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

[The_Impress]

I believe Ultima applied it already:

Tiering System

The following is a comprehensive overview of the hierarchical system which this wiki utilizes in order to properly categorize and index fictional characters, entities, and objects based on the scale of their feats, and the varying scopes which they can affect or create/destroy. However, it...

vsbattles.fandom.com

I forgot to notify it on this thread as well, sorry.

 

[Antvasima]

Okay. That is good then.

We still need to make the definition for tier 0 more precise though.

 

[The_Impress]

I will like to note though, the current Tier 0 definition does in fact line up with the previous Tier 0 definition and functioning pretty perfectly, and maybe by mathematically defining it we may run risk of invalidating some of the current occupiers for the tier? Similar to how DT argued High 1-A's mathematical definition ran that risk. That may be beyond the scope of this thread alone, but I'll let either DT or Ultima elaborate on its feasibility.

 

[Antvasima]

Yes, it is best to let the people who understand higher-order mathematics best here handle it.

 

[KingPin0422]

I believe Ultima and DontTalk were going to privately discuss the mathematics behind tier 0 at a later time, mainly regarding whether the tier should be defined as a universe of sets or as something else, and then one of them would make a thread to address it afterwards.

 

[Antvasima]

Okay. Thank you for the information. That sounds good to me.

 

[DontTalkDT]

So, some minor wording concerns with the new version Ultima edited in:
The "stand outside of any extensions of infinite hierarchies and sizes" as general description of 1-A just seems wrong. That applies, at the earliest, for High 1-A, although I would rather not see it there either. "Any extension" is just is either way too vague or straight up hyperbole.

Second, reading over it again, I think the High 1-A part should have a small change.
Specifically:

Characters who can affect objects that are larger than what the logical framework defining 1-A and below can allow

This should probably say mathematical framework, as logic in itself doesn't cover it.
"can allow" is also in so far wrong as that ZFC allows for those levels even if you can't show the existence of such cardinals. I think ZFC is the framework we are talking here, right? Instead, we should say "can prove to exist" or something of that nature, as that's more precise.

 

[Antvasima]

As usual, I strongly trust DontTalk's sense of judgement, but I would prefer confirmations from @Ultima_Reality and @KingPin0422 as well in order to make certain.

 

[KingPin0422]

Why is there even a general "1-A" section in the first place? The description given to it doesn't truly apply any earlier than High 1-A, as DontTalk said up there, not to mention that it makes the 1-A tiers somehow seem special or different, which is an idea we were supposed to have moved past by now.

The "stand outside of any extensions of infinite hierarchies and sizes" as general description of 1-A just seems wrong. That applies, at the earliest, for High 1-A, although I would rather not see it there either. "Any extension" is just is either way too vague or straight up hyperbole.

I mean, the idea is that no amount of successor operations or power sets of infinite cardinals can reach even the smallest inaccessible cardinal, which is the baseline for High 1-A. That's why it's known as an inaccessible cardinal. But I am open to suggestions to refine the words used.

This should probably say mathematical framework, as logic in itself doesn't cover it.

Logic and mathematics do sort of go hand-in-hand, but our tiering system is supposed to be a mathematical one, so sure.

"can allow" is also in so far wrong as that ZFC allows for those levels even if you can't show the existence of such cardinals. I think ZFC is the framework we are talking here, right? Instead, we should say "can prove to exist" or something of that nature, as that's more precise.

We do base our system on ZFC, yes, but I don't really care one way or the other. Both wordings are equally valid in my eyes: in a general sense, if a formal system can't prove that something exists, then that thing is just not accounted for and effectively does not exist, even if its nonexistence is similarly unprovable. I think the assumption in this case is that inaccessible cardinals basically exceed the purview of the default model of ZFC, and so in order to work with them, you have to construct a "bigger" model which can accommodate them.

 

[DontTalkDT]

I mean, the idea is that no amount of successor operations or power sets of infinite cardinals can reach even the smallest inaccessible cardinal, which is the baseline for High 1-A. That's why it's known as an inaccessible cardinal. But I am open to suggestions to refine the words used.

That's ok, it's just that the wording doesn't convey the idea very well. Extra axioms are also an extension of the prior. Inaccessible cardinals in and of themselves are an extension of ZFC... just sounds rather misleading.

Technically there is a number of successor operations / power sets that reach an inaccessibel cardinal.... an inaccessible cardinal many to be specific. But I get the idea.

