I'm bringing up the specific view that our Tiering System recognizes, this being the ability called Beyond-Dimensional Existence Type 2 (Being above spatial properties entirely), so, dunno what your issue is, since it's a definition we already all agreed to, I hope? I never said that no evidence would be required for us to conclude that a verse is abiding by the notion I'm speaking of. I'm talking about cases where we are already sure the verse is abiding by that notion.
What we recognize is that BDE Type 2 exists, we don't recognize that it is High 1-A and never did. I'm not sure where you take that from. All BDE Type 2 currently is, is that you are non-spatial in nature and are transcendent of dimensions within the scale of your verse.
Like, the BDE description we currently use states "These characters aren't necessarily superior to spacetime on every level, but just within the scope which they are shown." It actually is rather supportive of the principle that BDE characters aren't just above a high-end extrapolation beyond their showings.
And while you say you are talking about cases where we are sure the verse is abiding the notion... the entire debate is how you are against requiring explicit mention of the stuff you want to scale these characters above.
How can you be sure that a fiction that never mentions infinite dimensions, and much less cardinals, in any way follows your interpretation that being above dimensions makes you so powerful that you could destroy spaces whose size is of that of arbitrarily high cardinals? If a fiction doesn't mention an object like that, or one of equivalent size in composite hierarchies, you can't be sure.
Like, the best statement you can have without getting explicit is something along the lines of "regardless of how many dimensions there are, since this character is above dimensions he is superior to them all". Or something like you brought up "for a beyond dimensional character transcending one dimension and many are fundamentally the same". Like I made clear in my layout of proposed standards, I'm fine of upscaling by an infinite hierarchy if this type of statements are made. If a verse with 5D made such a statement, I'm fine with putting it at Low 1-A (or 1-A if anyone can properly justify the separation argument, I guess). But is it evidence that structures with higher cardinal sizes were considered? I don't think so!
You can say the idea presented should naturally extend to that, but I don't find it natural to do so, if the verse never plays with such concepts.
In essence, it is the same as the issue with Omnipotence. A verse can go and have a big lecture about Omnipotence. How it is logically contradicting, but the god in question doesn't care and how only the good conclusions apply to it and none of the bad. How truly everything is within its power etc. etc. However, if the verse never gets explicit about the god being able to wield its power to affect an object of a specific big size, or some other feat we can pin a tier to, we have Omnipotent characters still stick to "Omnipotent within the bounds of objects of the size the verse is known to have".
Or, to mention the only high-tier verse I support (I mentioned it already, but I will include it for first-time readers), Demon King Daimao has a character above all possible stories and a section where it's debated what possible stories are. It defines possible stories quite explicitly as "if it is logically consistent and can be expressed in words, it is a possible story". I would not be fine with upgrading the verse based on that using concepts the verse has never played with. If it never brings up an aleph_100 dimensions big space, I would not be fine with upgrading it just because by the verse's reasoning one can argue it should be included (as would large cardinals be...). Because, while I can run with the reasoning standards explained and reason that it technically should include lots of stuff, we have no guarantee that this was considered when the reasoning standards were made. It is a rule that gets extended beyond the scope it was made in. A hasty generalization, so to say. And I think that's similar to the dimensionality beyond the demonstrated scope case.
IMO it in spirit still is a lot like a NLF. Even if we knew the author intended to make an unbeatable character, we can't run with that idea to assume they considered everything humanity could imagine to beat it anyway. That's one part of why we don't extend such notions far. A rule as well should just also be only extended as far as we are certain it was considered to, so a fiction should provide some evidence that it considers all cardinals if we want to put a character above all cardinals.
With that said, let's get to the side points:
Yeah, and I'd say that's pretty untenable. As Agnaa pointed out, those things can get pretty arbitrary, but as soon we make an equivalence between these things, we are giving in to other implications of equality. For instance, as far as we are concerned, if you are in Layer A, transcending Layer B as fiction, putting together uncountably infinite things in Layer B is going to have something there transcend into Layer A (If we didn't treat it like that it would entail the difference between layers being greater than a dimensional jump). These implications get pretty bad when we're equating dimensional things to non-dimensional things.
