- 5,461
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Or, "Why did I make this system? Am I stupid?"
This thread has certainly been a long time coming. And though its placement in the general discussion board makes this clear already, it is probably best that I say it explicitly: I don't actually have any interest in bringing any changes to the Tiering System, as I am well aware that, ultimately, whatever I say can simply be vetoed regardless of its truth. So I post this not as a proposal of any kind, but an exposé, if you will.
The purpose of this text, first and foremost, is to simply bring to light the many, many absurdities which the system's higher tiers commit; no more, and no less. And all of this, of course, directly from the mouth of the one who revised it all those years ago. And mind you: Though I haven't originated all of these absurdities, I have greatly facilitated many of them and originated one, and so I don't deem myself blameless in this affair.
Of course, this is intended to be read in its entirety, so preferably don't start making up ideas in your head before even finishing the whole text. And before anyone asks: Yes, I am well aware of how large this ended up being. But to quote Alberto Brandolini:
The amount of energy needed to refute bullshit is an order of magnitude bigger than that needed to produce it.
And unfortunately energy seems to be something I have in abundance.
IF YOU WANT A TL;DR, GO HERE
Similarly, if I ask "What does purple taste like?", that is a category error, because "purple" is a color and thus not fall under the category of things which have taste. Likewise, if one were to ask "What is bigger, green or yellow?", that is also a category error, because colors are not under the category of things to which size applies.
A common trend that you'll probably noticed by now, of course, is that statements entailing category mistakes are inherently nonsensical. None of the parody-questions which I've posed above have any meaning. I might as well have said "Colorless green ideas sleep furiously." If we are in agreement as to the inherent nonsense of such sentences, we are already prepared to tackle the rest of the subjects pertinent to this text.
vsbattles.fandom.com
vsbattles.fandom.com
At the core, the concept is basically some loose sense in which something is "a higher infinity" than something else. The two foremost examples of the concept are, presently, dimensionality and Reality-Fiction Transcendences. The latter, in particular, expresses it pretty directly in its explanation page, quoted above: "Thus, they would be treated as more than infinitely greater, such as in this case Low 1-C. The gap between the higher world and the lower world would be strictly one of quality, not quantity."
So, if Character X views Character Y as part of a work of fiction, the gap between them is treated as, in a sense, "more than infinite" by virtue of a difference in quality: Character X is a reality, and Character Y is a fiction, and the superiority which the former holds over the latter thus logically cannot be surpassed by mere additions of power and size due to being beyond the reach of both. By contrast, a quantitative superiority would be one that involves numerical quantity, not quality.
For example: A volume of 27 m³ is greater than a volume of 10 m³, but quantitatively so. Likewise, a length of 10 m is greater than a length of 3 m, but once again, quantitatively so. Likewise, a set of 5 apples is greater than a set of 2 apples, but, again, quantitatively so.
Right off the bat, this already leads us to the first logical problem, which is the equating of two completely different kinds of superiority. A dimensional difference is not, in fact, a qualitative superiority, but a quantitative one. A 3-dimensional object, for example, is made of an infinite number of 2-dimensional objects (This number being the cardinality of the real numbers, or 2^aleph-0, the power set of the smallest infinity). And this generalizes to any two objects of dimensionality n and n+1 (3-D and 4-D. 4-D and 5-D, and so on)
Another way in which this is reflected in the Tiering System is how an uncountably infinite amount of universes is Low 1-C, whereas a countably infinite amount of universes is 2-A. The difference between the two is one of number, and thus by definition it is quantitative. You can add uncountably infinite new universes to a set of countably infinite universes to make it go from one tier to the other.
By contrast, reality is obviously not composed out of slices of fiction, and neither can a real object be obtained by summing up fictional things, because the difference between the two hinges on an existential quality (i.e. The fact one is real and the other isn't), and not on physical measurements such as volume. Whereas a 3-dimensional object still has lower-dimensional portions of itself (As a cube can be divided into squares, and squares into lines, and lines into points), a body in reality has no part of itself that is fictional (And so a real cube can only be divided into real squares, and real squares into real lines, and real lines into real points. It cannot be divided into fictional squares, and nor can squares be divided into fictional lines, and nor lines into fictional points)
Likewise, a set of uncountably infinite universes can be reduced to a set of countably infinite universes, if we simply eliminate the excess universes from the totality. This is to say: Through simple numerical elimination, it is possible to take a multiverse from Low 1-C to 2-A. Meanwhile, it is obviously impossible to subtract so much from a real object or quantity that all that is left of it is a fictional portion. The conclusion is simple here: You cannot create non-reality from reality, and therefore, you cannot create reality from non-reality, either.
From these facts, it becomes obvious that something like a Reality-Fiction Transcendence cannot be measured on a mathematical basis, as mathematics is definitionally a purely quantitative framework and has no say whatsoever regarding what a "qualitative" superiority is, and thus obviously no say regarding what the gap between "fiction" and "reality" is, either. More to the point: Dimensional jumps, as well as jumps in cardinality, are quantitative superiorities. They are not qualitative.
To illustrate this, consider what a dimensional space is in mathematics: It is nothing but a multiplication. Take the real number line (R), which is a 1-dimensional set, and multiply it by itself. What you obtain through that is a 2-dimensional set, the real number plane (R^2, which is to say R x R). Take the real number plane and multiply it by the real number line, and you obtain a 3-dimensional set, the real number space (R^3, which is to say R x R x R). Indeed, take as another example the rational and irrational numbers: They are both 0-dimensional sets, and yet their sum is a 1-dimensional thing, the real number line.
By contrast, take the empty set (∅): This, as the name suggests, is a set with no elements whatsoever. It is, in effect, the set-theoretical 0, and for preciseness' sake we must note that it isn't exactly nothing, per se, but rather a set containing nothing. Nevertheless it is, for obvious reasons, close enough to the idea of nothing to serve as an illustrative tool for our purposes, as a Reality-Fiction Transcendence is, as stated, nothing but a relationship where the superior side sees the inferior side as literal unreality, and thus, as nothing. So the empty set, from here and onwards, will serve as a stand-in for that "unreality."
A very intuitive property of the empty set is that the sum of empty sets is, itself, an empty set, which is to say that nothing added to nothing equals nothing. Likewise, multiplying the empty set with a non-empty set only yields the empty set itself. ∅ x {1, 2, 3, 4, 5}, for example, equals ∅. And so does ∅ x R, and ∅ x R^2, and ∅ x R^3, and ∅ x R^816, and so on.
This is to say that there is absolutely no set which, when multiplied by the empty set, yields a non-empty set. And so as far as set theory is concerned, the question "How big is the volume of the gap between nothing and something?" is meaningless. But since the Tiering System considers such a gap to be equal to a difference in dimensionality, it falls into absurdity by attempting to answer that question using a mathematical basis.
As a further illustration of the logical inconsistencies this causes: Consider a qualitative inferiority. Something that is literally "unreal" or "nonexistent" (In a manner that entails inferiority) to a 3-dimensional world, for example, would be tiered at 11-A, and thus as on par with 2-dimensional space. And from this, we draw three conclusions, all of which exist jointly, being equivalent to each other:
Conclusion 1: The Tiering System considers the empty set, by all accounts, to be 11-A, and thus as on par with 2-dimensional space. But this is contradictory, as the empty set has no elements whatsoever and is thus of cardinality 0, while a 2-dimensional space has a cardinality of 2^aleph-0. Indeed, the empty set is smaller than even a 0-D point (Which is 11-C)
Worse yet: As said above, the empty set serves as a good mathematical approximation of nothingness, but it is not, in fact, nothing, so much as it is a set containing nothing, and hence a set that contains the empty set as its only member is of cardinality 1, as the empty set is "something" in the same way a bag with nothing inside is still something. So what the Tiering System is saying, in truth, is that utter nothingness is equivalent to 2-dimensional space. However, we've seen that "nothing" in a sense that denotes inferiority is even less than something like the empty set, which is in turn less than even 11-C objects. As such, clearly this is an absurdity.
Conclusion 2: Since the empty set is equivalent to a 2-dimensional object, despite the difference in cardinality between the two, it follows then that the Tiering System implicitly claims that ∅ = 2^aleph-0, which is plainly absurd even to a layman. And this causes mathematical absurdities, too, as it means that all cardinalities then are equal to one single cardinality.
This may be demonstrated as follows: Let us henceforth call 2^aleph-0 by the name c, and then consider the exponentiation of this cardinal with itself, c^c. As per basic cardinal arithmetic, this exponentiation results in a cardinal with strictly greater cardinality than c. However, we've already established that, under the aforementioned "logic," c = ∅, and ∅^∅ in fact equals 1. Thus it follows that no cardinals other than 1 can be constructed, as any exponentiation we attempt to do is now between 1 and itself, and 1^1 = 1.
However, c was already assumed to be equivalent to ∅ in the premise of the argument (In order to follow the logic of the Tiering System), and it is, itself, just another name for 2^aleph-0. Now, it follows from above that 2 and aleph-0 are both equal to 1, and 1^1 = 1. Therefore, 0 = ∅ = 2^aleph-0 = 1^1 = 1. Cleaning that up, it means that 0 = 1. So not only are all cardinalities in truth actually one cardinality, but that cardinality is an incoherent value. Thus it is plain that the Tiering System's logical framework is an inconsistent one.
Yet, as mentioned before, what the Tiering System truly does is even worse, since by equating actual nothing (Something less than even the empty set) with some specific quantity, it reduces all quantities to utter nothing as well.
Conclusion 3: Since the empty set is equivalent to a 2-dimensional object, it follows, then, that the Tiering System seemingly claims that a square (2-D) is literally nonexistent to a cube (3-D), or that it is perfectly equivalent to something literally nonexistent, which is obviously untrue to anyone with the most elementary knowledge of either physics or mathematics, and which has already been extensively proven wrong in the above paragraphs.
Further, in claiming the above, the Tiering System also is effectively claiming that there is a certain amount of nothingness that, when added together, yields a certain amount of somethingness, which has been shown to be manifestly untrue with the empty set, and which thus obviously goes for actual nothingness as well. Worse yet, the idea that enough "nothing" put together will eventually add up to "something" also implies that, if you have "something," and add enough "nothing" to it, it will eventually get bigger. Which is, again, also transparent nonsense.
But of course, the system seems to actually acknowledge the quantitative nature of mathematical differences, as evidenced by this bit from the FAQ: "Of course, the same levels of superiority can also be reached via sufficiently explicit quantitative statements, such as when cardinalities above countably infinite get involved in a manner that implies a corresponding difference in power/size."
So in spite of openly acknowledging the difference between the kinds of superiority that are at play in differences in dimensionality and in actual qualitative differences, the Tiering System nevertheless equates them as if they are equivalent. Not identical, but equivalent. In summary, the Tiering System appears to insinuate that there is some mechanism by which something that exists (A lower-dimensional object) is made equivalent to something that does not exist (Fiction). That is to say, some reasoning that makes this seeming absurdity into a coherent position.
One might be thus tempted to ask what exactly it is that makes these things equivalent, but we will get to this shortly. We put this matter a bit to the side (But not aside) to tackle a different, though related, subject.
