On the Many, Many Incoherences of the Tiering System

[IdiosyncraticLawyer]

Well, it has been exactly 24 hours, and I've received no response on the question just above in spite of its brevity and DontTalk seemingly being active earlier today. As such, I'll simply move on to Agnaa. I'll reply to his posts from 1-2 pages ago and then personally notify him about it.

Agnaa's posts all seem quite barebones. What do you plan on replying to?

 

[Ultima_Reality]

I'll start off slow.

I completely and utterly disagree with this. I had a discussion with Ultima about this on Discord, which ended with him being unable to refute my points, after which he didn't bring it up again.

I've long shaved the "Fiction is complete nothingness" thing off of my arguments, which is what that debate largely revolved around. It's a semantical thing that ultimately doesn't change anything whatsoever about the discussion, so, that's that. The only noteworthy thing left from it, I'll address below.

I also think it's incoherent to define a standard based on "transcending dimensionality entirely" since that's impossible to prove.

It's perfectly possible to prove. A tier being broad doesn't make it unprovable, especially given that, by the "That's unprovable!" logic that's often perpetuated around these parts (Which is to say: "I's impossible to demonstrate, and therefore no character is that high"), basic infinities are impossible to prove, too.

---

Regardless, from what I gather, the reason you have for supporting the idea that R>F Transcendences are comparable to an uncountably infinite difference is:

Because it encompasses the broadly common feature of R>F; of being able to effortlessly mold it [lower-tiered things], and to being immutable to effects from it.

This is a rather poor justification, since R>F Transcendences and dimensional jumps are "immutable to effects from lower-tiered things" in two completely different ways, and for completely different reasons. Equating the two solely for having a superficially similar effect is just a false equivalence, and a nasty one at that.

Since Type 2 Beyond-Dimensional Existence, from previous discussions I've had with you, is something you treat the same way, I take the same argument goes for it? If so, I call that a poor justification as well.

 

[DontTalkDT]

Well, it has been exactly 24 hours, and I've received no response on the question just above in spite of its brevity and DontTalk seemingly being active earlier today.

Oh, I rarely read threads when I don't plan on replying to them, so I didn't see. Only came around just now because I wondered why there's activity.

Nearly all your points boil down to something like "Ultima's interpretations of what R/F is are too high-end. Here are low-end ones that are just as valid" (And to be clear, they aren't just as valid, because [insert every reply I gave to you in this thread], but let me pretend they are). This dodges the core subject spectacularly

Does it? I thought we agreed that we default to the lowest viable interpretation. So that a viable low-end interpretation of the same evidence exists seems pretty relevant to the core subject.

because it doesn't clarify whether you think my assessment of the tiering of the """high-end interpretations""" is even invalid to begin with.

Depends on the details. As I said in my last big reply, in principle what you lay out is a possible view of how R>F works. However, it's one amongst many. R>F in the literal real world way where the authors can just write about anything they like is also a possible contradiction-free idea of how R>F works, but it equally is not the one I'm willing to default to.
It's like ranking every character that's called omnipotent Tier 0, until omnipotence is contradicted, is technically a viable interpretation. It's just not what I would default to as an interpretation.

You keep silent and don't even say if you think Type 2 BDE is 1-A or not

I have for now not addressed that part any further for two reasons.
First, it somewhat seems secondary to the suggested tiering revision. I don't think that being viable would necessitate the revision and the revision would not necessitate that.
Second, unless I have missed it, you have yet to give me that practical example for that, despite me asking for one. I think it's pretty pointless to debate if, for all I am aware of, the kind of evidence you are going for doesn't exist. Instead of having a huge argument over whether such evidence can exist or not, you can just give an actual example to prove that it does exist, so I'm waiting for you to do that.

or if the exact conception of R>F that I outined is 1-A or not (Or, Tier 0, in the current system).

Well, you have defined it to be, haven't you?

At the very best, you said "Well, tiering them as such would lead to undesirable consequences," which is also incorrect, but even if it wasn't, it wouldn't constitute an answer either, because you are still refusing to respond to the question of "What tier are those things that I am talking about, in the first place?". If you said "Yeah, by that reasoning they are indeed 1-A, but that leads to undesirable consequences, so let's not tier them this way" that'd be a better answer and a step towards progress, but your silence on the matter is what's making this thread so unbearably sluggish.

