High 1-A Description Overhaul: The Inaccessible Cardinal Debacle

[FinePoint]

Tl;dr: The current description has too much distracting and confusing information, and needs to be presented in a way that's clearer and easier to digest. Draft proposal's at the bottom of the post.​

It seems like most people agree with there being some sort of problem with the current description which can be improved, but how exactly we do that is still being discussed.

The current description is a problem.​

First off, before anybody gets any sort of emotions about this, I'm not suggesting any change to the way we define the tiers or how we qualify them. You may remember me as the person who underwent the project to clean up and organize the rules pages, which were a horrific wall of completely user unfriendly bullets points before I got to them, and my goal here is actually really similar. I simply want to make the description text itself more clear and digestible without removing any of its meaning, as well as fixing some minor errors and/or questionable word choices.

Full disclaimer: I'm both a business major and a author, and this is basically going to be a nerdy deep-dive into everything wrong with the current description's ability to be understood, down to a very technical level. If you just want to hear the actual proposal which comes from it then skip down the heading titled "Solutions."

This is what the current description for High 1-A states:

High 1-A: High Outerverse level​

Characters or objects that can affect structures that are larger than what the logical framework defining 1-A and below can allow, and as such exceed any possible number of levels contained in the previous tiers, including an infinite or uncountably infinite number. Practically speaking, this would be something completely unreachable to any 1-A hierarchies.

A concrete example of such a structure would be an inaccessible cardinal, which in simple terms is a number so large that it cannot be reached ("accessed") by smaller numbers, and as such has to be "assumed" to exist in order to be made sense of or defined in a formal context (Unlike the standard aleph numbers, which can be straightforwardly put together using the building blocks of set theory). Even just the amount of infinite cardinals between the first inaccessible cardinal and aleph-2 (Which defines 1-A) is greater than cardinals such as aleph-0, aleph-1, aleph-2, aleph-3, etc., and even many aleph numbers whose index is an infinite ordinal.. More information on the concept is available on this page.

Now, there's nothing inherently wrong with most of this on an objective informational level, but there is a huge problem on the level of it being readable and understandable by a general audience. (There is, however, a double period after 'ordinal' for no reason, and even if the rest of this proposal is completely rejected, this should obviously be corrected.)

Everywhere I go and Tier 1 is mentioned, tons of users, even seasoned staff, will actively avoid the discussion on the explicitly stated basis that High 1-A and/or debates surrounding it are complicated, confusing, or otherwise difficult to follow. Instead, many people's first instinct is to only call on specific people they deem "experts" on the topic, and the sheer number of people who seem to misinterpret or not understand the tier is a testament to how poorly it's explained.

So what makes it poorly explained? To answer that, I sort of need to step into the marketing knowledge I've accrued during my college profession. (Only 1 more semester to go, by the way!) People often mistake marketing for advertising, but it refers to literally everything done to make a product appealing to and readily accessible to consumers. I know we don't sell anything, technically, but our product is information about the abilities of fictional characters, even if it's free. From that perspective, this description completely falls flat on some very important marketing and communications principles, which explains why the information is so often poorly received or understood.

What specifically is wrong with it?​

• Semantic Noise - In communications, there's something called "noise" - which refers to anything which makes it difficult for a listener of a message to either hear or understand it. One of these types of noise is semantic noise, things with the word choice and structure of the message itself which make it more difficult to understand. Some of this is present, and I'll get to the specifics later.
• Information Overload - Our brains have a lot of limitations, especially when it comes to learning new information. One of these factors is your short term memory. The human brain can literally only hold a certain amount of information at the same time before information starts to be lost and not committed to long-term memory. There's a lot of complicated and ultimately unneeded information shoved into a very small space in the description, which results in readers being unable to properly parse it all at once. Again, I'll get to the specifics later.
• Lack of Accessibility - Different people have different levels of knowledge, and different learning styles, and different ways they conceptualize information. For basic and/or grounded concepts, like those in the lower tiers, this isn't much of a problem. In fact, the lower tiers already have a built-in method of conceptualizing the information in multiple ways in the sense that they include very easy to visualize examples in their names, like a wall, or a mountain, or a solar system, which makes it even easier. For very complicated topics, it's important to have multiple ways to present the information. Firstly, there's zero visual aids, but even without that, there's multiple ways to explain something even just in text, but the tiering system, at least at High 1-A, only makes one attempt to do that, and the method it uses is terrible (more on that later).

The Inaccessible Cardinals Situation​

To me, one of the worst offenses of the current description is the terrible information overload, and the main offender of this is as you might've guessed from the title of the thread: the paragraph about cardinal numbers.

A concrete example of such a structure would be an inaccessible cardinal, which in simple terms is a number so large that it cannot be reached ("accessed") by smaller numbers, and as such has to be "assumed" to exist in order to be made sense of or defined in a formal context (Unlike the standard aleph numbers, which can be straightforwardly put together using the building blocks of set theory). Even just the amount of infinite cardinals between the first inaccessible cardinal and aleph-2 (Which defines 1-A) is greater than cardinals such as aleph-0, aleph-1, aleph-2, aleph-3, etc., and even many aleph numbers whose index is an infinite ordinal.. More information on the concept is available on this page.

This example makes up more than half of the description, and contains an absolute load of irrelevant information and very technical and complicated phrases and concepts which completely distract from the premise of the tier, which in all reality, is actually very simple. It throws an extremely complicated and hypothetical field of mathematics suddenly into the mix, linking to an entire Wikipedia page full of even more complex topics, puts multiple normal words in quotes without explaining why, brings up discussion of previous concepts, throws a bunch of numbers and more undefined terms like 'index' into the mix, then finally ends by linking a page which claims to be an explanation of the tiering system as a whole, but instead spends its entire length taking a deep-dive entirely into Set Theory, and then links even more things, including up to half an hour of videos.

To put it simply: by the time any reader makes it to the end of this paragraph, let alone all the supplementary material, their brain has probably already completely thrown out the actual relevant information about the tier and what actually defines it, in addition to now being confused about this esoteric mathematical concept as well.

While we're on the topic of this paragraph, let's address how it actually supplies a misconception about the tiering system that I keep seeing staff correct people on, although evidently not realizing that the misconception is literally perpetuated by the language of this paragraph. In short, it's this:

A concrete example of such a structure would be an inaccessible cardinal

First of all, this entire sentence in its current language is technically just not true.
We're talking about a High 1-A structure here, as defined by our tiering system, which is a character or structure which can affect something qualitatively superior to the entire logical framework and/or the boundaries of what 1-A includes.
If you can't see the obvious, let me lay it out: the concept itself of inaccessible cardinals is not even a structure or character, let alone one which fits the criteria of High 1-A.
What this sentence is trying to say is that a structure would be High 1-A if it contained a number of dimension which could only be mathematically described with inaccessible cardinals. A number itself, even a really big hypothetical one, means absolutely nothing in a vacuum, and absolutely does not grant anything a tier, and so alone is absolutely not an example of a High 1-A structure.

Second of all, if it were an example, it most certainly wouldn't be a "concrete" one. The following is the definition of concrete as it's used in this context:

existing in a material or physical form; not abstract.

