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Whether a structure that is stated to be above dimensions in a verse with only 4 dimensions is adequately modelled as 5D space is just of no relevance. Some might be. Some might not be (like your example). However, that is purely a question of the nature of the space, not a question of size. I think the size of such a space could very well be equalised to that of a 5D space. Think of a conceptless void, which is later replaced by a 3D universe. The void can't be modelled as space or dimension of any nature, as it lacks such concepts altogether, but in terms of "size", as we use it for tiering, it can be equalized to the 3D space that replaces it. Different isn't superior. I believe I mention that roughly every time we debate something tiering-related."Namely, that the statement doesn't take into account unmentioned spaces greater than everything in the verse, which we do not know can even exist" is a point that doesn't really properly address the reasoning I've made because it presupposes that the dimensions which physically exist (or can exist) in the setting are all that is relevant when it comes to indexing statements like this, which is something that I contested in my post. More specifically, I said:
As far as I can tell, you didn't address this (Though I suspect that the tangent about mathematicians and imprecise statements in the third paragraph was supposed to have been the answer. If it was, do elaborate more on it, since I don't understand how it works as a response at all), so I'll posit the question again: Do you really think that, if a verse has only 4 dimensions, and then a structure encompassing those four is described as surpassing dimensionality entirely, the structure in question can be appropriately modelled as a 5-dimensional space? Does it make sense to say that its size is on par with R⁵, even though it would exceed measure entirely? Does it make sense to say that it exceeds R⁴ in the same way R⁵ does? If so, why?
The answer is that it doesn't, because that would be taking the structure and applying to it properties that it lacks (In this case, volume), and whose foundational principles it does not participate in at all. It doesn't really matter if the dimensions in question are theoretical or physically existent, because neither notions would really apply to it regardless. So, for example, if you tried to make a measure-theoretic statement about it, you'd be unable to even write down anything because there isn't even a starting point to begin discourse about such a thing from within the framework's language. It doesn't even exist in that context, functionally speaking. It's a non-thing. In other words you might say that, even if it weren't possible for those higher dimensions to physically be brought to existence, it wouldn't really matter because of the nature of it alone.
(Inconsistent theories don't count for this argument, by the way. As you probably know, inconsistent theories have no models, which is to say there is no structure satisfying the statements in them, which is to say that they're not actually describing anything. For instance if it turns out an inaccessible cardinal doesn't exist, then there's no set that satisfies the formula describing one, and as such the formula itself might as well be air)
I can ground these questions with a scenario from a verse I've been wanting to index for a while, even. I won't get into specifics, but in that verse, there is a structure that is explicitly described as being unable to be equated to, charted out, of explained by, any model of spacetime, even when the characters attempted to include higher dimensions into the equation, due to the transcendent nature of it. Do you believe it makes sense to say the structure in question is just, itself, equivalent to something that's a couple dimensions higher? If not, what exactly distinguishes it from non-qualifying cases?
Now apply this point:
And it's not hard to see why it doesn't fall under a hasty generalization.
(And ontop of that you didn't answer a question I made: What of verses where the structure of reality is, in fact, not dictated entirely by physics? What of verses where mathematical structures are the basis of what exists?)
Also, now that I think about it, the Hitler example you made is a bad one, anyway, because by using it you're trying to make a point that generalized statements don't necessarily reflect the view and intent of the person who wrote them down, but the issue is that you're trying to use out-of-verse factors (Authorial intent) to try and make a conclusion about in-verse factors (The scope of the statement), acting as if the former is what ultimately matters, and not the latter, which is futile when the former is completely unknowable at the end of the day.
So, if a book says that "Murder is bad," then, sure, you can take this to mean that all murder is bad according to it. As for the deeper intent of the person who wrote it, though? That's a mystery. That person could've thought that murder, even if bad, is ultimately a necessary evil in certain cases. They could've indeed been against killing Hitler. They could even be a person who condones bad acts (Acknowledging something is bad doesn't mean you're against it, or specific instances of it). We just don't know, and this intent, being so cloudy, is thus a non-factor. When all we have is the text, we go by the text (And before you say something like "But the text doesn't mention that this thing is above aleph-many dimensions," the rest of this post is dedicated entirely to explaining why it doesn't need to, so, if that's on your mind, don't)
Bolded tidbit is not what my point is. Even if there is no physical mechanism that'd condition the material existence of higher dimensions, those higher dimension could still be a thing in the abstract, the logical, which segues into the argument above. Physical possibility isn't necessarily relevant here. Unicorns don't exist, sure (I wonder what one tastes like, though...), but the idea of a unicorn does.