I don't understand why "is the thing I defined to be superior to all dimensions including all large cardinals Tier 0" is a point of debate. If you define the thing as such it is, but the real debate is if the evidence you require actually makes it have that property. And I think I have given plenty of arguments as to why the evidence you require for that does not actually prove that it should have that property.
It's like asking "if I define this character to be truly omnipotent is it Tier 0?" Sure, it is. But the question is by which evidence we would accept a character to be that.

As such, I'll simply move on to Agnaa. I'll reply to his posts from 1-2 pages ago and then personally notify him about it.

Good.

@Ultima_Reality Can you clarify if what DDM said in the reply I quoted in my last post is correct? Since people are telling me that I don't understand the proposal again, I suppose it's better if I don't go and assume.

^I'm also repeating this request.

 

[Ultima_Reality]

Oh, I rarely read threads when I don't plan on replying to them, so I didn't see. Only came around just now because I wondered why there's activity.

Does it? I thought we agreed that we default to the lowest viable interpretation. So that a viable low-end interpretation of the same evidence exists seems pretty relevant to the core subject.

Depends on the details. As I said in my last big reply, in principle what you lay out is a possible view of how R>F works. However, it's one amongst many. R>F in the literal real world way where the authors can just write about anything they like is also a possible contradiction-free idea of how R>F works, but it equally is not the one I'm willing to default to.
It's like ranking every character that's called omnipotent Tier 0, until omnipotence is contradicted, is technically a viable interpretation. It's just not what I would default to as an interpretation.

I have for now not addressed that part any further for two reasons.
First, it somewhat seems secondary to the suggested tiering revision. I don't think that being viable would necessitate the revision and the revision would not necessitate that.
Second, unless I have missed it, you have yet to give me that practical example for that, despite me asking for one. I think it's pretty pointless to debate if, for all I am aware of, the kind of evidence you are going for doesn't exist. Instead of having a huge argument over whether it does or not, you can just give an actual example to prove that it does exist, so I'm waiting for you to do that.

Well, you have defined it to be, haven't you?

I don't understand why "is the thing I defined to be superior to all dimensions including all large cardinals Tier 0" is a point of debate. If you define the thing as such it is, but the real debate is if the evidence you require actually makes it have that property. And I think I have given plenty of arguments as to why the evidence you require for that does not actually prove that it should have that property.
It's like asking "if I define this character to be truly omnipotent is it Tier 0?" Sure, it is. But the question is by which evidence we would accept a character to be that.

Good.

^I'm also repeating this request.

I'll answer to all this after the back-and-forth between Agnaa and I is finished. He is quicker to reply than you, so, I expect it to be over pretty quick once it starts.

 

[Deagonx]

Agnaa is in the process of moving and doesn't have access to his computer for the time being, so I don't know that he'll be able to reply right away.

 

[Ultima_Reality]

I can wait for that. Whatever reply I give to DontTalk right now, it'll evidently just be the source of yet another back-and-forth, which in fact defeats the whole point of moving over to Agnaa.

 

[Ultima_Reality]

I'll answer to all this after the back-and-forth between Agnaa and I is finished. He is quicker to reply than you, so, I expect it to be over pretty quick once it starts.

Though, actually, taking the time to read that carefully: Yeah, it's become clear to me that, at this stage, we've reached the point where we really have absolutely nothing more to say to each other. Which in turn means whatever response either side can give to the other will just turn into a circular slugfest.

So, to DontTalk, if you're reading this: Consider the conversation we've been having up until now to be over, from here and onwards. After Agnaa and I are finished, I'll simply answer the last thing in that post and then we'll get to summarizing our points. Nothing else to be done save cast it to the votes.

 

[Agnaa]

Oh hey, I was almost exactly right about how long this would take.

It's perfectly possible to prove. A tier being broad doesn't make it unprovable, especially given that, by the "That's unprovable!" logic that's often perpetuated around these parts (Which is to say: "I's impossible to demonstrate, and therefore no character is that high"), basic infinities are impossible to prove, too.

No. Basic infinities have a pretty defined endpoint mathematically. "Dimensionality entirely", if we don't let R^R be the endpoint of that, can go to literally anywhere simply by chucking in more axioms. These are extremely, extremely different.

This is a rather poor justification, since R>F Transcendences and dimensional jumps are "immutable to effects from lower-tiered things" in two completely different ways, and for completely different reasons. Equating the two solely for having a superficially similar effect is just a false equivalence, and a nasty one at that.