Inaccessible cardinals cannot be proven using foundational principles of mathematics, and in fact exist using a logic separate from Set Theory itself which they're derived from, and rely on an added assumption not normally present. Even "imaginary numbers" are more "concrete" than inaccessible cardinals since they're actually linked to real observable trends and the math related to them. Inaccessible cardinals are a theoretical and abstract mathematical concept, and doesn't even indirectly have any real physical systems or patterns related to it. It is, in its literal and most basic form, just a thought experiment: "Yo, know how we made all those layers of infinities in Set Theory? What if there was another one but it was like so big it couldn't even be reached by any of that, wouldn't that be sick?" You can argue it's interesting, applicable in some specific hypothetical concept like ours, or whatever, but you most definitely can't argue that it's a "concrete example" of anything as per this definition.

Okay, but what about the version of "concrete" that's literally just a synonym for "specific".

That's probably what they meant, and I knew that, but I baited you and went on the previous rant to make a point: we want to avoid semantic confusion. When we're presenting information, especially complicated information, we need to be very careful with the words we use so that we don't give anyone the wrong idea. Besides, it's not specific either. It's literally an entire branch of abstract mathematics, and isn't even applied to anything in this paragraph, so it's as vague as can be as well.

The Primary Description​

Earlier I implied that other than the massive distraction of the inaccessible cardinals paragraph, there were some issues with the base description as well, so let's get into that. None of it is nearly as bad as the previous thing, but I think it serves us well to be extra picky on a topic that's caused so much confusion in the community.

The first problem is that most of this explanation is one long sentence with a lot of complicated words. Earlier I mentioned how our limited short-term memory can make it difficult to hold on to earlier information when reading something complex. I know I'm guilty of it in most of my writing, and love long sentences with many commas, but this isn't a prose page, this is an ordered list with information which should be relatively concise. There's a lot of ways to address this issue and make the information more digestible, and the first one is to simply use less complex sentence structure, and break the information into more separate ideas and/or sentences.

Let's break down the first sentence and second into the separate statements they actually hold. Each primary bullet point is an independent clause. Each secondary bullet point is a dependent clause. Each tertiary bullet point is a question raised either by assuming knowledge of the reader or being vague.

Characters or objects that can affect structures that are larger than what the logical framework defining 1-A and below can allow, and as such exceed any possible number of levels contained in the previous tiers, including an infinite or uncountably infinite number.

• Characters or objects that can affect structures
  • that are larger than the logical framework defining 1-A and below can allow
    • What does it mean to be larger than a logical framework?
    • What are the logical framework of all previous tiers?
• and as such exceed any possible number of levels
  • contained in the previous tiers
    • What does a "level" mean in this context?
    • What are the possible number of levels in the previous tiers?
  • including an infinite or uncountably infinite number
    • What's the difference between a countable or uncountable infinity?

Practically speaking, this would be something completely unreachable to any 1-A hierarchies.

• This would be something completely unreachable
  • practically speaking
    • Practical for what?
  • to any 1-A hierarchies
    • What does a hierarchy mean in this context?
    • What are all the 1-A hierarchies?

There's generally four types of sentence complexity. Simple (1 independent clause), compound (2 independent clauses), complex (At least 1 of each type of clause), and compound-complex (at least two independent clauses and at least one dependent clause).

The first sentence of the description has two independent clauses and three dependent clauses. This not only makes it a compound-complex sentence, but one that's well above the baseline criteria. In addition to the use of vague or technical terms, this makes it very hard to digest for the average reader. The second sentence has 1 independent clause and 2 dependent clauses, making it only a complex sentence, and is generally far easier to understand.

Now, obviously we don't need to talk like cavemen, and compound, complex, or even compound-complex sentences have a clear and beneficial purpose in language, especially in information. However, given the complexity of the topics being discussed, its role as an informational tool for a general audience, and how much the content itself already stresses our short term memory, the structure would benefit greatly from being broken down into more but simpler sentences with more clarification. Ironically, this will make it much longer, but easier to digest by allowing the reader to process less information at once.

Accessibility​

When we think of accessibility, we tend to think of accommodating for disabilities or unique circumstances, but the realm of accessibility extends to normal differences between all people, and thus benefits everyone. Culture, status, profession, interests, existing knowledge, vocabulary, region, language, preference, learning style, and many other things can change how accessible content is to a general audience. Many of these things are mitigated by the focused nature of our site. We're a mostly English platform appealing specifically to people interested in categorizing the powers and abilities of fictional characters and who have access to the internet. In addition, we assume that they have indeed read the rest of the tiers in this instance. However, even someone who has read the entire tiering system will often find themselves having to repeatedly scroll back up for reminders simply due to the extent to which the High 1-A description assumes a memorization of previous tiers. Some assumption is expected, but it shouldn't be so much that the reader won't possess the knowledge just from knowing the gist- we don't want them having to literally scroll back up and find specific quotes and definitions just to read the paragraph they're on.

As previously pointed out, the current description makes some pretty large assumptions of knowledge in the first section, and so many in the cardinal section that I'm not even going to bother analyzing it. Most notably, it makes very specific reference to certain technical terms and previous tiers, and to make it worse, it's inconsistent. "Logical framework", "levels", "hierarchies" are all words which mean the same thing in this context- we're talking about the bounds of the previous tiers: the minimum, maximum, and in-betweens, but the use of three different words, (some of them sounding technical) creates a needless implication that the subject is more complicated than it really is, and puts more stress on the reader in terms of processing each term and second-guessing if they missed something earlier which makes "hierarchies" different than "levels". Some of the vocabulary is just needlessly thesaurus sounding for no reason. Why would we say "logical framework" instead of simply saying "boundaries"? It makes it far less intuitive and again implies it's part of some larger concept we need to know.

In general, in the tiering system, I see a bias towards using mathematical terms where it's not needed. Math is one way for higher tiers to be reached, but it's not the only way, in fact I would argue it's not even the most common. The actual definitions of the tier reflect this, but the word choice and framing sort of implies differently, which I've personally seen lead to misconceptions in the past that math is the only way to reach these tiers, and outright rejecting the possibility of reaching them by any other means. If we have a concept which is general, then our wording should be general too.

As for different mediums, as mentioned previously, even while only using text there's many ways to reword information in a way that can stick for certain people who don't understand the first way. The most obvious way, and what seems very popular and effective in the previous tiers are examples. If you want to put it in terms of math, this is where you'd do it. The current description tries to do so, but it does it in a way that actually makes it more confusing rather than less so.

Solutions​

So, with all the context and reasoning laid out for the fact that there is an issue, how do we fix it? The following is a general solution for each problem explained earlier.

Description:​

• Break up the description into more but simpler sentences - This will make the concepts easier to mentally follow and digest, allowing it to more effectively be transferred from short term to long term memory.
• Add reminders of previous information as needed - This will reduce the amount of assumed knowledge baked into the explanation, which will make it more convenient to read and reduce the need to reread all of the previous tiers.
• Be consistent with the terminology used - This will reduce the appearance of complexity and make readers more confident that they understand the information, as opposed to questioning if they're missing an important distinction between two words which doesn't actually exist.
• Use vocabulary which is general and common if possible - This will remove the current bias towards technical subjects and mathematics which the current description has, better reflecting the actual definition of High 1-A not necessarily requiring any application of mathematical theories to reach.

