Eh, that sounds like a different context entirely if we're talking statements as all-encompassing as "All dimensions in mathematics" or "The notion of dimensions in general." For example, when physicists posit 11 dimensions for string theory, they're saying "The math tells us that strings have to vibrate in this many axes to generate the universe as we see it right now." They're not really pushing aside higher number of abstract dimensions entirely, so much as they're saying it's all not really useful for their purpose (Which is making a theory that adequately models reality)
But, regardless, that seems like a nitpick, no?
I'm just pointing out that it depends on how dimensions are explained exactly. Like, "all dimensions in mathematics" is probably fine. Unless the verse has some weird philosophical views on mathematics.
"The notion of dimensions in general" begs for more context, though, as we have no idea which notion is referred to. Like, even mathematics has several different definitions of dimensions, so not everyone means the same notion in every context. And physics just comes on top. I think there some more clarity that theoretical stuff and stuff beyond what's possible in physics is included should be had in addition to that statement.
Cardinality is just the concept of "How many things are there in this bag?", so I don't think that's particularly an issue that concerns us. Certainly, the judgements that we make about the fiction from the outside, using the real world as a reference point, may not necessarily be identical to the raw facts of the fiction itself, so much as they're jusy what we deem to best approximate them, but things like cardinality are too basic to dismiss or handwave in that manner, imo.
When I say cardinality I mean in the sense of "the knowledge that there are different sizes of infinity", something I bet the majority of people on Earth don't know.
In that regard, as said, we can't just take statements and assume they should be interpreted absolutely literally. Even a narrator speaks like a human and not with constant mathematical precision. Blowing up such statements by our own knowledge of what it should technically mean, is no better than blowing up statements of Omnipotence to Tier 0 based on our own knowledge of what omnipotence should include.
Overall it seems to boil back to the author intent argument, to a degree, which I think is fairly silly due to the reasons already said (The author's mindset isn't really knowable, and even if it was, we wouldn't apply it to the verse proper unless something explicitly tied the two together).
And, as already explained, taking an interpretation likely to be higher than the author statement can't be the solution to not knowing what a statement meant. The lowest reasonable interpretation would always be one that is lower or equal to what was actually meant. And, while we don't go for the author intend, we go for the lowest reasonable interpretation of the statement, not the most literal one.
I work by a chain of implication: The existence of an amount of things equal to the set of all real numbers would imply the cardinality of the real numbers (Since those are one and the same thing), and once that is a set, it spirals out.
Problem is, that chain of reasoning only holds in mathematics. In fact, you could just employ mathematical reasoning to proof infinite dimensions just from ZF. Or you could go a step further and say "they also know subset, so potency sets exist and hence a bunch of more cardinals".
The problem is that you view this as a game where you can apply as much reasoning to fiction as you like. But fiction doesn't work like that. It doesn't have the integrity of allowing all mathematical conclusions in it to just be true.
What you're doing is similar to watching a stone in an anime drop and recalculating the gravitational constant of the verse that way. Technically one can do that, but at that point you're putting more thought into it than the show. You stop evaluating what the fiction shows us and start evaluating the fiction based on what you reason it should show us.
Ultimately, it's quite simple, just because you can reason something should be a certain way, it doesn't mean a fictional universe draws all the same conclusions. It's not a machine drawing every possible step of reasoning the moment it establishes something.
So yeah, you can't just infer that different sizes of infinity are considered in statements in fiction, if the fiction itself does never acknowledge that. Because humans don't work like that. We have different grades of knowledge and opinions and philosophies, so if we want to understand something we are told we have to consider those things. We can't just take everything we're told to mean what it would mean if we ourselves said it.
An omniscient narrator is omniscient regarding the verse, not omniscient regarding real-life truths.
In view of that, I also don't really get how infinite-dimensional spaces being wacky compared to finite-dimensional ones ties into much. It's utterly irrelevant, at least independently from the "What the author probably knew about" thing.
One point we were talking about was whether we take Low 1-A or 1-A. I.e. whether putting the cut-off point at "above finite dimensions" or "above aleph_2". That they are "wacky" is relevant as it shows a much simpler argument: Finite dimensions are "easy" to grasp, infinite very hard.
That when some higher dimensions exist there could be some more is a more direct inference than that there could be infinite, especially since infinite ones are so much harder to understand. Hence it makes sense that a statement that has considered basic finite dimensions might not have considered the more complex infinite case. (Heck, some mathematical definition of dimensions don't extend to infinite either...)
So, at a basic level, I think in terms of a knowledge basis the difference between finite and infinite is bigger than between one cardinality and the next.