So currently, if a character is above, beyond and superior to the spatial and temporal dimensions of the cosmology of their setting (Superior to dimensionality as a whole, and not simply in a higher dimensionality), they are to be rated as equivalent to a single difference in dimensionality above that. So, for example, if a character is above dimensionality in a cosmology with 4 dimensions, they are to be rated as Low 1-C, and thus as equivalent to a 5-dimensional space. If a character is above dimensionality in a cosmology with 6 dimensions, they are to be rated as 1-C, and thus as equivalent to 7-dimensional space. And so on and so forth.
To see that this is yet another absurdity is just a basic exercise in identifying category errors, which we have went over in the first part of this text: Volume, higher-dimensional or lower-dimensional, is ultimately just a measure of the n-dimensional space which is occupied by a given body. As such, by definition, things that have neither time nor space do not have any volume, and so attempting to equate them to things that do is a fool's errand. It is, to draw from earlier, exactly the same as asking "How fast is the Pythagorean Theorem?" or "How deep is green?". Simply trying to impose into a thing a quality which it lacks (In this case, volume)
And yet, just as with Reality-Fiction Transcendences (Or, more generally, "Qualitative" superiorities), the Tiering System essentially justifies this by saying the following: Things that are aspatial indeed have no spatial quality and therefore no actual "size," and so their scope is indeed not really identical to that of spatial things, but simply equivalent instead. So for example, a character who transcends dimensionality in a cosmology with only 4 dimensions doesn't occupy a 5-dimensional volume, but exists in some state "equivalent" enough to it to be tiered as equal.
This is, point blank, also an absurdity, and to see why only requires one to remember the above explanations of what category errors are. This "justification," however, is arguably even worse than a simple category mistake, because it involves admitting that two things belong to different categories and that the terms applicable to one category are not applicable to the other, and yet still claiming the existence of some similarity between them that magically allows one to call them "equivalent," in spite of the total lack of characteristics shared between the two things.
A little scenario I've used before to illustrate the illogicality of that is as follows: Suppose I have two things, one is a formless, aspatial object, and the other is a cube with a volume of 30 m³. If I were to address the former and say "This thing has no spatial characteristics whatsoever, and so it has no volume nor position in space. Yet it is equivalent to that cube's volume," it would be more than rightful to say I would be speaking complete nonsense. And, for reference, there is no fundamental difference between finite volumes and infinite volumes, and therefore equating aspatial things to infinite volumes is exactly as absurd as in the case of a finite volume.
A possible justification that someone might use, then, is the argument that the two things could be equated by means of their practical properties, and how they are shown to relate. For example: Suppose you have a spaceless, timeless void preceding a Low 2-C reality. This reality is then created and now starts to exist contained by this void. The fact it is capable of "containing" the Low 2-C reality, then, could be argued to be something that can be tiered and used to deem it as equivalent in scope to other things that could also contain things that large, even if said things are spatial in nature, and the void is not.
That line of thought, however, is fairly clearly untenable, as it commits a very flagrant case of a false equivalence: Claiming that, just because two things share one property, they are equivalent, disregarding any number of other differences they might have that turn this impossible. In this case, it is claiming that an explicitly spatial realm and an explicitly aspatial realm are equivalent just because both are capable of containing a Low 2-C-sized reality.
And it is easy to see why this is fallacious: Consider, for instance, a fully-sized 6-dimensional realm and a fully-sized 5-dimensional realm. Both are certainly capable of containing a Low 2-C-sized reality within themselves, and yet obviously there is a distinction between them that makes it impossible for them to be equivalent, namely the fact one is 5-D and the other is 6-D. The same line of reasoning applies here: Though the hypothetical spatial realm and the hypothetical aspatial void share a commonality, this commonality is not sufficient to draw an equality between them, as they have other attributes which make such comparisons incoherent.
Furthermore, this kind of reasoning essentially amounts to only tiering half of the feat: The so-called method described above is not tiering the hypothetical void's superiority over dimensions, but only the fact of its containment of a Low 2-C universe, and as such it doesn't solve the issue nor negate the above facts. It simply dances around them entirely. It is like seeing an explosion feat and, to tier it, deciding to not actually base the evaluation on the explosion itself, but exclusively on its secondary effects.
And this, itself, leads us to another possible counterpoint: The fact that a "lack" of dimensionality does not necessarily translate to superiority over dimensionality. That I refer to this as a fact should already inform the you that I don't disagree with this claim, and in fact it is objectively unrelated to this point, as we are talking about actual superiority over dimensionality, not simply an absence of it. But nevertheless, it is an important point to mention, and before carrying on, it is necessary to once again quote from the FAQ:
As seen above, it is frequently talked about how, in order to qualify for the higher tiers (Such as 1-A and above) without infinite hierarchies and the like, it is necessary for them to be shown as unreachable to even additions of infinite more dimensions or "layers of transcendence" that didn't previously exist in their verse's cosmology. And currently it is argued that simple superiority over dimensionality does not necessarily grant one such an inaccessible standing.
To refute that, we firstly lay down our terms. We do this by noting that the aforementioned inaccessibility may come in two forms, which we will term "Inaccessibility-by-Alienness" and "Inaccessibility-by-Superiority." The meaning of the latter is plain from the term alone: It is to be inaccessible to additions of dimensions by virtue of inherent superiority over the numbers of dimensions which are being added to the cosmology. So, for example, it is futile to try and add 2, 5, 89 or countably infinite dimensions to a cosmology in order to try and reach a character with this trait, because their nature is already greater than all of this to start with.
"Inaccessibility-by-Alienness," in turn, is a kind of inaccessibility that does not actually interact with superiority at all, and comes from the thing deemed "inaccessible" being simply of a different nature than the thing attempting to reach it. For example, it is impossible to reach Left by traveling Right, but that is not because Left is infinitely superior to Right; it is simply a different direction. Likewise, if you consider an object that is not superior in nature to either space or time, but nevertheless lacks both, then obviously it still cannot be "reached" by adding dimensions to a cosmology, regardless of how many, but that is simply due to a difference in nature. The object then remains neither superior to dimensioned things nor inferior to them, just incomparable.
Included in this type are thus characters whose tiers do not (And cannot) derive from their lack of spatial properties at all, but rather from direct feats of force. For example, we can have a character who is fully aspatial, but is only 6-B due to having a feat of destroying Britain. But we cannot have a character who is fully aspatial and simultaneously 6-B due to being as large as Britain; that is a contradiction. Additionally, note that since all their power derives from their external AP, rather than from their non-dimensional physiology, these characters cannot be said to be "superior to dimensionality" in the sense that the FAQ means, either.
However, of importance to this discussion, then, are characters whose superiority is precisely because of their non-dimensional nature, as this is exactly what the FAQ is referring to in the section quoted above. To put it simply: If the fact they are different in nature from dimensionality is one and the same with the fact they are superior to dimensionality, then it follows that their Inaccessibility-by-Alienness results in Inaccessibility-by-Superiority, as their superiority is their alienness. Therefore, if a character is superior to dimensionality, then they are unreachable to any additions of dimensions, finite or infinite, even if their verse's cosmology lacks infinite dimensions.
Another way to put it would be as follows: If a character is completely superior to dimensionality, not by feats of external AP but as a result of their non-dimensional nature itself, then the gap between them and dimensional thing cannot be a quantitative one (i e. A dimensional jump), as the character has none of the spatial qualities that'd permit such a thing. Since the superiority comes from the very nature of their existence, then definitionally it is a qualitative one, and we've already extensively shown that qualitative superiorities are not at all equivalent to differences in dimensionality or cardinality.
So, why exactly do we claim they are, then? Well:
More specifically, a justification that is often given is that the main basis on which the Tiering System is built is neither dimensions nor Reality-Fiction Transcendences, but rather a loose idea of "levels of infinity" which both of these things are simply equalized to, and therefore the differing properties which those things have is no issue. This, of course, is also a complete non-answer, since it gives no precise elaboration on what exactly this idea of "A level of infinity" constitutes and nor does it explain how it can be equated to two things which, demonstrably, are completely unalike.
So, as said above, the Tiering System really is just positing the existence of some magical similarity between qualitative differences and quantitative differences that allows them to be equated with no issue despite everything that completely disproves this notion. And the only possible justification for that is something which we've already shown is essentially a false equivalence that is also tantamount to incompletely tiering a feat. The final point, then, is one that should be self-evident by now: Yes. Qualitative superiorities, such as Reality-Fiction Transcendences and transcendence over dimensionality, are in fact above any dimensional jump, as well as any cardinality. Under the current arrangement of the Tiering System, they are objectively Tier 0.
That this is so can also be intuitively observed simply enough. Ask yourself: Is the difference between reality and fiction equivalent to the difference between a square and a cube? Is the difference between reality and fiction equivalent to the difference between aleph-1 and aleph-2? Is there any justification for such a concept? The answer, of course, is no. And the reason behind the length and verbosity of this post was precisely to explain that tolerating such a false equivalence has consequences that make it ridiculous to operate on a system that works under it.
But of course, the Tiering System and its defenders have other lines of reasoning in which they acknowledge that the above equalizations are absurd and inaccurate, but nevertheless maintain that they are necessary compromises done in order to prevent the wiki from spiraling into even further inaccuracies. We will go over some of these arguments below and respond to each of them in turn.
Listed alongside these arguments are also arguments that I've formulated myself, and so some of them aren't even responding to anyone in particular but moreso dispelling potential misconceptions, as well as misconceptions I've personally seen being spread around.
In order to refer to the position that qualitative superiorities are inherently above any and all quantitative superiorities, we will use "qualitative superiorities as they truly are" as a shorthand. Without further addo...
Counterpoint 1: It would seem that tiering qualitative superiorities as they truly are is untenable, as doing so involves accepting No-Limits Fallacies, which would in turn force us to rate any blanket statements of limitlessness or boundlessness at Tier 0.
To quote the wiki's page on fallacies:
And a character that the opposition has presented before to illustrate this point is Fiamma of the Right, whose power is:
Basic logic, they argue, dictates that Fiamma being capable of defeating whatever target standing before him with the precise amount of force needed, with no stated or shown limit, would result in him being rated at Tier 0. And yet this is obviously generalizing the ability too far using too little, regarding of how logical it is, and as such we refrain from doing so. The argument then goes that the same applies to tiering qualitative superiorities as they truly are, and therefore they shouldn't be treated as such.
This, of course, is an utter false equivalence and a blatant misuse of even the wiki's own logic. Firstly, saying "Qualitative superiorities being necessarily above any and all quantitative superiorities is a NLF" is the exact same as saying "Infinity being necessarily above any and all finite things is a NLF." There is precisely zero difference between these two statements, and yet, obviously we do not accept the latter as true. Likewise, it is also the exact same as saying "The idea that no amount of nothing will ever add up to something is a NLF."
Now, that no amount of "nothing" will ever add up to "something" is simply a fact from both a mathematical perspective and a purely logical one, as has been extensively explored above. So, clearly, if the wiki's standards come to the conclusion that it is, somehow, a fallacious notion, something is clearly wrong with the way those standards are being applied.
Secondly, a statement/feat/ability being broad in scope does not necessarily make it a No-Limits Fallacy, particularly when there is a mechanism attached to it that justifies its limitlessness.