Examples/Cardinals Section:​

• Fix the inaccessible cardinals example to be accurate and actually apply the concept into practice - The current description's current wording implies and reinforces a common misconception that an "inaccessible cardinal" itself is High 1-A even without context, which doesn't actually make any sense.
• Vastly simplify the example using inaccessible cardinals and save any technical details for the separate page already made for them - The sheer length and complexity of the paragraph is hard to understand on its own, but also dramatically subtracts and confuses from the concept it's attempting to be an example for.
• Add a second example using non-mathematical concepts - The tier is not only reachable by mathematics, and it would be helpful and make it seem less intimidating by including an example which doesn't require an understanding of an obscure mathematical theory.

First Draft Proposal​

Now that we've established that there's problems with the current description, what they are, and a general strategy for fixing them, it's finally time for a first draft of a possible replacement. I'm more than willing to adjust and negotiate this, so please don't assume that I'm hard-set on proposing we replace it with exactly what I've written below, it's just a first draft to give us a springboard towards the discussion on what the replacement would actually be if this is accepted. It also includes some minor grammar changes. Without further ado, my first draft:

---

[Under construction]

 

[FinePoint]

This took me three and a half hours, by the way.

 

[KLOL506]

@Ultima_Reality @Executor_N0 @DontTalkDT @Elizhaa

 

[IdiosyncraticLawyer]

Tl;dr: The current description has too much distracting and confusing information, and needs to be presented in a way that's clearer and easier to digest. Draft proposal's at the bottom of the post.​

The current description is a problem.​

First off, before anybody gets any sort of emotions about this, I'm not suggesting any change to the way we define the tiers or how we qualify them. You may remember me as the person who underwent the project to clean up and organize the rules pages, which were a horrific wall of completely user unfriendly bullets points before I got to them, and my goal here is actually really similar. I simply want to make the description text itself more clear and digestible without removing any of its meaning, as well as fixing some minor errors and/or questionable word choices.

Full disclaimer: I'm both a business major and a author, and this is basically going to be a nerdy deep-dive into everything wrong with the current description's ability to be understood, down to a very technical level. If you just want to hear the actual proposal which comes from it then skip down the heading titled "Solutions."

This is what the current description for High 1-A states:

Now, there's nothing inherently wrong with most of this on an objective informational level, but there is a huge problem on the level of it being readable and understandable by a general audience. (There is, however, a double period after 'ordinal' for no reason, and even if the rest of this proposal is completely rejected, this should obviously be corrected.)

Everywhere I go and Tier 1 is mentioned, tons of users, even seasoned staff, will actively avoid the discussion on the explicitly stated basis that High 1-A and/or debates surrounding it are complicated, confusing, or otherwise difficult to follow. Instead, many people's first instinct is to only call on specific people they deem "experts" on the topic, and the sheer number of people who seem to misinterpret or not understand the tier is a testament to how poorly it's explained.

So what makes it poorly explained? To answer that, I sort of need to step into the marketing knowledge I've accrued during my college profession. (Only 1 more semester to go, by the way!) People often mistake marketing for advertising, but it refers to literally everything done to make a product appealing to and readily accessible to consumers. I know we don't sell anything, technically, but our product is information about the abilities of fictional characters, even if it's free. From that perspective, this description completely falls flat on some very important marketing and communications principles, which explains why the information is so often poorly received or understood.

What specifically is wrong with it?​

• Semantic Noise - In communications, there's something called "noise" - which refers to anything which makes it difficult for a listener of a message to either hear or understand it. One of these types of noise is semantic noise, things with the word choice and structure of the message itself which make it more difficult to understand. Some of this is present, and I'll get to the specifics later.
• Information Overload - Our brains have a lot of limitations, especially when it comes to learning new information. One of these factors is your short term memory. The human brain can literally only hold a certain amount of information at the same time before information starts to be lost and not committed to long-term memory. There's a lot of complicated and ultimately unneeded information shoved into a very small space in the description, which results in readers being unable to properly parse it all at once. Again, I'll get to the specifics later.
• Lack of Accessibility - Different people have different levels of knowledge, and different learning styles, and different ways they conceptualize information. For basic and/or grounded concepts, like those in the lower tiers, this isn't much of a problem. In fact, the lower tiers already have a built-in method of conceptualizing the information in multiple ways in the sense that they include very easy to visualize examples in their names, like a wall, or a mountain, or a solar system, which makes it even easier. For very complicated topics, it's important to have multiple ways to present the information. Firstly, there's zero visual aids, but even without that, there's multiple ways to explain something even just in text, but the tiering system, at least at High 1-A, only makes one attempt to do that, and the method it uses is terrible (more on that later).

The Inaccessible Cardinals Situation​

To me, one of the worst offenses of the current description is the terrible information overload, and the main offender of this is as you might've guessed from the title of the thread: the paragraph about cardinal numbers.

This example makes up more than half of the description, and contains an absolute load of irrelevant information and very technical and complicated phrases and concepts which completely distract from the premise of the tier, which in all reality, is actually very simple. It throws an extremely complicated and hypothetical field of mathematics suddenly into the mix, linking to an entire Wikipedia page full of even more complex topics, puts multiple normal words in quotes without explaining why, brings up discussion of previous concepts, throws a bunch of numbers and more undefined terms like 'index' into the mix, then finally ends by linking a page which claims to be an explanation of the tiering system as a whole, but instead spends its entire length taking a deep-dive entirely into Set Theory, and then links even more things, including up to half an hour of videos.

To put it simply: by the time any reader makes it to the end of this paragraph, let alone all the supplementary material, their brain has probably already completely thrown out the actual relevant information about the tier and what actually defines it, in addition to now being confused about this esoteric mathematical concept as well.

While we're on the topic of this paragraph, let's address how it actually supplies a misconception about the tiering system that I keep seeing staff correct people on, although evidently not realizing that the misconception is literally perpetuated by the language of this paragraph. In short, it's this:

First of all, this entire sentence in its current language is technically just not true.
We're talking about a High 1-A structure here, as defined by our tiering system, which is a character or structure which can affect something qualitatively superior to 1-A+.
If you can't see the obvious, let me lay it out: the concept itself of inaccessible cardinals is not even a structure or character, let alone one which fits the criteria of High 1-A.
What this sentence is trying to say is that a structure would be High 1-A if it was qualitatively superior in layers to a normal dimension in a way which could only be mathematically described with inaccessible cardinals. A number itself, even a really big hypothetical one, means absolutely nothing in a vacuum, and absolutely does not grant anything a tier, and so alone is absolutely not an example of a High 1-A structure.

Second of all, if it were an example, it most certainly wouldn't be a "concrete" one. The following is the definition of concrete as it's used in this context:

Inaccessible cardinals cannot be proven using foundational principles of mathematics, and in fact exist using a logic separate from Set Theory itself which they're derived from, and rely on an added assumption not normally present. Even "imaginary numbers" are more "concrete" than inaccessible cardinals since they're actually linked to real observable trends and the math related to them. Inaccessible cardinals are a theoretical and abstract mathematical concept, and doesn't even indirectly have any real physical systems or patterns related to it. It is, in its literal and most basic form, just a thought experiment: "Yo, know how we made all those layers of infinities in Set Theory? What if there was another one but it was like so big it couldn't even be reached by any of that, wouldn't that be sick?" You can argue it's interesting, applicable in some specific hypothetical concept like ours, or whatever, but you most definitely can't argue that it's a "concrete example" of anything as per this definition.

