SCP Foundation 'verse does as well. Of course, the former doesn't seem to actually reference those dimensions outside of one story and so is currently ignored for our purposes, and the latter has never had anyone scale exactly to them, but there's still a precedent to be argued.
• While I have no actually existing examples of this, what Ultima explained earlier also fits here: a "composite hierarchy" in which the lowest level is itself a High 1-B structure would have the second level as Low 1-A and any levels afterward as 1-A, provided that it is explained well enough.

 

[Antvasima]

This is just a note that DontTalk will be busy with exams for the next 2 weeks, so we will likely not get this revision finished during that time. Also, The_Impress is taking a break from this community to recover her health.

Please feel free to continue to help out here though. We really need to get this done.

 

[KingPin0422]

To be honest, I don't know if we can even move this forward at all while those two are on leave. Ultima already gave his response to DontTalk's points, and we don't have anyone else on-hand that's willing to engage in this kind of discussion, so unless we find some other people who know how to help and won't derail, I think we'll be at an impasse until DT and/or Zark return.

In the meantime, I could make another thread addressing the need for 1-A+, since that is an issue that's bothered me lately, but I have another ongoing revision (a non-staff one) that I think should be concluded before I tackle that.

 

[Antvasima]

Yes, let's wait until after we have finished here.

 

[Hop_Hoppington-Hoppenhiemer]

oh sheesh, this is a big one. Hop will return for more input, this is a useful thread indeed

 

[Antvasima]

Thank you for helping out.

 

[Elizhaa]

I will to reply more tomorrow.

 

[Antvasima]

Okay. Thank you for the help.

 

[Elizhaa]

I am kind of fine with the recent update from KingPin and Ultima's drafts. I want to ask though wouldn't it be better to just have the Malho cardinal analogy for starting point of Tier 0 similar to the aleph level of Tier 1-A?
On the math point, I feel like Tier 1-A+ can also have Aleph omega on the mathematical basis since I recall it was discussed.