The statement in this case would be referring to the nature of the being, of course. That is to say it would be a case where their physiology is tied to their AP (Being the source of it), rather than the two standing as independent things and the statement just so happening to refer to the latter. This sort of nitpicking doesn't really work here. Like, come on. It explicitly lays out the difference between 2-D and 3-D and says such a relationship doesn't begin to the describe the scope of the difference between that being and 3-D space, because the degree in which he is greater than it is not simply a matter of "He's infinitely larger!"
So, pushing all of that aside, why exactly isn't it adequate?
Problem with the question is that I don't know what "physiology is tied to their AP" is supposed to mean in context of the verse. It's a bit like saying "now assume that the nature of wetness is linked to AP".
I would similarly ask you to rewrite it so that it actually says exactly how a fiction would write what you think that is supposed to mean in a clear way.
But let's say for example we add "He has infinitely more power than what would be necessary to destroy any dimension that doesn't describe him" to the statements, as an example.
Then I would ask "how many dimensions are there in the verse?" and go above +1 above that, as I would assume that dimensions that the verse doesn't have aren't taken into that consideration. (i.e. does a dimension that doesn't exist not describe you? Not sure if that's a yes)
Let's further say we change the above addition to "He has infinitely more power than what would be necessary to destroy any dimension that doesn't describe him, including even the higher dimensions that are only described in mathematics".
Then I would be fine with Low 1-A.
And since you'd still want the statement to be more explicit, I welcome you to rewrite the hypothetical a bit, into something that you'd say qualifies. Sorta trying to carve a minimum here, so, although I don't really concede that the hypothetical doesn't qualify, I want to see what would to you.
For Low 1-A pretty much what I put above.
For High 1-A? Either add "is above every cardinal there is" or some explanation that is clearly equivalent to that. For the exact case of equivalent statements one would need to look case-by case. I would say main criteria is that it isn't just "several different infinities exist", but actually grasps the scope of cardinals to some extent, considering how vast the cardinal hierarchy is and how it needs various construction ideas to reach certain levels in it.
The precise border is obviously fuzzy.
Anyway, to ask a question in turn, have we by now agreed that statements need an indicator that purely theoretical dimensions are considered, instead of just meaning dimensions and dimensionality in the scope of physically existing concepts?
Yeah it seems really dumb to go through all these hoops when we can just refer to the written text and gather whatever evidence to support tier 1 ratings.
[...]
DT's suggestion is nothing if not limiting on how we apply our standards to objective evidence. If we cannot apply the full extent of our knowledge upon the verses we evaluate, why do we even bother trying to evaluate them anyway?
I never said we can't apply the extent of our knowledge on verses, though? My point was that you have to consider what a statement was supposed to mean and, in face of unclarity, go for a reasonable low-end.
I think it's not much different to how we have a standard that we don't give out Tier 0 (or other high tiers) just for a character being Omnipotent, but instead limit ourselves to what the Omnipotent character has in terms of actual feats. Sure, you could say "let's not have that standard and instead just evaluate case-by-case", but does that lead to anything better? Seems like that would just lead to lost of debates how "logically my omnipotent character should be tier 0". Not having any guidelines seems impractical and if that's what we're going with we would have to delete lots of staff from the Tiering FAQ...
I don't think "if the fiction with 5D spaces never mentioned any construct we would evaluate as even 1-A don't extrapolate general statements to High 1-A" is as much limiting as it is basic scrutiny. The whole debate was about cases where the fiction does
not show or state anything more explicit than "beyond dimensions", i.e. cases where there is not much objective evidence. For cases where the verse was specific we wouldn't have the debate, as I'm all for specific evidence getting corresponding tiers.
And, in general, this is as much about my suggestion to be conservative with extrapolation as it is about Ultima's to just drop High 1-A on most "beyond dimensionality" statements, even if the verse has never shown or mentioned anything remotely that high.
Like you don't need a degree in complex math to arrive at a decently complex description of higher order realms. In fact for the most part, it isn't even the authors that directly arrive at these conclusions anyway, since we ourselves apply our standards on the objective evidence and arrive at our own conclusions of the depicted ratings.
Yeah, but as I extended in my debate with Ultima we still have to interpret statements and just because we don't care much for author intent we can't just take all statements at face value. What the author meant is always one valid interpretation, but we have more we could take. However, is there ever a situation where we should interpret a statement as definitely meaning something higher than what was intended? We usually use the lowest reasonable interpretation and I think the one that covers the scope of what the author intended would be at least contained among the reasonable interpretation. Ultimately, I think interpreting it like a person that only has school knowledge in mathematics would is a reasonable interpretation, until the fiction adds context that demands more.
I totally I agree that it's plausible that someone could come up with infinite cardinal dimension stuff without a degree in mathematics, but I think it's not too much to ask that the work actually mentions that stuff or something equivalent if that's what's intended.