That's probably what they meant, and I knew that, but I baited you and went on the previous rant to make a point: we want to avoid semantic confusion. When we're presenting information, especially complicated information, we need to be very careful with the words we use so that we don't give anyone the wrong idea. Besides, it's not specific either. It's literally an entire branch of abstract mathematics, and isn't even applied to anything in this paragraph, so it's as vague as can be as well.

The Primary Description​

Earlier I implied that other than the massive distraction of the inaccessible cardinals paragraph, there were some issues with the base description as well, so let's get into that. None of it is nearly as bad as the previous thing, but I think it serves us well to be extra picky on a topic that's caused so much confusion in the community.

The first problem is that most of this explanation is one long sentence with a lot of complicated words. Earlier I mentioned how our limited short-term memory can make it difficult to hold on to earlier information when reading something complex. I know I'm guilty of it in most of my writing, and love long sentences with many commas, but this isn't a prose page, this is an ordered list with information which should be relatively concise. There's a lot of ways to address this issue and make the information more digestible, and the first one is to simply use less complex sentence structure, and break the information into more separate ideas and/or sentences.

Let's break down the first sentence and second into the separate statements they actually hold. Each primary bullet point is an independent clause. Each secondary bullet point is a dependent clause. Each tertiary bullet point is a question raised either by assuming knowledge of the reader or being vague.

• Characters or objects that can affect structures
  • that are larger than the logical framework defining 1-A and below can allow
    • What does it mean to be larger than a logical framework?
    • What are the logical framework of all previous tiers?
• and as such exceed any possible number of levels
  • contained in the previous tiers
    • What does a "level" mean in this context?
    • What are the possible number of levels in the previous tiers?
  • including an infinite or uncountably infinite number
    • What's the difference between a countable or uncountable infinity?

• This would be something completely unreachable
  • practically speaking
    • Practical for what?
  • to any 1-A hierarchies
    • What does a hierarchy mean in this context?
    • What are all the 1-A hierarchies?

There's generally four types of sentence complexity. Simple (1 independent clause), compound (2 independent clauses), complex (At least 1 of each type of clause), and compound-complex (at least two independent clauses and at least one dependent clause).

The first sentence of the description has two independent clauses and three dependent clauses. This not only makes it a compound-complex sentence, but one that's well above the baseline criteria. In addition to the use of vague or technical terms, this makes it very hard to digest for the average reader. The second sentence has 1 independent clause and 2 dependent clauses, making it only a complex sentence, and is generally far easier to understand.

Now, obviously we don't need to talk like cavemen, and compound, complex, or even compound-complex sentences have a clear and beneficial purpose in language, especially in information. However, given the complexity of the topics being discussed, its role as an informational tool for a general audience, and how much the content itself already stresses our short term memory, the structure would benefit greatly from being broken down into more but simpler sentences with more clarification. Ironically, this will make it much longer, but easier to digest by allowing the reader to process less information at once.

Accessibility​

When we think of accessibility, we tend to think of accommodating for disabilities or unique circumstances, but the realm of accessibility extends to normal differences between all people, and thus benefits everyone. Culture, status, profession, interests, existing knowledge, vocabulary, region, language, preference, learning style, and many other things can change how accessible content is to a general audience. Many of these things are mitigated by the focused nature of our site. We're a mostly English platform appealing specifically to people interested in categorizing the powers and abilities of fictional characters and who have access to the internet. In addition, we assume that they have indeed read the rest of the tiers in this instance. However, even someone who has read the entire tiering system will often find themselves having to repeatedly scroll back up for reminders simply due to the extent to which the High 1-A description assumes a memorization of previous tiers. Some assumption is expected, but it shouldn't be so much that the reader won't possess the knowledge just from knowing the gist- we don't want them having to literally scroll back up and find specific quotes and definitions just to read the paragraph they're on.

As previously pointed out, the current description makes some pretty large assumptions of knowledge in the first section, and so many in the cardinal section that I'm not even going to bother analyzing it. Most notably, it makes very specific reference to certain technical terms and previous tiers, and to make it worse, it's inconsistent. "Logical framework", "levels", "hierarchies" are all words which mean the same thing in this context- we're talking about the bounds of the previous tiers: the minimum, maximum, and in-betweens, but the use of three different words, (some of them sounding technical) creates a needless implication that the subject is more complicated than it really is, and puts more stress on the reader in terms of processing each term and second-guessing if they missed something earlier which makes "hierarchies" different than "levels". Some of the vocabulary is just needlessly thesaurus sounding for no reason. Why would we say "logical framework" instead of simply saying "boundaries"? It makes it far less intuitive and again implies it's part of some larger concept we need to know.

In general, in the tiering system, I see a bias towards using mathematical terms where it's not needed. Math is one way for higher tiers to be reached, but it's not the only way, in fact I would argue it's not even the most common. The actual definitions of the tier reflect this, but the word choice and framing sort of implies differently, which I've personally seen lead to misconceptions in the past that math is the only way to reach these tiers, and outright rejecting the possibility of reaching them by any other means. If we have a concept which is general, then our wording should be general too.

As for different mediums, as mentioned previously, even while only using text there's many ways to reword information in a way that can stick for certain people who don't understand the first way. The most obvious way, and what seems very popular and effective in the previous tiers are examples. If you want to put it in terms of math, this is where you'd do it. The current description tries to do so, but it does it in a way that actually makes it more confusing rather than less so.

Solutions​

So, with all the context and reasoning laid out for the fact that there is an issue, how do we fix it? The following is a general solution for each problem explained earlier.

Description:​

• Break up the description into more but simpler sentences - This will make the concepts easier to mentally follow and digest, allowing it to more effectively be transferred from short term to long term memory.
• Add reminders of previous information as needed - This will reduce the amount of assumed knowledge baked into the explanation, which will make it more convenient to read and reduce the need to reread all of the previous tiers.
• Be consistent with the terminology used - This will reduce the appearance of complexity and make readers more confident that they understand the information, as opposed to questioning if they're missing an important distinction between two words which doesn't actually exist.
• Use vocabulary which is general and common if possible - This will remove the current bias towards technical subjects and mathematics which the current description has, better reflecting the actual definition of High 1-A not necessarily requiring any application of mathematical theories to reach.

Examples/Cardinals Section:​

• Fix the inaccessible cardinals example to be accurate and actually apply the concept into practice - The current description's current wording implies and reinforces a common misconception that an "inaccessible cardinal" itself is High 1-A even without context, which doesn't actually make any sense.
• Vastly simplify the example using inaccessible cardinals and save any technical details for the separate page already made for them - The sheer length and complexity of the paragraph is hard to understand on its own, but also dramatically subtracts and confuses from the concept it's attempting to be an example for.
• Add a second example using non-mathematical concepts - The tier is not only reachable by mathematics, and it would be helpful and make it seem less intimidating by including an example which doesn't require an understanding of an obscure mathematical theory.