And they get pretty ridiculous if you don't. Are you saying a set of all sets in fiction could transcend into reality? Obviously not. Then by the argument you just presented R>F transcendence should be TIer 0.
Your argument is essentially no better than those that argue all omnipotent entities in fiction should be considered equal in power due to being omnipotent. It's technically not a non-logical standpoint, but not one we as a vs-debate community acknowledge. In vs debating feats trump philosophy. The Omnipotent entity with better feats is the more powerful one, even if both are supposed to be omnipotent. Because we only assume omnipotence exist in the realms that the verse explored and not further.
And, yeah, just as for Omnipotence and just as for R>F transcendence this applies here as well. You're above all dimensionality? Well, show your scope of dimensionality. If it's less than that of someone that has shown more, you will still get the worse ranking, because we don't buy into such extrapolative statements beyond what the verse explains.
So yeah, that's why R>F is as it is. Because it's the highest logical argument that can be made without adding something not mentioned to the verse.
Also, honestly, should I add "want R>F to be Tier 0" to the things you want to achieve here? Or is it the opposite "R>F should be untierable"?
I am aware you are going by some notion of "power," yes, but ultimately gauging what power it takes to significantly affect and destroy something is going to be tied into making an equivalence between the "size" of what's being affected and some given n-dimensional space, so, I think that distinction is one without a difference, as said prior. So, by that point, we're just saying "Those things are equivalent because we say they are equivalent." If you try to apply any actual reasoning to it, you see that the argument itself is a false equivalence: Making a equivalence between two things due to a property they both share (Superiority over some scope of existence. Both 4-D space and a conceptless void house 3-D space, so they're equivalent)
Frankly, I'd be fine with saying destroying a dimensionless void that's not superior to dimensions, but different in nature from them, would be untierable, for the reasons above. When you say "We tier it this way because if you can destroy a conceptless void capable of housing a 3-D space then you can destroy the 3-D space as well," you're not really tiering the non-dimensional properties of the void, just the fact that it can house a 3-D space, and this would in turn just loop back into my point: That, if this void isn't really superior to dimensions, then it is irrelevant to the conversation at hand, and that if it is and you're equating it to 4-D space solely from the fact they are both superior to a 3-D space, then that's fallacious logic.
Your argument seems to boil down to "Fiction can have different kinds of transcendence that aren't necessarily dimensional in nature, so being beyond dimensions doesn't inherently mean you jump infinite tiers," but I think that's also a weird argument that gets amended fairly straightforwardly once you apply Occam's Razor: Entities should not be multiplied unnecessarily. Which is to say that, if a verse never mentions or alludes to other equivalent methods of transcendence, we generally speaking would have to assume that dimensional.jumps are the only available avenue. Else we are effectively just assuming the cosmology allows for paradoxes without good reason, which to me is a no-no.
If you say that a non-dimensional space that is tiered by comparing to dimensions wouldn't really be superior, then you are contradicting yourself in that the High 1-A tier is also the result of comparing it to dimensions. I indeed do not tier the non-dimensional properties of any void, because those are just not tierable. The only thing we can tier is the relative relationship in "size", i.e. power needed to destroy them, when compared to dimensional spaces. If the spaces weren't tiered like that you would have no guarantee that those who destroy them are superior in power to dimensional characters. Only by asserting that they are "larger" (need more power to destroy) than some dimensional reference space you can do so.
You try to have those non-dimensional things be incomparable, yet simultaneously larger than, dimensional spaces. An obvious paradox.
What occam's razor is concerned, you're wrong and it actually goes against you. I'm not asserting any special kind of transcendence other than the one the source mentions: Transcendent of dimensions. What I demonstrated by showing that transcendence of dimensions in fiction can be one that is not equivalent to transcending all higher dimensions on a High 1-A scale is that transcendence of that kind can exist. Now you have the burden of proof to show that this transcendence of dimensions is not having that property.
And with that we loop back to the main point. You assume that the legitimate interpretation has to be the one based on how you imagine transcendence of this type should work, while that interpretation isn't in any way proven to be the legitimate one. Both author and reader can just as easily understand it as being within the scope of dimensionality the verse laid out.