For example, if a character had an ability that allowed them to "Harm any enemy, no matter how durable," then obviously this would be treated with scrutiny, and would be capped at the highest tier of durability it has been shown to work on, even if the highest showings aren't portrayed as hard caps to its power. If the ability was at most shown harming a character with 5-B durability, then it would not assumed to be capable of harming a character with High 3-A durability. However, if, for instance, it turns out this ability works by damaging the underlying "source code" of reality or the like, then we would indeed assume it can work on someone with High 3-A durability. As there is, after all, no fundamental difference between these levels of durability that'd prevent Information Manipulation of this sort from functioning on both. The same goes for any esoteric mean of negating durability.
This applies not only to offensive abilities, but also to defensive ones. For example, if a character was stated to be "Invulnerable to all damage, regardless of how strong" by virtue of some unexplained feature of their existence, then this would be treated with scrutiny and capped at its highest showings. However, certain abilities allow this to be extrapolated extremely far: As said here, a character who has Type 5 Acausality is treated as immune to all conventional attacks (E.g. An energy blast with no special properties aside from being strong), even if those come from characters with tiers as high as High 1-A, simply by virtue of the nature of the ability ensuring that. And since there is no fundamental difference between High 1-A power and Tier 0 power, it follows that Type 5 Acausality would allow one to ignore conventional attacks from Tier 0s as well.
So, in summary: No-Limits Fallacies only apply to statements of limitlessness that provide no basis for being as limitless as they claim to be. If a feat/ability/statement/nature actually does have something backing up the notion that it should not be limited by X or Y, then they are inapplicable. And we're already extensively demonstrated that qualitative superiorities have more than enough backing the idea that they are above any difference in dimensionality or cardinality.
Counterpoint 2: It would seem that tiering qualitative superiorities as they truly are is unneeded, as we only rate things based on the minimum viable interpretation of them, not the highest.
The problem of this objection is that it presupposes a single dimensional jump is the minimum viable interpretation for a qualitative superiority to begin with, without elaborating on what exactly makes it so. As we've seen above, tiering qualitative superiorities as above any and all quantitative superiorities is the minimum viable interpretation.
Framing this in logical terms, it really is just about the difference between necessary and sufficient conditions, and in order to prove an effect true, it is needed to prove sufficient conditions, not necessary ones. Now, let us ask ourselves: Given a square, a 2-dimensional object with only length and height, is being 3-dimensional sufficient to produce a qualitative superiority over the square?
The claim that a square is literally nonexistent to something like a cube is, of course, nonsensical. And saying that a square has "0 size" to the cube is also incorrect. The square has no 3-dimensional volume, but it nevertheless has size in two dimensions that are very real even for higher-dimensional beings (As a cube has length and height, even if it is one dimension higher than the square). As such, a square on the whole is still very much real to a 3-dimensional being and the difference between the two is very much a physical one, and so the two reside on the same qualitative level (As they are not separated by quality, but by quantity). Therefore a dimensional jump is not sufficient to produce a qualitative superiority.
Counterpoint 3: It would seem that we do not equate qualitative superiorities to quantitative ones, as we instead require higher-dimensional spaces to demonstrate qualitative superiority over lower-dimensional spaces, and give them no tier of their own. By extension, the same would go for lower-dimensional spaces, which would need showings of qualitative inferiority to 3-dimensional spaces to be rated at Tier 11.
On the contrary, the Tiering System FAQ says:
So it is very much acknowledged that dimensional jumps are quantitative in nature. Furthermore, that most lower-dimensional characters remain at Tier 11 is something that has been expressed before, with the reasoning being that "The lowest plausible tier for a lower-dimensional character without any other feats is Tier 11."
Counterpoint 4: It would seem that tiering qualitative superiorities as they truly are is untenable, as this would result in extremely inflated ratings that do not at all correspond to the portrayal of the characters being tiered. It would be saying these characters have levels of power that they've never demonstrated.
This objection is a particularly strange one. First and foremost because it fails to consider the fact that, as far as fiction is concerned, this wiki's higher-end Tiering System does not exist. The Tiering System for things above High 3-A is a constructed framework and so using it as a measuring stick to evaluate a verse's portrayal and depiction of a character's power is ridiculous. It is effectively forcing the fiction to fit the system, rather than forcing the system to fit the fiction.
Counterpoint 5: It would seem that tiering qualitative superiorities as they truly are is untenable, as this would inflate characters far beyond anything that most authors would have intended, and thus constitute intentional misinterpretation of the text.
A variation of the previous objection, and one which thus merits a similar answer: Versus Battles Wiki's Tiering System for things above High 3-A does not exist, as far as the authors of most fictions are concerned. So, of course, authors cannot intend a character to be something which they don't know exist.
This is an interesting and noteworthy point to mention, however, because while for example most authors obviously cannot intend for Reality-Fiction Interactions to be displays of powers corresponding to the exact ratings of the Tiering System, they can still intend them to be displays of transcendent power in general. By contrast, there are indeed many cases where authors do not intend them to be displays of such power at all (E.g. Jokes in gag cartoons), and so there is in fact a potential distinction to be made with regards to that. However, this obviously does not negate the instances where they are written and intended as actual power displays.
This response, along with the response to the previous objection, should also suffice to address potential appeals to similar line-drawings done in the Tiering System, such as with mass-energy conversions and kinetic energy feats, as these two kinds of feat deal with the more grounded parts of the Tiering System and therefore with things that authors of the vast majority of fiction can be assumed to have a sense of.
For example, "This author did not intend for this character to have the firepower to destroy a city just because they are able to create swords from nothing" is a reasonable assumption to make, as "destroying a city" is indeed something that exists in the minds of most writers of action/fantasy fiction. "The author did not intend this Reality-Fiction Transcendence to be above all cardinality and dimensionality" on the other hand is only vacuously true, as most authors would simply not know about any such things and thus not be capable of intending anything regarding them either way.
This is to say that it is technically true, but in the same way the statement "No phones are turned on" is true when directed towards a room with no phones in it: There are no phones there, so consequently there can be no phones that are turned on, either. Likewise, it is true in the same way the statement "They didn't intend for this house to be yellow" is true when directed towards a person who had no knowledge of the existence of said house: They didn't know about the house at all, so consequently they couldn't have intended for it to be yellow, either. Needless to say, vacuously true statements are nonsense.
As such, if the intentions of the author are to be accounted for by the Tiering System in an honest and consistent way, the division when it comes to tiers above High 3-A would not hinge on whether the author intended for the feat to correspond to a specific tier within it (As intent requires prior knowledge, which in this case is nonexistent), but rather on whether they intended it to be a showing of transcendent power at all.
Counterpoint 6: It would seem that tiering qualitative superiorities as they truly are is untenable, as extraordinary claims require extraordinary evidence, and simply seeing something as literally non-existing is far too little evidence to infer such vast power from.
The Sagan standard is certainly a good aphorism. When repeated ad-nauseum, however, it ceases to be a useful guide for thought and becomes little more than a platitude. As a small reminder of what "evidence" means:
As such, if evidence is what is required, then refer to the previous two sections of this post, both of which provide plenty of facts and information backing up their claims.
Counterpoint 7: It would seem that tiering qualitative superiorities as they truly are is unneeded, as fiction does not have to obey any rules, and therefore rating qualitative superiorities as equivalent to quantitative superiorities is no issue. We cannot enforce our views on fiction.
This objection is a quite weak one, since it is tantamount to claiming that, because fiction can break any logical rules it likes, we must therefore assume that it is always breaking a logical rule when tiering qualitative superiorities. It doesn't take much thinking to realize that this is nothing but claptrap: Verses that break rules should, by definition, constitute exceptions, and not rules. The rule-of-thumb is to always follow logic unless otherwise instructed that it does not apply to a given situation, as is evident from how tiering in general is constructed.
This objection, just like Objection 5, is a variation of Objection 4, and it is a part of a larger class of arguments that can be summarized as such: "If the majority of fiction does not treat something as X, we do not treat it as X, either." For example, in the real world, acceleration results in increased kinetic energy and thus anything that goes fast enough would also exert a lot of force. However, fiction almost universally disregards this and treats speed and strength as separate attributes, and so, we disregard it too. A line of reasoning that one could try to take, then, is that the same would apply to qualitative superiorities: "Fiction never treats qualitative superiorities as so powerful, therefore we should not, either."
As seen above, the opposition often likes to use Carl Sagan's famous saying of "Extraordinary claims require extraordinary evidence" in debates about this topic, so I will take the liberty to use another one of his quotes: Absence of evidence is not evidence of absence. Or as I like to put it: Ambiguity is not negation.
In essence, when a verse depicts a character throwing a steel ball at 58% of the Speed of Light with no significant environmental damage, what we have is evidence of the absence of a realistic treatment of kinetic energy. When a verse depicts a character throwing a punch at Mach 629 with no significant environmental damage, what we have is evidence of the absence of a realistic treatment of kinetic energy. When a verse depicts the Big Bang as a literal explosion, what we have is evidence of the absence of a realistic portrayal of the Big Bang. When a verse breaks any of our rules on Black Hole Feats, what we have is evidence of the absence of a realistic portrayal of black holes.
And when this evidence of absence starts to pile up and become a trend throughout the overwhelming majority of fiction, we adopt it as the method we use for tiering said fiction.
So, in such cases, we have things that serve as direct, positive evidence of the absence of a certain phenomenon (In this case, realistic KE, big bangs and black holes). Such evidence of absence, for obvious reasons, is nowhere to be seen in displays of qualitative superiority in fiction: There is nothing in any case of Reality-Fiction Transcendence in any verse that actually directly disproves the notion that it is above any dimensionality or cardinality. What we have, in these cases, is simply silence on the part of the verse, and to take this silence as positive evidence that this notion is absent from the verse is to conflate absence of evidence with evidence of absence.
Of course, I recognize how ridiculously easy it is to twist my words here, intentionally or not, so allow me to clarify: This is not to say that we should accept things without any evidence. What it is saying, however, is that mere ambiguity (Absence of evidence) is not the same as outright negation (Evidence of absence). Negation prevents a claim from ever being true, while ambiguity allows for the possibility that it might be either true or false. Of course, this possibility is completely useless left as is; it is up to something to collapse it into either certain truth or certain falsehood. But in this case, the certain truth of the claim "Qualitative superiorities are superior to all quantitative superiorities" has already been proven in-depth.
Counterpoint 8: It would seem that tiering qualitative superiorities as they truly are is untenable, as it makes far too many assumptions regarding how they work in specific verses
This is incorrect. For example, the argumentation involving Reality-Fiction Transcendences only assumes that the higher layer sees the lower layer as "unreality/nothing," which is already an assumption that the wiki explicitly makes. Everything else simply follows from it logically, and denying these consequences just causes the Tiering System to devolve into incoherence.
Overall, this objection just attempts to reduce the argumentation above by accusing it of being speculation, or conjecture. Saying it is just "speculation," though, is the same thing as saying that infinity being above finite things is speculation. This is obvious nonsense, so: No, it is not speculative in the slightest.
Counterpoint 9: It would seem that tiering qualitative superiorities as they truly are is untenable, as this would involve rating them as above things that are not explicitly mentioned in the verse's text.
This objection makes use of what I like to call "Wookiepedia logic," which can be summarized as follows: "If it is not explicitly mentioned in the text, it does not exist, and therefore shouldn't be taken into account." A quick look at the wiki's own standards will quickly show that this kind of logic is not consistently applied, if at all. For example, no verse explicitly mentions that a spacetime continuum is made up of uncountably infinite "snapshots" of the 3-dimensional universe. In fact, only very few verses explicitly mention cardinals or mathematical infinities at all, yet feats of full timeline destruction are Low 2-C, for all verses, based on reasoning that involves them.