First Draft Proposal​

Now that we've established that there's problems with the current description, what they are, and a general strategy for fixing them, it's finally time for a first draft of a possible replacement. I'm more than willing to adjust and negotiate this, so please don't assume that I'm hard-set on proposing we replace it with exactly what I've written below, it's just a first draft to give us a springboard towards the discussion on what the replacement would actually be if this is accepted. It also includes some minor grammar changes. Without further ado, my first draft:

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High 1-A: High Outerverse level​

Characters or objects which can affect structures larger than the boundaries of 1-A or any lower tier. This would include the structure being inaccessible, or unreachable even by things which have infinite layers of superiority over baseline 1-A, such as the previously defined 1-A+.

Mathematically, an example of this would be a structure with a number of dimensions which could only be expressed using inaccessible cardinals. This refers to a set which is unreachable by any operations using smaller cardinals or layers of infinite sets, instead requiring its own unique assumption. More about this topic can be found on this page.

This tier can also be reached by any proof of qualitative superiority over a 1-A+ structure, meaning superiority which extends beyond simply adding more layers of infinities. A possible example is a character who completely trivializes another character who's rated 1-A+ by viewing them as purely fictional.

Maybe.

 

[DontTalkDT]

We're talking about a High 1-A structure here, as defined by our tiering system, which is a character or structure which can affect something qualitatively superior to 1-A+.

That's not what High 1-A is.

If you can't see the obvious, let me lay it out: the concept itself of inaccessible cardinals is not even a structure or character, let alone one which fits the criteria of High 1-A.
What this sentence is trying to say is that a structure would be High 1-A if it was qualitatively superior in layers to a normal dimension in a way which could only be mathematically described with inaccessible cardinals.

I would rather say that it is trying to say that a space with a number of dimensions described by such a cardinal would be High 1-A.

Besides, it's not specific either. It's literally an entire branch of abstract mathematics, and isn't even applied to anything in this paragraph, so it's as vague as can be as well.

It's specific in the sense of "if you find a space with inaccessible cardinal many dimensions mentioned in a book it's High 1-A", as opposed to just a list of criteria.
"Specific" is a spectrum. An apple tree is a specific tree, even if it's not one particular apple tree.
Inaccessible cardinals are also not a branch of mathematics. Not sure where that comes from.

To be specific (heh), this is our reference object. We have decided some time ago that any tier should have a reference object associated with it. It's useful for edge cases.

What's the difference between a countable or uncountable infinity?

I will say that I believe that knowledge on that level is required for our tiering system in its current form. Without that you wouldn't even understand lesser tiers.

"Logical framework", "levels", "hierarchies" are all words which mean the same thing in this context

No?
Levels means a level of infinity. One cardinal to the next. Or specifically: Two things (any things, hence can't be more specific) that have a relationship of qualitative superiority (see TIering System FAQ) are on different levels.
Hierarchies are collection of these levels.
Logical Frameworks are what extrapolating certain types of hierarchies get you.

I will acknowledge that my words here aren't great, but that's because fiction doesn't give us a whole lot of choice as vastly different things need to be put in one bucket.

Why would we say "logical framework" instead of simply saying "boundaries"? It makes it far less intuitive and again implies it's part of some larger concept we need to know.

The boundary of a circle is its edge, while the logical framework is the totality of all possible circles. Or more specifically: The boundaries of an infinite hierarchy would usually be considered its lowest and highest level. Logical Frameworks add extensions (which go over several boundaries).
Boundary is ambiguous and overloaded.
Not that I have something against a better description of what a logical framework is. But that's not it.

In general, in the tiering system, I see a bias towards using mathematical terms where it's not needed. Math is one way for higher tiers to be reached, but it's not the only way, in fact I would argue it's not even the most common. The actual definitions of the tier reflect this, but the word choice and framing sort of implies differently, which I've personally lead to misconceptions in the past that math is the only way to reach these tiers, and outright rejecting the possibility of reaching them by any other mean. If we have a concept which is general, then our wording should be general too.

While I'm the guy that once proposed to just get rid of math as the basis of the tiering system... well, as long as math is the basis of the tiering system it bears to mention it. And currently it is.
(Honestly, even if it weren't, we would need to give specific explanations of the gap between some tiers.)

Vastly simplify the example using inaccessible cardinals and save any technical details for the separate page already made for them - The sheer length and complexity of the paragraph is hard to understand on its own, but also dramatically subtracts and confuses from the concept it's attempting to be an example for.

I'm generally fine with the other points, but here I wish to note that I think it's of importance to at least give a slight idea of how big the mathematical gap between the last and this tier is. I.e. shouldn't shorten it too much.

Now to the draft:

Characters or objects which can affect structures larger than the boundaries of 1-A or any lower tier. This would include the structure being inaccessible, or unreachable even by things which have infinite layers of superiority over baseline 1-A, such as the previously defined 1-A+.

That alters the sense of the definition and is rather vague. As mentioned, it is not clear what the boundary of 1-A is. Additionally, being unreachable by infinite layers over baseline 1-A is not sufficient for High 1-A. For High 1-A you need to also transcend every logical extension of that, including things like infinitely many higher infinite hierarchies of levels of infinity, as long as those are of the same nature.
Following your own criticism, I will note that it's not clear what layers are. The term "level" in the context of "level of infinity" is established throughout the rest of the tiering system and hence seems better suited. (The term even gets a brief description in the TIer 1 text)

Mathematically, an example of this would be a structure with a number of dimensions which could only be expressed using inaccessible cardinals. This refers to a set which is unreachable by any operations using smaller cardinals or layers of infinite sets, instead requiring its own unique assumption. More about this topic can be found on this page.

The "and as such has to be "assumed" to exist in order to be made sense of or defined in a formal context (Unlike the standard aleph numbers, which can be straightforwardly put together using the building blocks of set theory)." of the original draft are of greater relevance and should not be left out completely (reformulation is ok). They clarify exactly what you misunderstood about the definition for the given example: It's not simply about being infinite levels above, but it's about transcending a "logical system" i.e. in this case the system of all things which can be reasoned to exist from the ZFC axioms. That the cardinals are unreachable by prior operations is only what shows that they have the tiering relevant state of "beyond all logical extensions of the same nature".

Even just the amount of infinite cardinals between the first inaccessible cardinal and aleph-2 (Which defines 1-A) is greater than cardinals such as aleph-0, aleph-1, aleph-2, aleph-3, etc., and even many aleph numbers whose index is an infinite ordinal.

I would prefer to keep something like that, as it is a small note which puts it into clearer terms that an infinite hierarchy isn't enough and that even much larger cardinals are to be transcended. Just, y'know, a small attempt to give even the faintest idea of how large of a gap we are talking about is.

This tier can also be reached by any proof of qualitative superiority over a 1-A+ structure, meaning superiority which extends beyond simply adding more layers of infinities. A possible example is a character who completely trivializes another character who's rated 1-A+ by viewing them as purely fictional.

As already mentioned, that's sadly just wrong.

---

Assume I agree with anything relevant I didn't comment on.

 

[FinePoint]

That's not what High 1-A is.

I'll come back to this since you talk about it later too.

I would rather say that it is trying to say that a space with a number of dimensions described by such a cardinal would be High 1-A.

Indeed, but that is not clear in the sentence.