I would say it is about author intent, yes. Whenever you mention "what is actually supposed to be going on," you, like it or not, try to invoke the intention of the person who wrote the story. If your point is actually "This statement is satisfied by much lower tiers, and as such we will choose something around that range, instead of the highest possible takeaway from it," then you're more than free to bring it up (I am doing it myself, after all. I'm not proposing that being above dimensionality is automatically Tier 0, but High 1-A), but the point about what authors know or don't know is wholly unrelated to that and not even necessary for its formulation, as you yourself agreed to when you said "But even if we assume that authors are mysterious beings with unknowable thoughts, we would still not take it like that, because other reasonable interpretations are still available." I think it borders on a non-sequitur, actually.
And then, of course, there's the fact I'm arguing that "one dimension higher" is not a rating that satisfies statements about things being above dimensionality, to begin with, so, yeah. Those paragraphs don't actually do much to address what I said. I never, once, attempted to argue anything you're accusing me of.
The Sagan Standard is a good saying but it's not really what I'd call a good principle to base your stance on. This being due to the fact that, when you get down to it, it's not really clear that something like "If a character is above dimensionality, then they are above aleph-many dimensions" is an extraordinary claim. In fact, whether it is one or not is exactly what the above discussion is all about, so if you want to mention it, that's fine, but don't expect it to have any actual weight. Without something substantiating why it is that the claims I am making are extraordinary, it's just a platitude that rings quite hollow. At most it will make your argument seem more rational to some onlookers, but that is really it.
In short what you're saying doesn't mean much when my whole argument is that existing above dimensionality is already "good really clear evidence" on par with being explicit about cardinals. I acknowledge that this doesn't necessarily invalidate your arguments done in the paragraphs above, sure, but that's not the point here: The point is that you are acting like "High 1-A should be held to higher standards of evidence" is something that directly attacks my stance, when it isn't, since my whole argument is that a specific kind of statement does, in fact, hold up to standards of evidence. So you may as well not have brought that up at all, in my view.
Another thing I mention frequently is how you are required to meet sufficient conditions to claim something, not just necessary ones. Something being not "necessarily" restricted to existing dimensions is not a sufficient reason to consider it as definitely above such.
I believe I have sufficiently explained how laws besides physics can limit a verse's size. (or rather, how inherently there is no need for something to limit size. Nothing to give it size to begin with is sufficient.) What verses that run on mathematics are concerned: Same issue, really. Not every mathematical structure can be envisioned as space of any kind and where the line is drawn is unclear. If the statements aren't more specific, it's not hard to imagine that cardinal dimensions with their weird metrics are not necessarily considered.
And your point regarding authors is one again missing my explanation in their entirety. You can not just take the "murder is bad" statement is also applying to Hitler in the book. In the context of the book, you still need to interpret it. If you do so, you have to consider all reasonable interpretations, not just the literal one, and at least one of those would be what the author intended. Now, you don't know which that is since you can't read the authors mind, but you can't dismiss that the intended interpretation has to be amongst the possible interpretations. Otherwise, you would have failed in properly interpreting the text. Not knowing what the author thinks doesn't lead to more certainty as for which interpretation we need to take, but to less certainty. Obviously so, as it reduces the information we have. And if you think having less information can in any way justify giving a character higher ratings, then that's a sign that you should rethink your standards of reasoning. Less information can only increase the margin of error, it can never make us more certain about something.
So, to bring that back to the more specific case: If the author doesn't know about cardinals and large cardinals and stuff, then the statement wouldn't mean that. So it would be one of the viable interpretation. Now, we don't know whether or not the author intends that or not. So, operating under death of the author, we can not say "the author didn't mean cardinals are involved". However, neither can we say "the statement is mathematically literal and hence cardinals definitely are involved", as that too is making an assessment about the authors intention. We can merely say "both are some of the possible reasonable interpretations". I.e. we end up with more uncertainty. The set of possible reasonable interpretations taking author intent into account, is definitely a subset of the set of possible reasonable interpretations taking author intent not into account. In other words, if with author intention we can pick an interpretation where the character isn't High 1-A, then without it we can definitely still pick that interpretation, as we haven't gained more information that could exclude it. And, of course, that's what we would do as we never default to the massively high-end interpretations of statements.
What the whole "but not actually existing dimensions should count too!" is concerned: Nah. For a basic "above dimensions" statement you absolutely don't know whether those get considered in any way. Even if you had a "above all theoretical dimensions too!" statement you would then still need to know that the theoretical dimensions these people came up with actually cover the theories involving higher cardinals and stuff. Now, if you have that the verse actually mentions all those higher cardinals to confirm that it knows those theoretical and then have an explicit statement that the character would be above spaces of such sizes if they existed, then we have no problem. But notice how this ends up needing actual mention of those large stuff existing again?