Why do we treat a spacetime continuum as such, then? Because that is just how a temporal dimension works, and, more generally, how a continuum works. For a more down-to-earth case, consider the fact that most verses don't explicitly say that H2O is water, yet if a character was reliably stated (And only stated) to be able to magically manipulate H2O, they'd obviously be listed as having Water Manipulation.
So, the text of a verse is not, never was, and never should be, the sole point of reference taken when evaluating that verse's tiers. It is the primary point of reference, certainly, but standing right beneath it are reason and critical thinking, both of which include the ability to make inferences and apply them when needed. Remove that, and you have a body of thought defined by its strange and ultimately senseless refusal to allow people to use their brains for anything.
And before anyone tries to argue that: No, the reasoning given above doesn't imply that we should start allowing cross-scaling with other verses. If one attempts to argue that it does, they would have to argue that this implication is present in the current Tiering System as well, due to the examples I've shown. So, either way, it is not something that uniquely follows from my argumentation.
Objections 4-9 are all variations of each other, and as such the responses to them are more tightly bound than the responses to other counterpoints listed in this section. It is expected that the majority of counterpoints the reader formulates to one of those six will ultimately find themselves answered in some, or all, of the other six. Therefore it is advised that special attention be given to them
Counterpoint 10: It would seem that tiering qualitative superiorities as they truly are is unneeded, as the Tiering System's nature as a constructed framework makes its borders inherently arbitrary, and therefore all the matters is that whatever system is choosen remains consistent with itself.
This, in particular, is quite an absurd position to take here, as it essentially boils down to "We can literally do whatever we like as long as it follows some internal logic." However, this is absent here: The fact that I could so thoroughly demonstrate why and how the Tiering System's current treatment of qualitative superiorities leads to a number of absurdities (And is therefore not self-consistent) should already serve as proof that this objection is nothing more than vapid absurdism used to defend positions that are, otherwise, indefensible.
Of course, the position is actually correct if we reduce it to "If we are made to choose between two equally (ina)accurate systems, the decision is ultimately arbitrary." But the idea that the present Tiering System is no more accurate than any other possible alternatives has already been sufficiently demonstrated as simply untrue.
Counterpoint 11: It would seem that tiering qualitative superiorities as they truly are is untenable, as it would force us to rate any statement describing something as "Beyond reality" and similar at Tier 0.
That is untrue. "Beyond reality," even taken to mean superiority, does not necessarily imply a qualitative superiority. This is due to the fact that "reality" is often contextually used to refer to a single universe or the like. For example, in most fiction where the multiverse is a central theme, each universe will be referred to as "a reality." As such, the term would not be referring to "The quality of realness" but "A single spacetime continuum," and even a difference of one dimension is sufficient to be superior to a space-time continuum (As a 4-D spacetime can be embedded as an infinitesimal portion of a 5-D realm, just as a 2-D universe can be an infinitesimal portion of a 3-D universe).
However, if there is evidence that, by "Beyond reality," what is meant is "Beyond the quality of realness" itself, then obviously such a superiority would be a qualitative one, for the same reason something that is "Below the quality of realness" (And thus so lesser as to be nonexistent) would have a qualitative inferiority, and thus be inferior to all dimensionality, even 0-dimensionality, as demonstrated above.
Counterpoint 12: It would seem that tiering Reality-Fiction Transcendences as equal to dimensional jumps is a necessary compromise, as although treating them as above all quantitative superiorities is fully accurate, it is also fully accurate to treat them as not conferring any increase in power at all, as we living in the real world have a Reality-Fiction Trancendence over fictional characters, and yet no one would say Mike Tyson can beat Superman. Thus a middle ground is needed.
The failure of this objection is a fairly simple matter: If we are to apply the logic of Reality-Fiction Transcendences to the real world, then Mike Tyson is indeed more powerful than Superman, as he is real and Superman is not. To say otherwise can only be a valid position if one takes "power" to refer exclusively to acts of strength showcased in one's respective "world," and by this metric, Superman is indeed more powerful than Mike Tyson. It is not at all obvious why this would be a valid framework to pick when analyzing fiction, however, especially when any and all arguments about Reality-Fiction Transcendences have, as a starting point, the trust that the verse being discussed does portray the Reality-Fiction Interaction as a showing of transcendent power. If it doesn't, we'd indeed not tier them at all.
Thus in order to tier such verses it is necessary to, from the start, abide by the notion that a superiority is conferred by a R-F Trancendence. Under those lenses, if Superman were to be magically made real and put to fight against Mike Tyson, then obviously he would win. However that would only be because Superman was made real and thus allowed to have a level of existence which he normally lacks, and thus we might call this an amplification of his power.
Counterpoint 13: It would seem that tiering Reality-Fiction Transcendences as equal to dimensional jumps is a necessary compromise, as there are verses that conflate the two
Verses that conflate the two kinds of superiority are easily evaluated by simply tiering them based on which of the two the transcendent thing in question is most closely aligned with.
For example, if Realm X is described as "a higher dimension" or as "higher-dimensional," yet doesn't display any of the actual properties expected of a genuine higher-dimensional space, while also displaying all of the properties expected of a Reality-Fiction Transcendence (E.g. Seeing lesser things as literally lacking existence, and/or being "more real" than them), then it would be tiered as a qualitative superiority.
On the other hand, if Realm X is stated to be a higher-dimensional space and is described in ways analogous to a Reality-Fiction Transcendence, while otherwise behaving exactly as a higher-dimensional space would be expected to (E.g. The difference between it and the lower realms is demonstrated as a physical one), then it would be tiered as a quantitative superiority.
Counterpoint 14: It would seem that dimensional jumps are qualitative superiorities, as a cube is made bigger than a square by the fact it has volume, while the square only has area. Therefore, the difference between both is one of quality, not of quantity.
This is again an equivocation. The difference between a cube and a square is such that the square has 0 volume, while the cube has infinite area. Volume and Area are quantities, and as such the difference between the two is by definition a quantitative one. Furthermore, a cube has infinite area due to the fact it is formed by the sum of infinite squares, which once again demonstrates the strictly quantitative nature of dimensionalities.
Counterpoint 15: It would seem that the argument for why qualitative superiorities are superior to all quantitative superiorities applies to dimensional jumps, as a square has 0 volume, and one cannot obtain something non-zero by adding together things with 0 value. As such it follows that a dimensional difference, itself a quantitative superiority, is above all quantitative superiorities, which is a contradiction. Therefore the argument is incoherent.
The mistake of this objection is that it conflates the 0 that represents an absence of things with the 0 that represents the lack of extension in some n-dimensional space. The first type of "0" we call the empty set, as above explained, and the second type we call a "null set." As the latter still applies to sets that are non-empty (E.g. A square is a null set in 3-dimensional space, as it lacks volume, but it still has elements and is thus not empty), the principles behind operations on the empty set do not apply to it.
Counterpoint 16: It would seem that Ultima is cringe and therefore the argument is false a priori
Well, shit, man. Can't argue against that.
So, all-in-all: What we have is a bizarre, Frankenstein-like Tiering System that obsesses far too much over mathematics and likewise attempts to reduce everything to a very specific mathematical framework while, ironically, disregarding its most elementary principles as needed. It openly makes direct false equivalences and labels any argument that contests them as "fallacious" while, in truth, committing far more fallacies than it avoids and creating gross inconsistencies both with itself and with the basis it claims to utilize.
The first step to constructing a better Tiering System would be to, of course, entirely separate qualitative superiorities and quantitative superiorities, instead of trying to shoehorn one into the other as is currently done. As made clear by now, qualitative superiorities are necessarily above any and all quantitative superiorities, and as such a tier for them would be above the entirety of the current Tiering System.
As said before, what this means, bluntly speaking, is that anyone with an actual qualitative transcendence (E.g. Reality-Fiction Transcendences, transcendence over dimensionality, etc) over lesser realms would, in the current arrangement of the tiers, be Tier 0, and high into it at that. This is an obvious issue. Why? Because there are a lot of verses who have not just characters with qualitative superiority over lesser things, but also hierarchies of qualitative superiority, and things beyond these hierarchies, and things beyond those things, too. If we shoved such a wildly variable array of characters into a single tier, we would fall into the same issue that caused 1-A to be divided into four tiers all these years ago.
So, would the solution be to split 0, then? We could, but I think that's stupid. The Tiering System in general is built with the idea of having a single endpoint in mind. That's why the tiers count backwards from 10, instead of forwards. Splitting this endpoint into high and low-ends defeats the whole purpose of this, so I don't believe this would be the best course of action, no.
Ontop of that, there are more characters whose high tiers derive from metaphysics than characters whose high tiers derive from mathematics, and this discrepancy basically doubles when entering 1-A and above. As such, if we were to simply upgrade all qualitative superiorities to Tier 0, it would result in there being more Tier 0s than there are 1-As, High 1-As and Low 1-As. And I don't think I'm the only one who sees the logistical problems with that.
Furthermore, there is already a tier that is listed as an entirely separate category from the rest of Tier 1: 1-A. So with that in mind, what would my suggestion, be, pray tell? Well, in short: Make 1-A the tier for qualitative superiorities, and kick all quantitative superiorities down to the rest of Tier 1.
That is to say: Dimensional jumps and differences in cardinality would simply all peak at High 1-B, with perhaps a High 1-B+ tier for infinite-dimensional spaces that are larger than countably infinite dimensions. Meanwhile, strictly qualitative superiorities, such as Reality-Fiction Transcendences, transcendences over dimensionality, and etc. would land at 1-A.
Down under, something similar would happen: For qualitative inferiorities, a new tier below 11-C would need to be created. So, this would be for characters that are fiction even to a 3-D reality, as well as beings who are "nonexistent" in a way that indicates inferiority over other things. Hypothetically, a character who is inferor to dimensionality, rather than superior to it, would also fall under this tier.
1-A+ and High 1-A would stay effectively the same. The former would be for an infinite hierarchy of qualitative superiorities. The latter would be for characters who are above the "quality" defining the lower hierarchy altogether, while still working on their own, higher form of qualitative superiority. For example, in Marvel Comics, the omniverse has an infinite hierarchy of dreams-within-dreams in itself, and above that, then, is the Outside, which transcends all forms of reality and dream and yet nevertheless still has its own hierarchy that works on something else entirely.
And so, I am done.
This thread has certainly been a long time coming. And though its placement in the general discussion board makes this clear already, it is probably best that I say it explicitly: I don't actually have any interest in bringing any changes to the Tiering System, as I am well aware that, ultimately, whatever I say can simply be vetoed regardless of its truth. So I post this not as a proposal of any kind, but an exposé, if you will.
The purpose of this text, first and foremost, is to simply bring to light the many, many absurdities which the system's higher tiers commit; no more, and no less. And all of this, of course, directly from the mouth of the one who revised it all those years ago. And mind you: Though I haven't originated all of these absurdities, I have greatly facilitated many of them and originated one, and so I don't deem myself blameless in this affair.
Of course, this is intended to be read in its entirety, so preferably don't start making up ideas in your head before even finishing the whole text. And before anyone asks: Yes, I am well aware of how large this ended up being. But to quote Alberto Brandolini:
The amount of energy needed to refute bullshit is an order of magnitude bigger than that needed to produce it.