It's specific in the sense of "if you find a space with inaccessible cardinal many dimensions mentioned in a book it's High 1-A", as opposed to just a list of criteria.
"Specific" is a spectrum. An apple tree is a specific tree, even if it's not one particular apple tree.
Inaccessible cardinals are also not a branch of mathematics. Not sure where that comes from.

Again, the sentence itself makes no reference to dimensions or what the cardinals are being applied to or counting. I understand this is what was intended to be implied, but it's simply not clear, so I think it should be made more explicit.

I will say that I believe that knowledge on that level is required for our tiering system in its current form. Without that you wouldn't even understand lesser tiers.

Fair enough. Though, after spending three and a half hours on this I certainly don't feel like evaluating if this information is presenting appropriately earlier on the page, it's probably alright to include. Keep in mind that it's not reasonable to expect to never assume some knowledge, but I do believe it's appropriate to reduce it when possible. You may have a point that this particular thing cannot be.

No?
Levels means a level of infinity. One cardinal to the next. Or specifically: Two things (any things, hence can't be more specific) that have a relationship of qualitative superiority (see TIering System FAQ) are on different levels.
Hierarchies are collection of these levels.
Logical Frameworks are what extrapolating certain types of hierarchies get you.

Following your own criticism, I will note that it's not clear what layers are. The term "level" in the context of "level of infinity" is established throughout the rest of the tiering system and hence seems better suited. (The term even gets a brief description in the TIer 1 text)

My apologies, I didn't mean they meant the same thing literally, but that they were being used to discuss the same thing, and could therefore probably be expressed with more consistent vocabulary. If level is clearly defined and used frequently, then simply stick to that, would be my suggestion.

And you're right, I was actually thinking the same thing when I drafted it, but I couldn't think of anything better. As stated, it's just a rough draft to get things started. The feedback is appreciated.

The boundary of a circle is its edge, while the logical framework is the totality of all possible circles. Or more specifically: The boundaries of an infinite hierarchy would usually be considered its lowest and highest level. Logical Frameworks add extensions (which go over several boundaries).
Boundary is ambiguous and overloaded.
Not that I have something against a better description of what a logical framework is. But that's not it.

Now I will return to the "that's not what High 1-A" is. You are right that I misinterpreted 1-A+, but that is a simple correction.
It seems like we're disagreeing on semantics more than the actual concept, which is a good discussion to have, since it's the cause of this thread and a lot of the confusion. However, I think that objectively, we are describing the same thing. Consider the following:

I actually didn't know there was an official case of "qualitative superiority" defined on the wiki, so thanks for pointing it out.
I've been operating on the actual implied meaning of the word, meaning simply "superior in a way which cannot be quantified."
Though, I'm not sure it matters. Reading through the definition of qualitative superiority linked, it specifically mentions that infinities and higher infinites still count as quantities, and this would include the cardinals.

Coming back to the idea of a "logical framework", the two examples given are a higher dimension and a reality-fiction difference.
These are both unique in that they exceed the logical framework of the lower dimension or the fiction, and this superiority over the logical framework is sort of what defines "qualitative superiority" in the first place.

Now we can connect with this:

That alters the sense of the definition and is rather vague. As mentioned, it is not clear what the boundary of 1-A is. Additionally, being unreachable by infinite layers over baseline 1-A is not sufficient for High 1-A. For High 1-A you need to also transcend every logical extension of that, including things like infinitely many higher infinite hierarchies of levels of infinity, as long as those are of the same nature.

By boundary here, I am not referring to a physical boundary. I am referring to the scope of 1-A via the tiering system.
Though, as you point out, 1-A+ specifically says "infinite" levels. I misinterpreted it as referring to any higher level of infinity, but I see now that's not technically implied. That's my bad. In that sense, your original statement of "that not being what" High 1-A is, is correct, and so I will adjust that portion.

That said, 1-A+ is actually not important, I just mistook it for more convenient than it is. The wording will have to become a bit longer, but should still generally work.
The boundaries of 1-A, meaning the upper limit of the tier as described by our tiering system, includes these "infinitely many higher infinite hierarchies of levels of infinity" and so to say "qualitatively superior to the boundaries of 1-A" would work, since this would imply, literally: "existing beyond the logical extensions of infinitely many higher infinite hierarchies of levels of infinity", which is how you just defined High 1-A.

In this sense, we're describing exactly the same thing.
Or so it would seem to me, outside of my mistake with 1-A+.

While I'm the guy that once proposed to just get rid of math as the basis of the tiering system... well, as long as math is the basis of the tiering system it bears to mention it. And currently it is.
(Honestly, even if it weren't, we would need to give specific explanations of the gap between some tiers.)

I am not suggesting getting rid of math, lol. I was simply suggesting making mathematical terms less of a default when describing things which aren't inherently mathematical.

I'm generally fine with the other points, but here I wish to note that I think it's of importance to at least give a slight idea of how big the mathematical gap between the last and this tier is. I.e. shouldn't shorten it too much.

I can understand that. Perhaps it's possible to do so with less symbols and jargon, though.

The "and as such has to be "assumed" to exist in order to be made sense of or defined in a formal context (Unlike the standard aleph numbers, which can be straightforwardly put together using the building blocks of set theory)." of the original draft are of greater relevance and should not be left out completely (reformulation is ok). They clarify exactly what you misunderstood about the definition for the given example: It's not simply about being infinite levels above, but it's about transcending a "logical system" i.e. in this case the system of all things which can be reasoned to exist from the ZFC axioms. That the cardinals are unreachable by prior operations is only what shows that they have the tiering relevant state of "beyond all logical extensions of the same nature".

There is indeed a simplified version of that in the draft.
This mathematical concept, as essentially just an example of the tier, doesn't need an entire explanation of itself within the paragraph listing it as an example. I think it would be far more user-friendly and clean to leave all the really complex portions on the separate explanation page.
Like, if we listed Superman as an example of someone with Super Strength, we wouldn't need to give his backstory and exact strength calculations in the sentence listing him as an example. The idea that there's more details which prove it as an example is always implied, and why a separate page is linked to, no?

---

Assume I agree with anything relevant I didn't comment on.

Thank you for the comment, and for pointing out my mistake.
I did not expect my first draft to be perfect by any means, and I'm glad to have you here to jumpstart this discussion.

Regardless of the nitty gritty of the exact wording, I'm glad to see that you at least seem in support of making the description more user-friendly.
(I've edited some of the inaccuracy in the OP, such as the previous erroneous use of 1-A+ and some miswording.)

Also added the logical framework thing as a "in other words"- does that make it better?
Anyways, it's 4AM and I'm sleep deprived. Have been for a few days actually, which might explain some of my errors, lol.
I go sleep now.

 

[Antvasima]

As usual, I support DontTalk's knowledge and experience here.

@Qawsedf234 @Executor_N0

What do you think?

 

[Qawsedf234]

I've always held that the way we explain things is very word salad heavy and confuses people. So if we can adjust it to make it more understandable without losing the meaning I think it's fine.

trivializes another character who's rated as such by viewing them as purely fictional.

Viewing something as fictional isn't enough for High 1-A. Aleph-3 to Aleph-2 is already a gap of such magnitude that it's beyond just being superior or R>F. An infinite amount of ever increasing Aleph-2 spaces still would never make it to Aleph-3.