You talk about "if a verse never mentions or alludes to other equivalent methods of transcendence", but forget that in the scenario we are talking about the verse hasn't established that the method of trasncendence in question involves being above cardinality-many dimensions. That's the problem of this whole debate. That what you try to sell as the default viewpoint of dimensional transcendence has no right to be the default.
Now, what occasm's razor is concerned, assuming that the dimensionality that the "above dimensionality" statements are referring might be limited to the dimensionality explicitly mentioned in the verse, requires 0 assumptions on my part. I'm only asserting a possibility, not a definitive truth, and then argue based on it being possible to not refer to something that's infinite infinite levels of infinity bigger we should not rank it as such. I'm never arguing that it couldn't be possible. On the other hand, arguing that the character is High 1-A requires you to assume that the extrapolation you propose holds, i.e. that the author interpreted these things the way you do. If you didn't assume that a lower interpretation would be possible and we wouldn't hand out such a high tier faced with the uncertainty. So my position does in fact use less assumptions and would hence be favored by occam's razor.
Occam's razor just generally can't free you from a burden of proof in our tiering context, as in face of large uncertainty we default to the lowest reasonable values. Extraordinary evidence... you know the drill.
Not if you're taking the standard constructions in math into account, no. Like, if you can get R^5 to begin with, then implicitly you're saying cartesian products up to that point are already a thing, and by then nothing really stops you from going arbitarily far with this, so it doesn't really carry the same weight as something that exceeds dimensions, in my view.
The example itself is especially weird because that set is... just a collection, it has no structure to speak of. So what you're describing wouldn't be equivalent to some transcendent space containing R^4, R^2, and other things (Or even a collection of things so big that it forms one). It'd be just those very spaces you mention, and nothing else (In other words it'd be like considering only 4-dimensional space and 2-dimensional space and absolutely nothing else). And it wouldn't be larger than the spaces it consists of, either: Saying that would be like saying that a set of 3 apples has more volume than a single apple (Not talking about the added sizes of the apples. Just the set of apples itself)
Actually, no. I don't really say anything about cartesian products. Real number vector spaces are frequently only uniquely defined up to isomorphisms. And for the sake of my argument I also could just remove the 5-tuple. It's not really required to be there.
And, yeah, I defined no structure. Given, I could easily define some structure on it. Just wouldn't be a vector space structure, which I believe is the point. The universe of sets has an equal lack of structure, being little more than a collection, yet you make a size comparison regardless. That's the point of the comparison. I can define a structure which doesn't meet the axioms for dimensions, but can equally much be compared to dimensional structures as the universe of sets. Whether that be not at all or just by inclusion.
In fact, thinking about it, it's perfectly reasonable for a verse to might not take the axiom of choice, in which case it can have infinite dimensional vector spaces that have no dimensions. So I guess those would be other examples of dimensionless structures clearly "bigger" than one by the same standard as the set of sets, but not bigger than all dimensional structures that could occur in other fictions.
You did say that stuff like "Beyond all dimensions is mathematics" would be something you're willing to extrapolate up to Low 1-A, yeah. But I find that quite bizarre when you say that stuff like "transcends the definition of dimensions" would also be equivalent to a dimensional jump above the rest of what physically exists in the verse. Presumably the same would apply to stuff like "Beyond the quality of having dimensions" or "Beyond the idea of dimensions." If you're making such all-inclusive statements, then you're inherently also including dimensions that exist only in the abstract, too (Supposing the statement can be taken literally that is). It's not like further dimensions not physically existing makes them outside the definition of dimensions or anything.
The specific formulation as I included in my layout was:
"If "possible" is clarified to mean dimensions that can be modelled by some system of mathematics, and said system is known to be able to model higher dimensional spaces, we assume at least all finite dimensions would reasonably be included and a character with qualitative superiority over them would hence be Low 1-A. [I think as far as extrapolation is concerned, this is a reasonable compromise based on what I discussed with Agnaa]"
And that was just a rough draft with rather unspecific wording for ease of reading.