And unfortunately energy seems to be something I have in abundance.
IF YOU WANT A TL;DR, GO HERE
Category Errors
Category errors are a pretty elementary thing in logic, and so explaining them is not really a complicated matter. Simply put: They are the act of assigning a thing, any given thing, properties from a category which it does not belong to. For example, if I ask "How heavy is the quadratic formula?", that is a category error, because a mathematical formula is an abstraction and thus doesn't fall under the category of things which have mass and weight.Similarly, if I ask "What does purple taste like?", that is a category error, because "purple" is a color and thus not fall under the category of things which have taste. Likewise, if one were to ask "What is bigger, green or yellow?", that is also a category error, because colors are not under the category of things to which size applies.
A common trend that you'll probably noticed by now, of course, is that statements entailing category mistakes are inherently nonsensical. None of the parody-questions which I've posed above have any meaning. I might as well have said "Colorless green ideas sleep furiously." If we are in agreement as to the inherent nonsense of such sentences, we are already prepared to tackle the rest of the subjects pertinent to this text.
"Qualitative" Superiority
An extremely prominent idea in discussions pertaining to high tiers is that of "qualitative superiority." To quote the wiki's policy pages on the matter:
Tiering System FAQ
A: Whether higher-dimensional entities qualify for such high tiers or not depends on several different factors, which may take root both in and out-of-verse. To explain this situation, we must first clarify what exactly being higher-dimensional entails. In a way, yes, though not how most would...
vsbattles.fandom.com
Reality-Fiction Transcendence
It is not uncommon in fiction for characters to view lesser realities as if they were fiction, in much the same way as a real world human would view fiction. Frequently that comes in the form of almighty author characters which can freely rewrite those lesser realities. The other way around...
vsbattles.fandom.com
At the core, the concept is basically some loose sense in which something is "a higher infinity" than something else. The two foremost examples of the concept are, presently, dimensionality and Reality-Fiction Transcendences. The latter, in particular, expresses it pretty directly in its explanation page, quoted above: "Thus, they would be treated as more than infinitely greater, such as in this case Low 1-C. The gap between the higher world and the lower world would be strictly one of quality, not quantity."
So, if Character X views Character Y as part of a work of fiction, the gap between them is treated as, in a sense, "more than infinite" by virtue of a difference in quality: Character X is a reality, and Character Y is a fiction, and the superiority which the former holds over the latter thus logically cannot be surpassed by mere additions of power and size due to being beyond the reach of both. By contrast, a quantitative superiority would be one that involves numerical quantity, not quality.
For example: A volume of 27 m³ is greater than a volume of 10 m³, but quantitatively so. Likewise, a length of 10 m is greater than a length of 3 m, but once again, quantitatively so. Likewise, a set of 5 apples is greater than a set of 2 apples, but, again, quantitatively so.
Right off the bat, this already leads us to the first logical problem, which is the equating of two completely different kinds of superiority. A dimensional difference is not, in fact, a qualitative superiority, but a quantitative one. A 3-dimensional object, for example, is made of an infinite number of 2-dimensional objects (This number being the cardinality of the real numbers, or 2^aleph-0, the power set of the smallest infinity). And this generalizes to any two objects of dimensionality n and n+1 (3-D and 4-D. 4-D and 5-D, and so on)
Another way in which this is reflected in the Tiering System is how an uncountably infinite amount of universes is Low 1-C, whereas a countably infinite amount of universes is 2-A. The difference between the two is one of number, and thus by definition it is quantitative. You can add uncountably infinite new universes to a set of countably infinite universes to make it go from one tier to the other.
By contrast, reality is obviously not composed out of slices of fiction, and neither can a real object be obtained by summing up fictional things, because the difference between the two hinges on an existential quality (i.e. The fact one is real and the other isn't), and not on physical measurements such as volume. Whereas a 3-dimensional object still has lower-dimensional portions of itself (As a cube can be divided into squares, and squares into lines, and lines into points), a body in reality has no part of itself that is fictional (And so a real cube can only be divided into real squares, and real squares into real lines, and real lines into real points. It cannot be divided into fictional squares, and nor can squares be divided into fictional lines, and nor lines into fictional points)
Likewise, a set of uncountably infinite universes can be reduced to a set of countably infinite universes, if we simply eliminate the excess universes from the totality. This is to say: Through simple numerical elimination, it is possible to take a multiverse from Low 1-C to 2-A. Meanwhile, it is obviously impossible to subtract so much from a real object or quantity that all that is left of it is a fictional portion. The conclusion is simple here: You cannot create non-reality from reality, and therefore, you cannot create reality from non-reality, either.
From these facts, it becomes obvious that something like a Reality-Fiction Transcendence cannot be measured on a mathematical basis, as mathematics is definitionally a purely quantitative framework and has no say whatsoever regarding what a "qualitative" superiority is, and thus obviously no say regarding what the gap between "fiction" and "reality" is, either. More to the point: Dimensional jumps, as well as jumps in cardinality, are quantitative superiorities. They are not qualitative.
To illustrate this, consider what a dimensional space is in mathematics: It is nothing but a multiplication. Take the real number line (R), which is a 1-dimensional set, and multiply it by itself. What you obtain through that is a 2-dimensional set, the real number plane (R^2, which is to say R x R). Take the real number plane and multiply it by the real number line, and you obtain a 3-dimensional set, the real number space (R^3, which is to say R x R x R). Indeed, take as another example the rational and irrational numbers: They are both 0-dimensional sets, and yet their sum is a 1-dimensional thing, the real number line.
By contrast, take the empty set (∅): This, as the name suggests, is a set with no elements whatsoever. It is, in effect, the set-theoretical 0, and for preciseness' sake we must note that it isn't exactly nothing, per se, but rather a set containing nothing. Nevertheless it is, for obvious reasons, close enough to the idea of nothing to serve as an illustrative tool for our purposes, as a Reality-Fiction Transcendence is, as stated, nothing but a relationship where the superior side sees the inferior side as literal unreality, and thus, as nothing. So the empty set, from here and onwards, will serve as a stand-in for that "unreality."
A very intuitive property of the empty set is that the sum of empty sets is, itself, an empty set, which is to say that nothing added to nothing equals nothing. Likewise, multiplying the empty set with a non-empty set only yields the empty set itself. ∅ x {1, 2, 3, 4, 5}, for example, equals ∅. And so does ∅ x R, and ∅ x R^2, and ∅ x R^3, and ∅ x R^816, and so on.
This is to say that there is absolutely no set which, when multiplied by the empty set, yields a non-empty set. And so as far as set theory is concerned, the question "How big is the volume of the gap between nothing and something?" is meaningless. But since the Tiering System considers such a gap to be equal to a difference in dimensionality, it falls into absurdity by attempting to answer that question using a mathematical basis.
As a further illustration of the logical inconsistencies this causes: Consider a qualitative inferiority. Something that is literally "unreal" or "nonexistent" (In a manner that entails inferiority) to a 3-dimensional world, for example, would be tiered at 11-A, and thus as on par with 2-dimensional space. And from this, we draw three conclusions, all of which exist jointly, being equivalent to each other:
Conclusion 1: The Tiering System considers the empty set, by all accounts, to be 11-A, and thus as on par with 2-dimensional space. But this is contradictory, as the empty set has no elements whatsoever and is thus of cardinality 0, while a 2-dimensional space has a cardinality of 2^aleph-0. Indeed, the empty set is smaller than even a 0-D point (Which is 11-C)
Worse yet: As said above, the empty set serves as a good mathematical approximation of nothingness, but it is not, in fact, nothing, so much as it is a set containing nothing, and hence a set that contains the empty set as its only member is of cardinality 1, as the empty set is "something" in the same way a bag with nothing inside is still something. So what the Tiering System is saying, in truth, is that utter nothingness is equivalent to 2-dimensional space. However, we've seen that "nothing" in a sense that denotes inferiority is even less than something like the empty set, which is in turn less than even 11-C objects. As such, clearly this is an absurdity.
Conclusion 2: Since the empty set is equivalent to a 2-dimensional object, despite the difference in cardinality between the two, it follows then that the Tiering System implicitly claims that ∅ = 2^aleph-0, which is plainly absurd even to a layman. And this causes mathematical absurdities, too, as it means that all cardinalities then are equal to one single cardinality.
This may be demonstrated as follows: Let us henceforth call 2^aleph-0 by the name c, and then consider the exponentiation of this cardinal with itself, c^c. As per basic cardinal arithmetic, this exponentiation results in a cardinal with strictly greater cardinality than c. However, we've already established that, under the aforementioned "logic," c = ∅, and ∅^∅ in fact equals 1. Thus it follows that no cardinals other than 1 can be constructed, as any exponentiation we attempt to do is now between 1 and itself, and 1^1 = 1.
However, c was already assumed to be equivalent to ∅ in the premise of the argument (In order to follow the logic of the Tiering System), and it is, itself, just another name for 2^aleph-0. Now, it follows from above that 2 and aleph-0 are both equal to 1, and 1^1 = 1. Therefore, 0 = ∅ = 2^aleph-0 = 1^1 = 1. Cleaning that up, it means that 0 = 1. So not only are all cardinalities in truth actually one cardinality, but that cardinality is an incoherent value. Thus it is plain that the Tiering System's logical framework is an inconsistent one.
Yet, as mentioned before, what the Tiering System truly does is even worse, since by equating actual nothing (Something less than even the empty set) with some specific quantity, it reduces all quantities to utter nothing as well.
Conclusion 3: Since the empty set is equivalent to a 2-dimensional object, it follows, then, that the Tiering System seemingly claims that a square (2-D) is literally nonexistent to a cube (3-D), or that it is perfectly equivalent to something literally nonexistent, which is obviously untrue to anyone with the most elementary knowledge of either physics or mathematics, and which has already been extensively proven wrong in the above paragraphs.
Further, in claiming the above, the Tiering System also is effectively claiming that there is a certain amount of nothingness that, when added together, yields a certain amount of somethingness, which has been shown to be manifestly untrue with the empty set, and which thus obviously goes for actual nothingness as well. Worse yet, the idea that enough "nothing" put together will eventually add up to "something" also implies that, if you have "something," and add enough "nothing" to it, it will eventually get bigger. Which is, again, also transparent nonsense.
But of course, the system seems to actually acknowledge the quantitative nature of mathematical differences, as evidenced by this bit from the FAQ: "Of course, the same levels of superiority can also be reached via sufficiently explicit quantitative statements, such as when cardinalities above countably infinite get involved in a manner that implies a corresponding difference in power/size."
So in spite of openly acknowledging the difference between the kinds of superiority that are at play in differences in dimensionality and in actual qualitative differences, the Tiering System nevertheless equates them as if they are equivalent. Not identical, but equivalent. In summary, the Tiering System appears to insinuate that there is some mechanism by which something that exists (A lower-dimensional object) is made equivalent to something that does not exist (Fiction). That is to say, some reasoning that makes this seeming absurdity into a coherent position.
One might be thus tempted to ask what exactly it is that makes these things equivalent, but we will get to this shortly. We put this matter a bit to the side (But not aside) to tackle a different, though related, subject.