Most verses obtain their ratings for completely different reasons. We shouldn't create different tiering systems for each of them. At some point, we have to draw some amount of comparison between things like "Every universe grows from a seed in this endless garden" and "Each universe is a membrane that's part of a larger bulk". Even though those function in different ways and for different reasons.

If we call comparisons between cosmologies false equivalences then we cannot index them.

Fundamentally, I don't think the cause of a power difference matters, when we're indexing the power. I don't even care too much about whether it grants other abilities (as our Resistance page explains). A tiering system based on size should only care about the size of the difference.

Since Type 2 Beyond-Dimensional Existence, from previous discussions I've had with you, is something you treat the same way, I take the same argument goes for it? If so, I call that a poor justification as well.

I don't remember what you're talking about here.

 

[DarkDragonMedeus]

^I'm also repeating this request.

He clarified what he was proposing on Discord, and I am now on board with it. There was actually a big difference between a true R>F Transcendence and a pseudo R>F. Some random gag of a cosmic character pulling a human out of a board game and pointing to said board game that he came from there is not evidence of 1-A and would simply not be anything beyond a regular transcendence. I was told that in order to qualify for a true R>F, there needs to be a beyond dimensional existence statement that is made literal. And it basically needs to perceive fiction as mere illusions; like how in a R>F setting, any humanoid from the R can hack or reprogram a Infinite-D being as they see fit is an example. And as for verse specifics, Chronicles of Narnia was considered a perfect example of a verse that qualifies. As Wood Between Worlds is a R>F over both "The Real World" and Narnia (Which are parallel universes of each other) and that there is an infinite cardinal amount of stackings of R>F above WBW and Aslan's Country happens to be at the very top of those infinite stacks.

 

[Ultima_Reality]

No. Basic infinities have a pretty defined endpoint mathematically. "Dimensionality entirely", if we don't let R^R be the endpoint of that, can go to literally anywhere simply by chucking in more axioms. These are extremely, extremely different.

They are not at all different, no. "There is no largest cardinal, so we can arbitrarily increase dimensionality by chucking in axioms" is the same as "There is no largest finite number, so we can arbitrarily increase finite numbers by adding +1 to the pile." So this same argument does indeed result in basic infinities being unprovable by your lenses.

Ultimately, "The set of all finite numbers" has no (finite) endpoint and is thus fundamentally impossible to demonstrate, and so we just accept the existence of it as a totality and label that "∞" or "ω" or "aleph_0" or whatever else. Likewise, the collection of all possible dimensionalities has no "quantitative" endpoint. That doesn't, however, prevent it from having a qualitative endpoint.

If we call comparisons between cosmologies false equivalences then we cannot index them.

Fundamentally, I don't think the cause of a power difference matters, when we're indexing the power. I don't even care too much about whether it grants other abilities (as our Resistance page explains). A tiering system based on size should only care about the size of the difference.

That doesn't really follow because it assumes that the only options are: a) R>F is equated to something mathematical, or b) R>F is untierable. Basically presupposing mathematics are the end-all-be-all, which is hardly a given.

Fundamentally, the cause does matter if it results in different gaps in size. If you have a "qualitative superiority," then the reason you're unreachable to expansions of quantitative things is the same as the reason you're superior to them at all. Therefore you are, in fact, above all quantitative things. Which also works downwards, as well: If you're qualitatively inferior to things, for example, I would say you are inferior even to 0-D objects (Which goes into what DDM alluded to up there, btw: I'd say genuine R>F and existing beyond dimensions do go hand-in-hand)

I don't remember what you're talking about here.

That, at the core, is to ask: "Do you equate Type 2 Beyond-Dimensional Existence to dimensional jumps for the same reason you do so with R>F Transcendences?"

 

[Agnaa]

They are not at all different, no. "There is no largest cardinal, so we can arbitrarily increase dimensionality by chucking in axioms" is the same as "There is no largest finite number, so we can arbitrarily increase finite numbers by adding +1 to the pile." So this same argument does indeed result in basic infinities being unprovable by your lenses.

Ultimately, "The set of all finite numbers" has no (finite) endpoint and is thus fundamentally impossible to demonstrate, and so we just accept the existence of it as a totality and label that "∞" or "ω" or "aleph_0" or whatever else. Likewise, the collection of all possible dimensionalities has no "quantitative" endpoint. That doesn't, however, prevent it from having a qualitative endpoint.