Like DT said it's about being superior to the logical framework of a cardinal and that framework being taken to infinity but still never able to access an Inaccessible Cardinal space.

 

[Ultima_Reality]

I'm fine with rewording the description to be less confusing, myself. I'll probably pitch in some things later (Or opinate on potential pitches) when I have the time.

 

[Isaiah_ZaMangaka]

Following (mainly cuz i wanna understand High 1-A better)

 

[DontTalkDT]

My apologies, I didn't mean they meant the same thing literally, but that they were being used to discuss the same thing, and could therefore probably be expressed with more consistent vocabulary. If level is clearly defined and used frequently, then simply stick to that, would be my suggestion.

They aren't discussing the same thing, though. They are discussing three very different things.
If "level" represents a cardinality, "hierarchy" represents an ordered collection of cardinals and "Logical Framework" is the totality of all sets that can be proven to exist using the ZFC Axioms.
I do not know how you could use "level" to describe how large "above ZFC is". The amount of levels (i.e. cardinals) in ZFC is indescribably large, after all.

Coming back to the idea of a "logical framework", the two examples given are a higher dimension and a reality-fiction difference.
These are both unique in that they exceed the logical framework of the lower dimension or the fiction, and this superiority over the logical framework is sort of what defines "qualitative superiority" in the first place.

No? Transcending a logical framework involves indescribably many levels of qualitative superiority.
A reality-fiction difference is one level of qualitative superiority.
The totality of all imaginable reality-fiction differences is what a logical framework is and hence involves indescribably many levels of qualitative superiority (or, if you want to be more precise, you can make a chain of objects, each qualitative superior to the last, that is of any length, even any number of higher infinities long).

Now we can connect with this:

By boundary here, I am not referring to a physical boundary. I am referring to the scope of 1-A via the tiering system.
Though, as you point out, 1-A+ specifically says "infinite" levels. I misinterpreted it as referring to any higher level of infinity, but I see now that's not technically implied. That's my bad. In that sense, your original statement of "that not being what" High 1-A is, is correct, and so I will adjust that portion.

That said, 1-A+ is actually not important, I just mistook it for more convenient than it is. The wording will have to become a bit longer, but should still generally work.
The boundaries of 1-A, meaning the upper limit of the tier as described by our tiering system, includes these "infinitely many higher infinite hierarchies of levels of infinity" and so to say "qualitatively superior to the boundaries of 1-A" would work, since this would imply, literally: "existing beyond the logical extensions of infinitely many higher infinite hierarchies of levels of infinity", which is how you just defined High 1-A.

Two things:
1. I don't think it's clear at all that boundaries is meant in this sense if you use the term without additional explanation. Explanation can be added, although I would consider whether it's worth using the term then as we do not reuse it. It adds one more thing the reader tries to remember.
2. You should be careful of circular definition. 1-A(+) does not define what its upper limit is. So saying that something is above the upper boundary of 1-A is not well defined until you have defined what that upper boundary of 1-A even is. We typically define the upper boundary of tiers implicitly as the lower boundary of the next tier. As such one could question whether there is even a point to mentioning that High 1-A is above the upper bound of 1-A, as that appears to be a tautology. It is essentially a rewording of "Something High 1-A is above something 1-A".

In this sense, we're describing exactly the same thing.
Or so it would seem to me, outside of my mistake with 1-A+.

If you mean to say the same thing you need to mention logical frameworks, or the idea behind them, somewhere in a much more epxlicit way. Just "above 1-A" is not an adequate representation of it.

I am not suggesting getting rid of math, lol. I was simply suggesting making mathematical terms less of a default when describing things which aren't inherently mathematical.

If you can do so precisely that's fine.

I can understand that. Perhaps it's possible to do so with less symbols and jargon, though.

It is always a compromise between mathematical terms, precision and brevity. But I'm open to suggestions.

There is indeed a simplified version of that in the draft.
This mathematical concept, as essentially just an example of the tier, doesn't need an entire explanation of itself within the paragraph listing it as an example. I think it would be far more user-friendly and clean to leave all the really complex portions on the separate explanation page.
Like, if we listed Superman as an example of someone with Super Strength, we wouldn't need to give his backstory and exact strength calculations in the sentence listing him as an example. The idea that there's more details which prove it as an example is always implied, and why a separate page is linked to, no?

I disagree. As said, this is about our mathematical reference object. At least a brief explanation of how the concept of logical systems applies to it is a basic necessity.
Saying "inaccessible cardinals are an example" and then not explaining in any way why they are an example makes the example in itself useless and confusing.
This part of the description is the very core why inaccessible cardinals even qualify as High 1-A. The rest of the description is flavour text in comparison.

Thank you for the comment, and for pointing out my mistake.
I did not expect my first draft to be perfect by any means, and I'm glad to have you here to jumpstart this discussion.

Regardless of the nitty gritty of the exact wording, I'm glad to see that you at least seem in support of making the description more user-friendly.
(I've edited some of the inaccuracy in the OP, such as the previous erroneous use of 1-A+ and some miswording.)

Also added the logical framework thing as a "in other words"- does that make it better?
Anyways, it's 4AM and I'm sleep deprived. Have been for a few days actually, which might explain some of my errors, lol.
I go sleep now.

Well, aside from what I already said above some more things.

which would include any higher levels of infinity

That is mathematically not a provable statement and could be wrong. Better not include that.

While you added a mention of logical frameworks, you cut out any nearer description of what that means, so I would say the description is too vague on that point.
Like, ask yourself this: From reading this description, would you understand that the logical framework of a 1-A reality-fiction hierarchy, is the totality of all possible stories including those featuring more than infinitely large reality-fiction hierarchies?

 

[Nehz_XZX]

I've removed one of the periods after ordinal.

 

[Antvasima]

Thank you very much for helping out, DontTalk.

 

[FinePoint]

Like, ask yourself this: From reading this description, would you understand that the logical framework of a 1-A reality-fiction hierarchy, is the totality of all possible stories including those featuring more than infinitely large reality-fiction hierarchies?

Eh, probably not without the context I already have from having written it. Point taken. I suppose the inherent struggle is that there's not really a brief way to say all that clearly, and so my attempt to do so has come with some meaningful sacrifices as pointed out. Perhaps, though, while maybe not brief, there is a way that's at least more accessible than hypothetical branches of set theory. I'll have to think on it. I've been essentially hibernating recently.

I have a few college assignments due this weekend, but I am at least less sleep-deprived than before.

Looking back on it with fresh eyes, I don't really like my first draft much either, though I obviously still hate the current one, and I think "word salad" is a good and more succinct way to put it.

Thank you for the feedback so far, though, I think it's given me some ideas on how to improve the draft while retaining more of the original meaning. I'll draft it sometime soon in the next couple of days.

---

In the meantime, if anyone has any suggestions or ideas for a way to simplify the concept without subtracting clarity, please let us know.

I know it's really hard to speak up sometimes with new ideas, there's an inherent fear of being told you're wrong, and feeling embarrassed, and I think this topic lends itself to that a lot. I feel a little bit of it myself, but I think an important step in progress is having the bravery to speak your mind and learn from your mistakes.