Space and Time and the Lack Thereof
For this, I direct myself to yet another part of the Tiering System FAQ:So currently, if a character is above, beyond and superior to the spatial and temporal dimensions of the cosmology of their setting (Superior to dimensionality as a whole, and not simply in a higher dimensionality), they are to be rated as equivalent to a single difference in dimensionality above that. So, for example, if a character is above dimensionality in a cosmology with 4 dimensions, they are to be rated as Low 1-C, and thus as equivalent to a 5-dimensional space. If a character is above dimensionality in a cosmology with 6 dimensions, they are to be rated as 1-C, and thus as equivalent to 7-dimensional space. And so on and so forth.
To see that this is yet another absurdity is just a basic exercise in identifying category errors, which we have went over in the first part of this text: Volume, higher-dimensional or lower-dimensional, is ultimately just a measure of the n-dimensional space which is occupied by a given body. As such, by definition, things that have neither time nor space do not have any volume, and so attempting to equate them to things that do is a fool's errand. It is, to draw from earlier, exactly the same as asking "How fast is the Pythagorean Theorem?" or "How deep is green?". Simply trying to impose into a thing a quality which it lacks (In this case, volume)
And yet, just as with Reality-Fiction Transcendences (Or, more generally, "Qualitative" superiorities), the Tiering System essentially justifies this by saying the following: Things that are aspatial indeed have no spatial quality and therefore no actual "size," and so their scope is indeed not really identical to that of spatial things, but simply equivalent instead. So for example, a character who transcends dimensionality in a cosmology with only 4 dimensions doesn't occupy a 5-dimensional volume, but exists in some state "equivalent" enough to it to be tiered as equal.
This is, point blank, also an absurdity, and to see why only requires one to remember the above explanations of what category errors are. This "justification," however, is arguably even worse than a simple category mistake, because it involves admitting that two things belong to different categories and that the terms applicable to one category are not applicable to the other, and yet still claiming the existence of some similarity between them that magically allows one to call them "equivalent," in spite of the total lack of characteristics shared between the two things.
A little scenario I've used before to illustrate the illogicality of that is as follows: Suppose I have two things, one is a formless, aspatial object, and the other is a cube with a volume of 30 m³. If I were to address the former and say "This thing has no spatial characteristics whatsoever, and so it has no volume nor position in space. Yet it is equivalent to that cube's volume," it would be more than rightful to say I would be speaking complete nonsense. And, for reference, there is no fundamental difference between finite volumes and infinite volumes, and therefore equating aspatial things to infinite volumes is exactly as absurd as in the case of a finite volume.
A possible justification that someone might use, then, is the argument that the two things could be equated by means of their practical properties, and how they are shown to relate. For example: Suppose you have a spaceless, timeless void preceding a Low 2-C reality. This reality is then created and now starts to exist contained by this void. The fact it is capable of "containing" the Low 2-C reality, then, could be argued to be something that can be tiered and used to deem it as equivalent in scope to other things that could also contain things that large, even if said things are spatial in nature, and the void is not.
That line of thought, however, is fairly clearly untenable, as it commits a very flagrant case of a false equivalence: Claiming that, just because two things share one property, they are equivalent, disregarding any number of other differences they might have that turn this impossible. In this case, it is claiming that an explicitly spatial realm and an explicitly aspatial realm are equivalent just because both are capable of containing a Low 2-C-sized reality.
And it is easy to see why this is fallacious: Consider, for instance, a fully-sized 6-dimensional realm and a fully-sized 5-dimensional realm. Both are certainly capable of containing a Low 2-C-sized reality within themselves, and yet obviously there is a distinction between them that makes it impossible for them to be equivalent, namely the fact one is 5-D and the other is 6-D. The same line of reasoning applies here: Though the hypothetical spatial realm and the hypothetical aspatial void share a commonality, this commonality is not sufficient to draw an equality between them, as they have other attributes which make such comparisons incoherent.
Furthermore, this kind of reasoning essentially amounts to only tiering half of the feat: The so-called method described above is not tiering the hypothetical void's superiority over dimensions, but only the fact of its containment of a Low 2-C universe, and as such it doesn't solve the issue nor negate the above facts. It simply dances around them entirely. It is like seeing an explosion feat and, to tier it, deciding to not actually base the evaluation on the explosion itself, but exclusively on its secondary effects.
And this, itself, leads us to another possible counterpoint: The fact that a "lack" of dimensionality does not necessarily translate to superiority over dimensionality. That I refer to this as a fact should already inform the you that I don't disagree with this claim, and in fact it is objectively unrelated to this point, as we are talking about actual superiority over dimensionality, not simply an absence of it. But nevertheless, it is an important point to mention, and before carrying on, it is necessary to once again quote from the FAQ:
As seen above, it is frequently talked about how, in order to qualify for the higher tiers (Such as 1-A and above) without infinite hierarchies and the like, it is necessary for them to be shown as unreachable to even additions of infinite more dimensions or "layers of transcendence" that didn't previously exist in their verse's cosmology. And currently it is argued that simple superiority over dimensionality does not necessarily grant one such an inaccessible standing.
To refute that, we firstly lay down our terms. We do this by noting that the aforementioned inaccessibility may come in two forms, which we will term "Inaccessibility-by-Alienness" and "Inaccessibility-by-Superiority." The meaning of the latter is plain from the term alone: It is to be inaccessible to additions of dimensions by virtue of inherent superiority over the numbers of dimensions which are being added to the cosmology. So, for example, it is futile to try and add 2, 5, 89 or countably infinite dimensions to a cosmology in order to try and reach a character with this trait, because their nature is already greater than all of this to start with.
"Inaccessibility-by-Alienness," in turn, is a kind of inaccessibility that does not actually interact with superiority at all, and comes from the thing deemed "inaccessible" being simply of a different nature than the thing attempting to reach it. For example, it is impossible to reach Left by traveling Right, but that is not because Left is infinitely superior to Right; it is simply a different direction. Likewise, if you consider an object that is not superior in nature to either space or time, but nevertheless lacks both, then obviously it still cannot be "reached" by adding dimensions to a cosmology, regardless of how many, but that is simply due to a difference in nature. The object then remains neither superior to dimensioned things nor inferior to them, just incomparable.
Included in this type are thus characters whose tiers do not (And cannot) derive from their lack of spatial properties at all, but rather from direct feats of force. For example, we can have a character who is fully aspatial, but is only 6-B due to having a feat of destroying Britain. But we cannot have a character who is fully aspatial and simultaneously 6-B due to being as large as Britain; that is a contradiction. Additionally, note that since all their power derives from their external AP, rather than from their non-dimensional physiology, these characters cannot be said to be "superior to dimensionality" in the sense that the FAQ means, either.
However, of importance to this discussion, then, are characters whose superiority is precisely because of their non-dimensional nature, as this is exactly what the FAQ is referring to in the section quoted above. To put it simply: If the fact they are different in nature from dimensionality is one and the same with the fact they are superior to dimensionality, then it follows that their Inaccessibility-by-Alienness results in Inaccessibility-by-Superiority, as their superiority is their alienness. Therefore, if a character is superior to dimensionality, then they are unreachable to any additions of dimensions, finite or infinite, even if their verse's cosmology lacks infinite dimensions.
Another way to put it would be as follows: If a character is completely superior to dimensionality, not by feats of external AP but as a result of their non-dimensional nature itself, then the gap between them and dimensional thing cannot be a quantitative one (i e. A dimensional jump), as the character has none of the spatial qualities that'd permit such a thing. Since the superiority comes from the very nature of their existence, then definitionally it is a qualitative one, and we've already extensively shown that qualitative superiorities are not at all equivalent to differences in dimensionality or cardinality.
So, why exactly do we claim they are, then? Well:
Complete Arbitrariness
To make it short: These kinds of superiority are deemed equivalent because we say so. It's as simple as that.More specifically, a justification that is often given is that the main basis on which the Tiering System is built is neither dimensions nor Reality-Fiction Transcendences, but rather a loose idea of "levels of infinity" which both of these things are simply equalized to, and therefore the differing properties which those things have is no issue. This, of course, is also a complete non-answer, since it gives no precise elaboration on what exactly this idea of "A level of infinity" constitutes and nor does it explain how it can be equated to two things which, demonstrably, are completely unalike.
So, as said above, the Tiering System really is just positing the existence of some magical similarity between qualitative differences and quantitative differences that allows them to be equated with no issue despite everything that completely disproves this notion. And the only possible justification for that is something which we've already shown is essentially a false equivalence that is also tantamount to incompletely tiering a feat. The final point, then, is one that should be self-evident by now: Yes. Qualitative superiorities, such as Reality-Fiction Transcendences and transcendence over dimensionality, are in fact above any dimensional jump, as well as any cardinality. Under the current arrangement of the Tiering System, they are objectively Tier 0.
That this is so can also be intuitively observed simply enough. Ask yourself: Is the difference between reality and fiction equivalent to the difference between a square and a cube? Is the difference between reality and fiction equivalent to the difference between aleph-1 and aleph-2? Is there any justification for such a concept? The answer, of course, is no. And the reason behind the length and verbosity of this post was precisely to explain that tolerating such a false equivalence has consequences that make it ridiculous to operate on a system that works under it.
But of course, the Tiering System and its defenders have other lines of reasoning in which they acknowledge that the above equalizations are absurd and inaccurate, but nevertheless maintain that they are necessary compromises done in order to prevent the wiki from spiraling into even further inaccuracies. We will go over some of these arguments below and respond to each of them in turn.
Listed alongside these arguments are also arguments that I've formulated myself, and so some of them aren't even responding to anyone in particular but moreso dispelling potential misconceptions, as well as misconceptions I've personally seen being spread around.
The Counterarguments
Now that we've established all our terms, we will from here and onwards use "Qualitative Superiorities" as an umbrella term to refer any and all kinds of superiority that are not quantitative (So Reality-Fiction Trancendence and transcendence over dimensionality both fall under said umbrella). By contrast, "Quantitative Superiorities" will be an umbrella term used to encapsulate both dimensional jumps and cardinality junps.In order to refer to the position that qualitative superiorities are inherently above any and all quantitative superiorities, we will use "qualitative superiorities as they truly are" as a shorthand. Without further addo...
Counterpoint 1: It would seem that tiering qualitative superiorities as they truly are is untenable, as doing so involves accepting No-Limits Fallacies, which would in turn force us to rate any blanket statements of limitlessness or boundlessness at Tier 0.
To quote the wiki's page on fallacies:
And a character that the opposition has presented before to illustrate this point is Fiamma of the Right, whose power is:
Basic logic, they argue, dictates that Fiamma being capable of defeating whatever target standing before him with the precise amount of force needed, with no stated or shown limit, would result in him being rated at Tier 0. And yet this is obviously generalizing the ability too far using too little, regarding of how logical it is, and as such we refrain from doing so. The argument then goes that the same applies to tiering qualitative superiorities as they truly are, and therefore they shouldn't be treated as such.
This, of course, is an utter false equivalence and a blatant misuse of even the wiki's own logic. Firstly, saying "Qualitative superiorities being necessarily above any and all quantitative superiorities is a NLF" is the exact same as saying "Infinity being necessarily above any and all finite things is a NLF." There is precisely zero difference between these two statements, and yet, obviously we do not accept the latter as true. Likewise, it is also the exact same as saying "The idea that no amount of nothing will ever add up to something is a NLF."