Ultima, if "character that has no that impressive cosmological feats is actually countless infinite infinities more powerful than we have seen" is not an extraordinary claim, then I'm not sure what is. And I have my doubts that "Character x is above dimensions" is a statement anyone would consider extraordinary evidence, given how incredibly unspecific it is.
But, as is my point, if not even all physically existing and widely known things like a black holes would reasonably be considered in such extremely general statements without explicitly being mentioned, then there is no way physically non-existing and widely unknown things, like cardinal dimensions, are likely to be considered. That goes back to the whole thing where you can't expect lesser evidence to be believed for more extraordinary cases.This seems to be a misunderstanding of my point, and a false equivalence ontop of that. "Nothing in this world can damage this character" is a statement that relies on things that physically exist in the verse, because something that doesn't exist cannot be said to be "in this world" under ordinary definitions. Being above dimensionality doesn't necessarily rely on the dimensions that physically exist in the setting, like I said up there, and which you yourself acknowledge to a degree when you allow characters to scale above "possible" dimensionalities. That's the point I've made that you, it seems, have left unanswered.
Because a statement like "He is so durable nothing in the universe can harm him" is an extremely unspecific throwaway statement on invulnerability that would need much more evidence to be interpreted as included infinitely strong forces. Given, if the verse has actually shown a black hole, it is becoming more reasonable. If the verse has mentioned a realistic black hole in some relation to the character it might even be somewhat reasonable. But if it's just a random throwaway statement and there was a black hole once 10 years ago in one episode, it's rather hard to say if there is actually an intended connection. Brings us back to the whole point about how statements can be interpreted in not the most literal way.And why is that, exactly? To all of those things. If you translate that line of reasoning to the case of dimensionality, then the argument becomes "Even if the verse actually presented a space with X number of dimensions, it would still be assumptive to assume that a character described as above dimensionality would be superior to it." So, for example, you'd have to make it possible for there to be cases where a character is "beyond-dimensional" to a 2-D structure but not so to a 3-D structure, even if 3-D structures exist elsewhere in their verse, because right now you are saying that, if a statement says that a character is beyond a class of things, we won't treat them as above all things in that class even if the verse presents said things as existing physically.
Needless to say, this is an absurdity, because you are positing a fundamental difference between spaces of different dimension that makes it so you can exist beyond the nature of one without doing the same to the other, which is very much incorrect. For an n-dimensional space, all the dimensions that comprise it are interchangeable, they are the exact same dimension, ultimately. Dimensions have no ordinal positions (There is no such thing as the "first" dimension, and neither is there a "second" or "fourth" dimension. It makes no sense to consider length as coming before height, for instance, and neither does it make sense to consider height as coming before depth), and the distinction between them breaks down entirely when you examine it closely, too.
For example, take a cube. It has length, height and breadth. Now, remove the length and the breadth of it. What you have left is just a line segment standing on the vertical, laid over the y-axis, which... is literally just a length. Now remove its length and its height, and all you have now is its breadth, which ultimately is just a line segment laid over the z-axis. Once again, literally just a length. So you see here that there quite literally is no intrinsic distinction between one dimension and another. They're all the exact same.
As such, I repeat what I said up there: When you transcend one dimension, you already transcended all of them. If you are above dimension in relation to a 4-dimensional space, then you are also above it in relation to a 30-dimensional space, because all the dimensions that comprise the 30-D space are just additional lengths that are in no way different from the ones comprising the 4-D space. So if you transcend "length" (Or "measure," for the more mathematicaly inclined) in general, then you're above all those other lengths as well, not just a single one.
And, do I even have to take how "above one dimension = above all" is a terrible take? Like, dude, really? We just making all characters High 1-A now? "You transcend all concepts of your universe? That would include 3 dimensions. High 1-A it is!"
You can be of non-dimensional nature without transcending dimensions. And you can transcend 3 dimensions without being above 4. And you can also be both of those at once. Again, being different isn't the same as being superior. You can be unquantifiable by any dimensions and still not more powerful than 3. Or 5 or 50. How you can be described is no measure of power.
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I'm reasonably sure nobody aside from us reads through all of those long posts and I will never agree to your ideas of giving character ridiculously high rankings based on massive extrapolation of vague statements. So while I'm sure we can keep this debate going for ages, I doubt it will ever go anywhere. I mean, we had pretty much this same debates in several other threads and DMs in the recent years and the arguments really never gotten better.I don't know if that's necessary as of yet. DontTalk and I exchanged just a couple posts, so far, and the thread hasn't even left the first few pages. The discussion seems like it's in its infancy, still.
So, if someone else wishes to enter the debate that would be worth engaging, but I doubt a debate amongst just us two will contribute much more.
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