So I'm not just willy nilly includig abstract dimensions. They have to first have a statement of being qualitatively superior to all possible dimensions. So what you bring up as alternative formulations is to be evaluated as for whether it qualifies for that first. Then the verse explicitly has to specify that all dimensions that can be modelled in their system of mathematics are included, by that explicitly saying that the abstract dimensions which don't necessarily exist get considered. And then they have to demonstrate that they use a system of mathematics in which higher dimensions are a thing. And under those conditions, I am willing to extrapolate to the point of them being beyond finite dimensions. Not infinite or cardinal many dimensions that were not mentioned.
I think why I can compromise on that and not on your suggestion should be quite clear.
Contrary to your proposal all the concepts involved in the scaling are explicitly mentioned. That's ensured by the mentioning of at least finite higher dimensions. You meanwhile insist that you can upscale to High 1-A without infinite dimensions and the various levels cardinals being mentioned at all.
In this case, the verse gives us a guarantee that their dimensionality that if referred to regarding the transcendence stuff isn't limited by physical or supernatural factors. It does so by specifying that specifically the dimensionality of their system of mathematics is mentioned, not any of the real existing stuff. Meanwhile, you wish to default to the verse having an understanding where transcending dimensions means transcending arbitrarily many, even higher cardinals, without explicit evidence of such restrictions not being present.
The only point I'm compromising here, when compared to my initial stance, is the lack of explicit evidence for the system of mathematics to have truly any finite dimensions. But, as Agnaa argued, it seems rather plausible that mathematicians with a mathematical model of 8 dimensions can do the step to 9 dimensions on paper. It's a much lesser jump than to infinite (where dimensions don't necessarily exist without the axiom of choice) and to actual cardinal stuff.
So yeah, I think I don't contradict myself much by accepting a reasoning of a lower tier with this much more explicit evidence, while rejecting the proposal of a much higher tier via less explicit evidence.
Being uncountably infinitely larger than 6 1D axes separately doesn't mean you're above their multiplication, no, just like being larger than 1-D space doesn't mean you are larger than 2-D space, but being above the very notion of "length" certainly does. It's as I said before: We are infinitely larger than something that has only height, but we are not above the quality of height itself by any means.
Being above height itself however isn't being above area. And being above area isn't being above volume. So, no, there is no reason being above the notion of length requires to being larger than 2-D space. Measures (i.e. quantifications of size) are usually defined completely separately for each dimension. It requires quite some mathematical work to get to the point where you can compare them and then that comparison indicates nothing about something beyond the notion of 1D being larger than 2D. So yeah, you can have a notion of dimensional size separately of 1 dimensional size in particular.
In fact, the prior example regarding the axiom of choice demonstrates how adding infinite more dimensions can lead to non-dimensionality, in a sense.
So... is being above the concept of a 1D axis non-spatial? Yeah, maybe. But no indication of being "larger" in any sense. The superiority part just doesn't survive the switch to higher D measures. Simply because A > 1D & 2D > 1D does not imply any relationship between 2D and A.
If non-dimensional things not superior to all dimensions can exist, then so can non-dimensional things superior to just some could as well.
Physically, it may have a limit, yes, but in the abstract, not really. And I'd say a fair few kind of statements would lead to you transcending purely theoretical dimensions by nature (And this ties into the previous point about verses where mathematical structures are what define reality, not solely physics)
Yeah, no. The idea that in the abstract a verse can't have a limit on its dimensions is incredibly speculative. It's just as bad of an assumption as that a character that is above anything humanity can imagine should be Tier 0, because naturally that would include abstract stuff like the class of sets.
You just can't assume that such statements are made with everything you can come up with in mind, when the verse doesn't say it extrapolates as much. But yeah, that's ultimately just the first point again.
Gonna make this short. Promised Ultima I'll respond here before it's closed so I will.
Originally I was planning on writing a several thousand word wall of text, but every time I was close to done something else needed my attention more and when I came back it was already outdated. So instead I'll just quickly sum up my thoughts on the last things I actually read before coming back now.