Me personally, I'm not the type to recognize a problem and just give up on it. Even if it takes me a hundred drafts, and being embarrassed a dozens times, uphill battles are a pattern in my life and I'm committed to fixing this. One of the most fundamental parts of this website shouldn't be reserved for a select few to understand. I hope that my passion for that shows itself, at the very least.

 

[Antvasima]

@DontTalkDT

Do you have any constructive suggestions here?

 

[DontTalkDT]

Well, a good definition of logical framework is probably a necessity.
It's just that making that precise while keeping it general is hard. Two possible criteria one could bring up:

1. It should be larger than an infinite (in this context 1-A) hierarchy. I don't think we would accept a logical framework of just 13 levels of qualitative superiority as being a proper thing. Basically, I think it makes sense to require that a logical framework contains at least (countably) infinite levels of infinite (/qualitative superiority) and is larger than baseline 1-A+.
2. Thinking about how one could define it precisely I thought maybe something in the following direction could help: A logical framework contains all hierarchies of levels of infinity, where the kind of qualitative superiority is of one specific type. (e.g. one dimension to a higher dimension, a R>F difference or one cardinality to the next) That means that it would be logically contradictory for there to be a level with the same kind of qualitative superiority that is superior to the logical framework.

And then one could probably bring up R>F hierarchies with stories as an additional non-mathematical example. I.e. The logical framework of (story-based) the reality-fiction transcendence type would be the sum total of all possible stories, including all possible hierarchies of stories within stories. There couldn't be a story that contains all stories, as if there were one, it in itself would have to be part of the collection of all stories and hence would not actually be qualitatively superior to the logical framework.
And then one could mention that restriction that don't majorly affect the size are allowed. I.e. All stories that don't feature paradoxes are also a logical framework.

 

[Antvasima]

Well, a good definition of logical framework is probably a necessity.
It's just that making that precise while keeping it general is hard. Two possible criteria one could bring up:

1. It should be larger than an infinite (in this context 1-A) hierarchy. I don't think we would accept a logical framework of just 13 levels of qualitative superiority as being a proper thing. Basically, I think it makes sense to require that a logical framework contains at least (countably) infinite levels of infinite (/qualitative superiority) and is larger than baseline 1-A+.
2. Thinking about how one could define it precisely I thought maybe something in the following direction could help: A logical framework contains all hierarchies of levels of infinity, where the kind of qualitative superiority is of one specific type. (e.g. one dimension to a higher dimension, a R>F difference or one cardinality to the next) That means that it would be logically contradictory for there to be a level with the same kind of qualitative superiority that is superior to the logical framework.

And then one could probably bring up R>F hierarchies with stories as an additional non-mathematical example. I.e. The logical framework of (story-based) the reality-fiction transcendence type would be the sum total of all possible stories, including all possible hierarchies of stories within stories. There couldn't be a story that contains all stories, as if there were one, it in itself would have to be part of the collection of all stories and hence would not actually be qualitatively superior to the logical framework.
And then one could mention that restriction that don't majorly affect the size are allowed. I.e. All stories that don't feature paradoxes are also a logical framework.

That is probably fine, as long as it won't make it easier to reach higher tiers.

@Ultima_Reality @Executor_N0 @Agnaa @Elizhaa @Qawsedf234 @PrinceofPein @Everything12 @Planck69 @Ovy7 @TheUnshakableOne @IdiosyncraticLawyer

What do you think?

 

[Agnaa]

I currently have 59 threads in my "to-evaluate" backlog, I've added this to the list, and will get to it eventually.

 

[Qawsedf234]

What do you think?

I mean, DT is right, but it's just a suggestion of what needs to be included in an explanation. It's not really a proposal.

 

[Antvasima]

Okay. That is probably good then.

 

[Elizhaa]

That is probably fine, as long as it won't make it easier to reach higher tiers.

@Ultima_Reality @Executor_N0 @Agnaa @Elizhaa @Qawsedf234 @PrinceofPein @Everything12 @Planck69 @Ovy7 @TheUnshakableOne @IdiosyncraticLawyer

What do you think?

I think it is already accepted that it is possible to reach a tier like High 1-A without having an infinite hierarchy in the tiering system FAQ; I think changing the description to reflect it seems ideal, regarding the first bullet point.
Otherwise, it seems okay at a glance.

 

[Ultima_Reality]

And then one could probably bring up R>F hierarchies with stories as an additional non-mathematical example. I.e. The logical framework of (story-based) the reality-fiction transcendence type would be the sum total of all possible stories, including all possible hierarchies of stories within stories. There couldn't be a story that contains all stories, as if there were one, it in itself would have to be part of the collection of all stories and hence would not actually be qualitatively superior to the logical framework.

That sounds like a neat enough way to define it, yeah. It would form a rough equivalence with the way High 1-A is defined mathematically, too: There cannot be a set of all sets, because if there were one, it would still be contained in the set of all sets, and thus contain itself, which is a contradiction. So High 1-A in principle would be something that exceeds all sets (In a given logical framework) and is not included in the definition of what a "set" is.

God from Unsong comes to mind as a character that expresses the notion well enough: The story quotes Georg Cantor's statement that the "Absolute" is not the "genus supremum (highest of a species) of the infinite," meaning that it isn't "the highest infinity," or anything of the sort, because there is no such highest infinity. Rather, it's beyond both finiteness and infinity.

Granted, fiction does whatever it wants, so, it could just have a set of all sets or a story of all stories be an actual cosmological structure, in principle. How would we handle that?

I think it is already accepted that it is possible to reach a tier like High 1-A without having an infinite hierarchy in the tiering system FAQ; I think changing the description to reflect it seems ideal, regarding the first bullet point.

As far as "Unreachable by additions of layers" goes, I think it should be clarified that High 1-A is a bit distinct from 1-A in that regard. I'd say the point of High 1-A is being unreachable to layer-stacking for qualitative reasons, rather than quantitative ones.

To better explain what I mean: A 1-A+ space would be unreachable to layer-stacking for quantitative reasons. That is to say, you can't reach it because it's too large for you to practically reach just by starting from a 1-A realm and expanding that into a hierarchy one layer at a time. However, if infinite time passes, then, yeah, you reached the 1-A+ space, because it was really just a matter of quantity at the end of it all. So in that sense 1-A+ is just "really far away."

High 1-A, meanwhile, would be unreachable to layer-stacking due to the fact it surpasses the "quality" defining the layers, to begin with. Which is to say the transcendence goes in another, superior direction that no adding, finite or infinite, can reach.

To illustrate that: A lot of the time we say "Being of a different nature from something doesn't mean you are superior to it," which is why simply lacking spacetime without showcasing superiority to spacetime doesn't grant you any tier. Of course, no matter how many dimensions you add to an object, you won't ever equal something that has no dimensions at all, but that's not to say the non-dimensional thing is greater than the dimensional object. It's just inexpressible to it, but not necessarily "larger."

And sometimes we say "This character is both different in nature from that thing and superior to it," too.

What I just explained would be more along the lines of "This character is superior to this thing because it is different in nature from it." Which is to say that the reason for why it can't be expressed by the things in the lesser hierarchy is the same as the reason for why its "size" can't be reached by them.

 

[Elizhaa]

Alright.

 

[IdiosyncraticLawyer]

Update: In light of Ultima's new mass revisions for the Tiering System, this thread has been rendered obsolete and will be closed.