Now, that no amount of "nothing" will ever add up to "something" is simply a fact from both a mathematical perspective and a purely logical one, as has been extensively explored above. So, clearly, if the wiki's standards come to the conclusion that it is, somehow, a fallacious notion, something is clearly wrong with the way those standards are being applied.
Secondly, a statement/feat/ability being broad in scope does not necessarily make it a No-Limits Fallacy, particularly when there is a mechanism attached to it that justifies its limitlessness.
For example, if a character had an ability that allowed them to "Harm any enemy, no matter how durable," then obviously this would be treated with scrutiny, and would be capped at the highest tier of durability it has been shown to work on, even if the highest showings aren't portrayed as hard caps to its power. If the ability was at most shown harming a character with 5-B durability, then it would not assumed to be capable of harming a character with High 3-A durability. However, if, for instance, it turns out this ability works by damaging the underlying "source code" of reality or the like, then we would indeed assume it can work on someone with High 3-A durability. As there is, after all, no fundamental difference between these levels of durability that'd prevent Information Manipulation of this sort from functioning on both. The same goes for any esoteric mean of negating durability.
This applies not only to offensive abilities, but also to defensive ones. For example, if a character was stated to be "Invulnerable to all damage, regardless of how strong" by virtue of some unexplained feature of their existence, then this would be treated with scrutiny and capped at its highest showings. However, certain abilities allow this to be extrapolated extremely far: As said here, a character who has Type 5 Acausality is treated as immune to all conventional attacks (E.g. An energy blast with no special properties aside from being strong), even if those come from characters with tiers as high as High 1-A, simply by virtue of the nature of the ability ensuring that. And since there is no fundamental difference between High 1-A power and Tier 0 power, it follows that Type 5 Acausality would allow one to ignore conventional attacks from Tier 0s as well.
So, in summary: No-Limits Fallacies only apply to statements of limitlessness that provide no basis for being as limitless as they claim to be. If a feat/ability/statement/nature actually does have something backing up the notion that it should not be limited by X or Y, then they are inapplicable. And we're already extensively demonstrated that qualitative superiorities have more than enough backing the idea that they are above any difference in dimensionality or cardinality.
Counterpoint 2: It would seem that tiering qualitative superiorities as they truly are is unneeded, as we only rate things based on the minimum viable interpretation of them, not the highest.
The problem of this objection is that it presupposes a single dimensional jump is the minimum viable interpretation for a qualitative superiority to begin with, without elaborating on what exactly makes it so. As we've seen above, tiering qualitative superiorities as above any and all quantitative superiorities is the minimum viable interpretation.
Framing this in logical terms, it really is just about the difference between necessary and sufficient conditions, and in order to prove an effect true, it is needed to prove sufficient conditions, not necessary ones. Now, let us ask ourselves: Given a square, a 2-dimensional object with only length and height, is being 3-dimensional sufficient to produce a qualitative superiority over the square?
The claim that a square is literally nonexistent to something like a cube is, of course, nonsensical. And saying that a square has "0 size" to the cube is also incorrect. The square has no 3-dimensional volume, but it nevertheless has size in two dimensions that are very real even for higher-dimensional beings (As a cube has length and height, even if it is one dimension higher than the square). As such, a square on the whole is still very much real to a 3-dimensional being and the difference between the two is very much a physical one, and so the two reside on the same qualitative level (As they are not separated by quality, but by quantity). Therefore a dimensional jump is not sufficient to produce a qualitative superiority.
Counterpoint 3: It would seem that we do not equate qualitative superiorities to quantitative ones, as we instead require higher-dimensional spaces to demonstrate qualitative superiority over lower-dimensional spaces, and give them no tier of their own. By extension, the same would go for lower-dimensional spaces, which would need showings of qualitative inferiority to 3-dimensional spaces to be rated at Tier 11.
On the contrary, the Tiering System FAQ says:
So it is very much acknowledged that dimensional jumps are quantitative in nature. Furthermore, that most lower-dimensional characters remain at Tier 11 is something that has been expressed before, with the reasoning being that "The lowest plausible tier for a lower-dimensional character without any other feats is Tier 11."
Counterpoint 4: It would seem that tiering qualitative superiorities as they truly are is untenable, as this would result in extremely inflated ratings that do not at all correspond to the portrayal of the characters being tiered. It would be saying these characters have levels of power that they've never demonstrated.
This objection is a particularly strange one. First and foremost because it fails to consider the fact that, as far as fiction is concerned, this wiki's higher-end Tiering System does not exist. The Tiering System for things above High 3-A is a constructed framework and so using it as a measuring stick to evaluate a verse's portrayal and depiction of a character's power is ridiculous. It is effectively forcing the fiction to fit the system, rather than forcing the system to fit the fiction.
Counterpoint 5: It would seem that tiering qualitative superiorities as they truly are is untenable, as this would inflate characters far beyond anything that most authors would have intended, and thus constitute intentional misinterpretation of the text.
A variation of the previous objection, and one which thus merits a similar answer: Versus Battles Wiki's Tiering System for things above High 3-A does not exist, as far as the authors of most fictions are concerned. So, of course, authors cannot intend a character to be something which they don't know exist.
This is an interesting and noteworthy point to mention, however, because while for example most authors obviously cannot intend for Reality-Fiction Interactions to be displays of powers corresponding to the exact ratings of the Tiering System, they can still intend them to be displays of transcendent power in general. By contrast, there are indeed many cases where authors do not intend them to be displays of such power at all (E.g. Jokes in gag cartoons), and so there is in fact a potential distinction to be made with regards to that. However, this obviously does not negate the instances where they are written and intended as actual power displays.
This response, along with the response to the previous objection, should also suffice to address potential appeals to similar line-drawings done in the Tiering System, such as with mass-energy conversions and kinetic energy feats, as these two kinds of feat deal with the more grounded parts of the Tiering System and therefore with things that authors of the vast majority of fiction can be assumed to have a sense of.
For example, "This author did not intend for this character to have the firepower to destroy a city just because they are able to create swords from nothing" is a reasonable assumption to make, as "destroying a city" is indeed something that exists in the minds of most writers of action/fantasy fiction. "The author did not intend this Reality-Fiction Transcendence to be above all cardinality and dimensionality" on the other hand is only vacuously true, as most authors would simply not know about any such things and thus not be capable of intending anything regarding them either way.
This is to say that it is technically true, but in the same way the statement "No phones are turned on" is true when directed towards a room with no phones in it: There are no phones there, so consequently there can be no phones that are turned on, either. Likewise, it is true in the same way the statement "They didn't intend for this house to be yellow" is true when directed towards a person who had no knowledge of the existence of said house: They didn't know about the house at all, so consequently they couldn't have intended for it to be yellow, either. Needless to say, vacuously true statements are nonsense.
As such, if the intentions of the author are to be accounted for by the Tiering System in an honest and consistent way, the division when it comes to tiers above High 3-A would not hinge on whether the author intended for the feat to correspond to a specific tier within it (As intent requires prior knowledge, which in this case is nonexistent), but rather on whether they intended it to be a showing of transcendent power at all.
Counterpoint 6: It would seem that tiering qualitative superiorities as they truly are is untenable, as extraordinary claims require extraordinary evidence, and simply seeing something as literally non-existing is far too little evidence to infer such vast power from.
The Sagan standard is certainly a good aphorism. When repeated ad-nauseum, however, it ceases to be a useful guide for thought and becomes little more than a platitude. As a small reminder of what "evidence" means:
As such, if evidence is what is required, then refer to the previous two sections of this post, both of which provide plenty of facts and information backing up their claims.
Counterpoint 7: It would seem that tiering qualitative superiorities as they truly are is unneeded, as fiction does not have to obey any rules, and therefore rating qualitative superiorities as equivalent to quantitative superiorities is no issue. We cannot enforce our views on fiction.
This objection is a quite weak one, since it is tantamount to claiming that, because fiction can break any logical rules it likes, we must therefore assume that it is always breaking a logical rule when tiering qualitative superiorities. It doesn't take much thinking to realize that this is nothing but claptrap: Verses that break rules should, by definition, constitute exceptions, and not rules. The rule-of-thumb is to always follow logic unless otherwise instructed that it does not apply to a given situation, as is evident from how tiering in general is constructed.
This objection, just like Objection 5, is a variation of Objection 4, and it is a part of a larger class of arguments that can be summarized as such: "If the majority of fiction does not treat something as X, we do not treat it as X, either." For example, in the real world, acceleration results in increased kinetic energy and thus anything that goes fast enough would also exert a lot of force. However, fiction almost universally disregards this and treats speed and strength as separate attributes, and so, we disregard it too. A line of reasoning that one could try to take, then, is that the same would apply to qualitative superiorities: "Fiction never treats qualitative superiorities as so powerful, therefore we should not, either."
As seen above, the opposition often likes to use Carl Sagan's famous saying of "Extraordinary claims require extraordinary evidence" in debates about this topic, so I will take the liberty to use another one of his quotes: Absence of evidence is not evidence of absence. Or as I like to put it: Ambiguity is not negation.
In essence, when a verse depicts a character throwing a steel ball at 58% of the Speed of Light with no significant environmental damage, what we have is evidence of the absence of a realistic treatment of kinetic energy. When a verse depicts a character throwing a punch at Mach 629 with no significant environmental damage, what we have is evidence of the absence of a realistic treatment of kinetic energy. When a verse depicts the Big Bang as a literal explosion, what we have is evidence of the absence of a realistic portrayal of the Big Bang. When a verse breaks any of our rules on Black Hole Feats, what we have is evidence of the absence of a realistic portrayal of black holes.
And when this evidence of absence starts to pile up and become a trend throughout the overwhelming majority of fiction, we adopt it as the method we use for tiering said fiction.
So, in such cases, we have things that serve as direct, positive evidence of the absence of a certain phenomenon (In this case, realistic KE, big bangs and black holes). Such evidence of absence, for obvious reasons, is nowhere to be seen in displays of qualitative superiority in fiction: There is nothing in any case of Reality-Fiction Transcendence in any verse that actually directly disproves the notion that it is above any dimensionality or cardinality. What we have, in these cases, is simply silence on the part of the verse, and to take this silence as positive evidence that this notion is absent from the verse is to conflate absence of evidence with evidence of absence.
Of course, I recognize how ridiculously easy it is to twist my words here, intentionally or not, so allow me to clarify: This is not to say that we should accept things without any evidence. What it is saying, however, is that mere ambiguity (Absence of evidence) is not the same as outright negation (Evidence of absence). Negation prevents a claim from ever being true, while ambiguity allows for the possibility that it might be either true or false. Of course, this possibility is completely useless left as is; it is up to something to collapse it into either certain truth or certain falsehood. But in this case, the certain truth of the claim "Qualitative superiorities are superior to all quantitative superiorities" has already been proven in-depth.
Counterpoint 8: It would seem that tiering qualitative superiorities as they truly are is untenable, as it makes far too many assumptions regarding how they work in specific verses
This is incorrect. For example, the argumentation involving Reality-Fiction Transcendences only assumes that the higher layer sees the lower layer as "unreality/nothing," which is already an assumption that the wiki explicitly makes. Everything else simply follows from it logically, and denying these consequences just causes the Tiering System to devolve into incoherence.
Overall, this objection just attempts to reduce the argumentation above by accusing it of being speculation, or conjecture. Saying it is just "speculation," though, is the same thing as saying that infinity being above finite things is speculation. This is obvious nonsense, so: No, it is not speculative in the slightest.