Not gonna argue on whether it should be low 1-A, 1-A, H 1-A or even 0 for that matter. All I will say is that "+1 dimension to what is shown" is a ridiculous prospect for something that has sufficiently demonstrated that it is in fact not of dimensional nature, while also being superior to it. Gonna just lazily copy what I just told someone on discord:
"my main argument has always been "the character in question needs to transcend dimensionality, not just a dimensional structure. Simply "beyond dimensions" is obviously not enough, as it doesn't give any information of the nature of transcendence. Actually transcending dimensionality means that each dimension in a structure is equally irrelevant (as in they are superior) to them and that they are not participating in any of them or anything of equivalence. If one is beyond a dimension in such a way, one is beyond all dimensions in a n-dimensional structure just the same."",
as anything else would mean breaking Occam's razor over your knee.
Quite the opposite. Occam's razor says to take the least amount of assumptions. Interpreting dimensionality to mean what the verse has shown in the scope of dimensions requires 0 assumptions. Assuming that it means stuff not actually mentions requires to assume extrapolation holds, which is at least 1 assumption.
Aside from that this point has in great detail been adressed in my debate wit Ultima, so I won't get into it further.
Whether an infinite hierarchy is implied or not is utterly irrelevant to this. Just to be clear, this is not NLF either by any means. Assuming that someone is beyond the notion of up and down, but not forth and back and left and right, when those are the same things, simply viewed from a different angle is nonsensical. If this is true for two dimensional axes, as well as three axes for the same reason, it is true for any n-dimension structure. This is one of the most basic proofs there are.
Dimensional spaces are not just directions. That's a false equivalence. Left and right, might be just up and down but rotated differently (given, that one can rotate it is an assumption in itself. Regularly you can't just rotate something into higher D directions). However, those are all 1D objects. An n-dimensional space can't be rotated into an n+1 dimensional space. The size of a n-dimensional space is larger than the the of the unification of the n 1D axis that span it. Being able to transcend a number of 1D axis literally just lands you in Tier 11. So if that's what your "above dimensions" means you don't even get anywhere. Only transcending all n-dimensional spaces (for all n) gets you anywhere and those can't be equalized to each other in any way.
Like, really, we talk about size here (or some equivalent). Obviously transcending any small object wouldn't proof that you transcend any large object as well. It's like saying that someone larger than any 1 m^3 object is automatically larger than every object in existence. Or that a being that transcends reality itself is above any imaginable reality by nature…
Just to make this clear so that nobody will twist my words like they have been doing with Ultima over and over again. This is not referring to stuff that is just different. No, I am not advocating for throwaway and flowery statements to grant such a tier. The actual evidence would obviously need to be sufficient. What is sufficient? I honestly don't care, as that was never an actual topic Ultima even brought up. Still confused how half the replies he got ended up revolving around that.
That is quite a cop-out.
If you can't specify what sufficient evidence is, then I will just claim that there is no realistic way for the fiction to give sufficient evidence under the conditions we debate (i.e. no explicit mention of anything). You basically destroyed your whole argument by not showing that it's even possible to attain sufficient evidence under the debated condition of not mentioning cardinals and infinities and stuff at all. It’s the key point of the debate that sufficient evidence can’t be acquired without getting explicit statements, after all.
The only exception to that in my opinion are verses with dimensions that aren't (necessarily) equivalent to the ones we use for tiering. For example, a verse that uses string theory shouldn't be assumed to be "beyond all dimensions" for something like that, as those dimensions aren't even necessarily infinite.
...As are the dimensions of verses that don't mention anything about infinite dimensions? Like, it's weird how you acknowledge that verses can have limits to dimensionality which aren't High 1-A, yet you argue for the suggestion of extrapolating them to High 1-A without explicit evidence that those realms of scale are even considered in the verse.
If you acknowledge that it's possible for such statements to not mean High 1-A, it seems like a large failure in scrutiny to not demand evidence that the verse considers things like aleph_1000 dimensional spaces. It's not like any verse will tell you that its dimensions are "equivalent to the ones we use for tiering". That's a conclusion you can only draw by explicit evidence of scales like those in the tiering system being included.
(Whew, that took a few hours to write...)