One could now clarify in which sense it is meant, but at that point we would just be explaining what an inaccessible cardinal is and we already do that. For the general explanation, I would just delete it without replacing that part with anything. The current High 1-A text already doesn't include it and that can just stay that way.

Logic and mathematics do sort of go hand-in-hand, but our tiering system is supposed to be a mathematical one, so sure.

Mathematics needs logic, logic not necessarily mathematics. It's mostly just that logical framework sounds like formal/logical system for me and that's not what we mean.

We do base our system on ZFC, yes, but I don't really care one way or the other. Both wordings are equally valid in my eyes: in a general sense, if a formal system can't prove that something exists, then that thing is just not accounted for and effectively does not exist, even if its nonexistence is similarly unprovable. I think the assumption in this case is that inaccessible cardinals basically exceed the purview of the default model of ZFC, and so in order to work with them, you have to construct a "bigger" model which can accommodate them.

Uh, mathematicians would throw some hard words at you for that position. Consider: ZFC even contains an axiom which's only purpose it is to state that certain sets do not exist. If ZFC is consistent you can't construct any such sets anyways, but knowing that they actually do not exist is really important to people.
So yeah, controversal opinion. Do not support that <.<

 

[Antvasima]

So what should we do with the more generalised 1-A section text? Should it be removed (together with the redundant "1-A: Transcendent" section itself), or be incorporated into the High 1-A section text?

 

[Antvasima]

So what should we do with the more generalised 1-A section text? Should it be removed (together with the redundant "1-A: Transcendent" section itself), or be incorporated into the High 1-A section text?

@DontTalkDT @KingPin0422 @Ultima_Reality

 

[Antvasima]

So what should we do with the more generalised 1-A section text? Should it be removed (together with the redundant "1-A: Transcendent" section itself), or be incorporated into the High 1-A section text?

@DontTalkDT @Ultima_Reality @KingPin0422

We still greatly need your help here.

 

[KingPin0422]

Sorry, Ant, but I need to step away from this site for a bit to recover from surgery.

 

[DontTalkDT]

So what should we do with the more generalised 1-A section text? Should it be removed (together with the redundant "1-A: Transcendent" section itself), or be incorporated into the High 1-A section text?

How about changing that part to:

Characters who functionally transcend the rest of the Tiering System. These characters are of infinitely higher power than even those that have absolute power over a single infinite hierarchy of levels of infinity.

It's simple, but should serve as general description just fine.

 

[Antvasima]

Sorry, Ant, but I need to step away from this site for a bit to recover from surgery.

Oh. I am very sorry to hear that. I really hope that you make a full recovery soon.

 

[Antvasima]

@DontTalkDT

That seems fine to me. Would you be willing to make the adjustment please?

Also, what do you think, @Ultima_Reality ?

 

[DontTalkDT]

@DontTalkDT

That seems fine to me. Would you be willing to make the adjustment please?

I have applied it.

 

[Antvasima]

Thank you. However, doesn't "these characters have infinitely higher power" just sound like a higher degree of High 1-B?

 

[Antvasima]

I have applied it.

Thank you. However, doesn't "these characters have infinitely higher power" just sound like a higher degree of High 1-B?

@DontTalkDT @Ultima_Reality

 

[Ultima_Reality]

Thank you. However, doesn't "these characters have infinitely higher power" just sound like a higher degree of High 1-B?

I don't think it's necessary to go too in-depth on that section. Its whole purpose is just to serve as a primer for the basic concept that's elaborated upon by the tier descriptions proper.

 

[Antvasima]

Okay. So it can remain as it is then? I just think that the current description can likely be easily misunderstood.

 

[Antvasima]

I have applied it.

Thank you. However, doesn't "these characters have infinitely higher power" just sound like a higher degree of High 1-B?

I don't think it's necessary to go too in-depth on that section. Its whole purpose is just to serve as a primer for the basic concept that's elaborated upon by the tier descriptions proper.

Okay. So it can remain as it is then? I just think that the current description can likely be easily misunderstood.

@Ultima_Reality @DontTalkDT

 

[Ultima_Reality]

Okay. So it can remain as it is then?

It can, yes.

 

[Antvasima]

Okay. Thank you for the reply. Is there anything left to do here, or should I close this thread?

 

[Ultima_Reality]

I don't believe there is? Last I've checked, some of the topics that started being tackled extended beyond the scope of this thread and were reserved for later, anyway.

 

[Antvasima]

Okay. I will close this thread then. Thank you to everybody who helped out here.