Counterpoint 9: It would seem that tiering qualitative superiorities as they truly are is untenable, as this would involve rating them as above things that are not explicitly mentioned in the verse's text.
This objection makes use of what I like to call "Wookiepedia logic," which can be summarized as follows: "If it is not explicitly mentioned in the text, it does not exist, and therefore shouldn't be taken into account." A quick look at the wiki's own standards will quickly show that this kind of logic is not consistently applied, if at all. For example, no verse explicitly mentions that a spacetime continuum is made up of uncountably infinite "snapshots" of the 3-dimensional universe. In fact, only very few verses explicitly mention cardinals or mathematical infinities at all, yet feats of full timeline destruction are Low 2-C, for all verses, based on reasoning that involves them.
Why do we treat a spacetime continuum as such, then? Because that is just how a temporal dimension works, and, more generally, how a continuum works. For a more down-to-earth case, consider the fact that most verses don't explicitly say that H2O is water, yet if a character was reliably stated (And only stated) to be able to magically manipulate H2O, they'd obviously be listed as having Water Manipulation.
So, the text of a verse is not, never was, and never should be, the sole point of reference taken when evaluating that verse's tiers. It is the primary point of reference, certainly, but standing right beneath it are reason and critical thinking, both of which include the ability to make inferences and apply them when needed. Remove that, and you have a body of thought defined by its strange and ultimately senseless refusal to allow people to use their brains for anything.
And before anyone tries to argue that: No, the reasoning given above doesn't imply that we should start allowing cross-scaling with other verses. If one attempts to argue that it does, they would have to argue that this implication is present in the current Tiering System as well, due to the examples I've shown. So, either way, it is not something that uniquely follows from my argumentation.
Objections 4-9 are all variations of each other, and as such the responses to them are more tightly bound than the responses to other counterpoints listed in this section. It is expected that the majority of counterpoints the reader formulates to one of those six will ultimately find themselves answered in some, or all, of the other six. Therefore it is advised that special attention be given to them
Counterpoint 10: It would seem that tiering qualitative superiorities as they truly are is unneeded, as the Tiering System's nature as a constructed framework makes its borders inherently arbitrary, and therefore all the matters is that whatever system is choosen remains consistent with itself.
This, in particular, is quite an absurd position to take here, as it essentially boils down to "We can literally do whatever we like as long as it follows some internal logic." However, this is absent here: The fact that I could so thoroughly demonstrate why and how the Tiering System's current treatment of qualitative superiorities leads to a number of absurdities (And is therefore not self-consistent) should already serve as proof that this objection is nothing more than vapid absurdism used to defend positions that are, otherwise, indefensible.
Of course, the position is actually correct if we reduce it to "If we are made to choose between two equally (ina)accurate systems, the decision is ultimately arbitrary." But the idea that the present Tiering System is no more accurate than any other possible alternatives has already been sufficiently demonstrated as simply untrue.
Counterpoint 11: It would seem that tiering qualitative superiorities as they truly are is untenable, as it would force us to rate any statement describing something as "Beyond reality" and similar at Tier 0.
That is untrue. "Beyond reality," even taken to mean superiority, does not necessarily imply a qualitative superiority. This is due to the fact that "reality" is often contextually used to refer to a single universe or the like. For example, in most fiction where the multiverse is a central theme, each universe will be referred to as "a reality." As such, the term would not be referring to "The quality of realness" but "A single spacetime continuum," and even a difference of one dimension is sufficient to be superior to a space-time continuum (As a 4-D spacetime can be embedded as an infinitesimal portion of a 5-D realm, just as a 2-D universe can be an infinitesimal portion of a 3-D universe).
However, if there is evidence that, by "Beyond reality," what is meant is "Beyond the quality of realness" itself, then obviously such a superiority would be a qualitative one, for the same reason something that is "Below the quality of realness" (And thus so lesser as to be nonexistent) would have a qualitative inferiority, and thus be inferior to all dimensionality, even 0-dimensionality, as demonstrated above.
Counterpoint 12: It would seem that tiering Reality-Fiction Transcendences as equal to dimensional jumps is a necessary compromise, as although treating them as above all quantitative superiorities is fully accurate, it is also fully accurate to treat them as not conferring any increase in power at all, as we living in the real world have a Reality-Fiction Trancendence over fictional characters, and yet no one would say Mike Tyson can beat Superman. Thus a middle ground is needed.
The failure of this objection is a fairly simple matter: If we are to apply the logic of Reality-Fiction Transcendences to the real world, then Mike Tyson is indeed more powerful than Superman, as he is real and Superman is not. To say otherwise can only be a valid position if one takes "power" to refer exclusively to acts of strength showcased in one's respective "world," and by this metric, Superman is indeed more powerful than Mike Tyson. It is not at all obvious why this would be a valid framework to pick when analyzing fiction, however, especially when any and all arguments about Reality-Fiction Transcendences have, as a starting point, the trust that the verse being discussed does portray the Reality-Fiction Interaction as a showing of transcendent power. If it doesn't, we'd indeed not tier them at all.
Thus in order to tier such verses it is necessary to, from the start, abide by the notion that a superiority is conferred by a R-F Trancendence. Under those lenses, if Superman were to be magically made real and put to fight against Mike Tyson, then obviously he would win. However that would only be because Superman was made real and thus allowed to have a level of existence which he normally lacks, and thus we might call this an amplification of his power.
Counterpoint 13: It would seem that tiering Reality-Fiction Transcendences as equal to dimensional jumps is a necessary compromise, as there are verses that conflate the two
Verses that conflate the two kinds of superiority are easily evaluated by simply tiering them based on which of the two the transcendent thing in question is most closely aligned with.
For example, if Realm X is described as "a higher dimension" or as "higher-dimensional," yet doesn't display any of the actual properties expected of a genuine higher-dimensional space, while also displaying all of the properties expected of a Reality-Fiction Transcendence (E.g. Seeing lesser things as literally lacking existence, and/or being "more real" than them), then it would be tiered as a qualitative superiority.
On the other hand, if Realm X is stated to be a higher-dimensional space and is described in ways analogous to a Reality-Fiction Transcendence, while otherwise behaving exactly as a higher-dimensional space would be expected to (E.g. The difference between it and the lower realms is demonstrated as a physical one), then it would be tiered as a quantitative superiority.
Counterpoint 14: It would seem that dimensional jumps are qualitative superiorities, as a cube is made bigger than a square by the fact it has volume, while the square only has area. Therefore, the difference between both is one of quality, not of quantity.
This is again an equivocation. The difference between a cube and a square is such that the square has 0 volume, while the cube has infinite area. Volume and Area are quantities, and as such the difference between the two is by definition a quantitative one. Furthermore, a cube has infinite area due to the fact it is formed by the sum of infinite squares, which once again demonstrates the strictly quantitative nature of dimensionalities.
Counterpoint 15: It would seem that the argument for why qualitative superiorities are superior to all quantitative superiorities applies to dimensional jumps, as a square has 0 volume, and one cannot obtain something non-zero by adding together things with 0 value. As such it follows that a dimensional difference, itself a quantitative superiority, is above all quantitative superiorities, which is a contradiction. Therefore the argument is incoherent.
The mistake of this objection is that it conflates the 0 that represents an absence of things with the 0 that represents the lack of extension in some n-dimensional space. The first type of "0" we call the empty set, as above explained, and the second type we call a "null set." As the latter still applies to sets that are non-empty (E.g. A square is a null set in 3-dimensional space, as it lacks volume, but it still has elements and is thus not empty), the principles behind operations on the empty set do not apply to it.
Counterpoint 16: It would seem that Ultima is cringe and therefore the argument is false a priori
Well, shit, man. Can't argue against that.
So, all-in-all: What we have is a bizarre, Frankenstein-like Tiering System that obsesses far too much over mathematics and likewise attempts to reduce everything to a very specific mathematical framework while, ironically, disregarding its most elementary principles as needed. It openly makes direct false equivalences and labels any argument that contests them as "fallacious" while, in truth, committing far more fallacies than it avoids and creating gross inconsistencies both with itself and with the basis it claims to utilize.
Aftermath
Now, I've repeatedly thrown some rather harsh critiques at the Tiering System in the above sections, and following all of that, some may wonder what I actually even have to offer beyond pure criticism. Surely, at least what the wiki has right now is as good as it gets, yes? I find that the answer to that is a resounding "No." There are, in fact, objectively better alternatives.The first step to constructing a better Tiering System would be to, of course, entirely separate qualitative superiorities and quantitative superiorities, instead of trying to shoehorn one into the other as is currently done. As made clear by now, qualitative superiorities are necessarily above any and all quantitative superiorities, and as such a tier for them would be above the entirety of the current Tiering System.
As said before, what this means, bluntly speaking, is that anyone with an actual qualitative transcendence (E.g. Reality-Fiction Transcendences, transcendence over dimensionality, etc) over lesser realms would, in the current arrangement of the tiers, be Tier 0, and high into it at that. This is an obvious issue. Why? Because there are a lot of verses who have not just characters with qualitative superiority over lesser things, but also hierarchies of qualitative superiority, and things beyond these hierarchies, and things beyond those things, too. If we shoved such a wildly variable array of characters into a single tier, we would fall into the same issue that caused 1-A to be divided into four tiers all these years ago.
So, would the solution be to split 0, then? We could, but I think that's stupid. The Tiering System in general is built with the idea of having a single endpoint in mind. That's why the tiers count backwards from 10, instead of forwards. Splitting this endpoint into high and low-ends defeats the whole purpose of this, so I don't believe this would be the best course of action, no.
Ontop of that, there are more characters whose high tiers derive from metaphysics than characters whose high tiers derive from mathematics, and this discrepancy basically doubles when entering 1-A and above. As such, if we were to simply upgrade all qualitative superiorities to Tier 0, it would result in there being more Tier 0s than there are 1-As, High 1-As and Low 1-As. And I don't think I'm the only one who sees the logistical problems with that.
Furthermore, there is already a tier that is listed as an entirely separate category from the rest of Tier 1: 1-A. So with that in mind, what would my suggestion, be, pray tell? Well, in short: Make 1-A the tier for qualitative superiorities, and kick all quantitative superiorities down to the rest of Tier 1.
That is to say: Dimensional jumps and differences in cardinality would simply all peak at High 1-B, with perhaps a High 1-B+ tier for infinite-dimensional spaces that are larger than countably infinite dimensions. Meanwhile, strictly qualitative superiorities, such as Reality-Fiction Transcendences, transcendences over dimensionality, and etc. would land at 1-A.
Down under, something similar would happen: For qualitative inferiorities, a new tier below 11-C would need to be created. So, this would be for characters that are fiction even to a 3-D reality, as well as beings who are "nonexistent" in a way that indicates inferiority over other things. Hypothetically, a character who is inferor to dimensionality, rather than superior to it, would also fall under this tier.
1-A+ and High 1-A would stay effectively the same. The former would be for an infinite hierarchy of qualitative superiorities. The latter would be for characters who are above the "quality" defining the lower hierarchy altogether, while still working on their own, higher form of qualitative superiority. For example, in Marvel Comics, the omniverse has an infinite hierarchy of dreams-within-dreams in itself, and above that, then, is the Outside, which transcends all forms of reality and dream and yet nevertheless still has its own hierarchy that works on something else entirely.
And so, I am done.
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