There is no last finite number, but we don't need that, because we can rigorously define infinite numbers that are beyond all finite numbers.

Any attempt to try to define something that is "above all possible dimensionalities" is fruitless, as it will either have to be so maximally vague as to not communicate anything, or its definition could be easily worked around by adding more axioms.

This is because, ultimately, creating infinite numbers involves declaring a well-known class of numbers "finite" and putting other numbers outside of that purview. You cannot do the same thing with dimensionality (unless you have it stop somewhere like R^R), since that new definition could also be used to construct dimensions. You're not just saying that 1-A is beyond certain things with certain definitions, you're saying it's beyond every mathematical construct that anyone could ever define.

I have other angles I can approach this from, but I hope you see what I'm getting at.

That doesn't really follow because it assumes that the only options are: a) R>F is equated to something mathematical, or b) R>F is untierable. Basically presupposing mathematics are the end-all-be-all, which is hardly a given.

Those aren't the only options and I have no clue where you got that idea from. I really don't see how such logic would be involved in my post at all.

"We sometimes have to equate things because most verses have different cosmologies" does not require assuming "Either R>F is mathematical or untierable".

Fundamentally, the cause does matter if it results in the difference gaps in size. If you have a "qualitative superiority," then the reason you're unreachable to expansions quantitative things is the same as the reason you're superior to them at all. Therefore you are, in fact, above all quantitative things. Which also works downwards, as well: If you're qualitatively inferior to things, for example, I would say you are inferior even to 0-D objects (Which goes into what DDM alluded to up there, btw: I'd say genuine R>F and existing beyond dimensions do go hand-in-hand)

You could assume that, but without things substantiating that, I don't think there's good reason to believe it. Who are we to declare the exact extent to which they're unreachable, beyond a certain reasonable lowball?

Hence, R>F should be lowballed to a difference of being uncountably infinitely stronger, until feats establish something greater.

Also, the same argument you're putting forward could be made for many examples of lower worlds embedded in higher ones. Why assume that the material world created by gods that reside on a higher plane, or which is only a metaphor for the true higher world, is only uncountably infinitely weaker?

That, at the core, is to ask: "Do you equate Type 2 Beyond-Dimensional Existence to dimensional jumps for the same reason you do so with R>F Transcendences?"

Yeah.

 

[Ultima_Reality]

There is no last finite number, but we don't need that, because we can rigorously define infinite numbers that are beyond all finite numbers.

Any attempt to try to define something that is "above all possible dimensionalities" is fruitless, as it will either have to be so maximally vague as to not communicate anything, or its definition could be easily worked around by adding more axioms.

This is because, ultimately, creating infinite numbers involves declaring a well-known class of numbers "finite" and putting other numbers outside of that purview. You cannot do the same thing with dimensionality (unless you have it stop somewhere like R^R), since that new definition could also be used to construct dimensions. You're not just saying that 1-A is beyond certain things with certain definitions, you're saying it's beyond every mathematical construct that anyone could ever define.

"It will have to be so maximally vague as to not communicate anything" implies that "Above all possible dimensionalities" doesn't communicate anything intelligible, which is very blatantly false. "Its definition could be easily worked around by adding more axioms" is false, as well. If you transcend the very notion and definition of "dimensional space," you do indeed transcend those extensions as well, since they would fall under that same definition, by... Well, definition.

By that token, "we can rigorously define infinite numbers that are beyond all finite numbers" doesn't mean you can prove them from finite numbers, which is what your argument requires to be consistent. Even the Axiom of Infinity is, after all, unprovable (For the same reason large cardinal axioms are)

Those aren't the only options and I have no clue where you got that idea from. I really don't see how such logic would be involved in my post at all.

"We sometimes have to equate things because most verses have different cosmologies" does not require assuming "Either R>F is mathematical or untierable".

What I said does indeed practically follow from what you said. If you say that the only way to compare non-mathematical things with mathematical things at all is to treat the two as equivalent, and that otherwise we can't index them at all, then you're basically saying non-math things have no real tiering outside of what math thing we map them to.

You could assume that, but without things substantiating that, I don't think there's good reason to believe it. Who are we to declare the exact extent to which they're unreachable, beyond a certain reasonable lowball?

Hence, R>F should be lowballed to a difference of being uncountably infinitely stronger, until feats establish something greater.

Also, the same argument you're putting forward could be made for many examples of lower worlds embedded in higher ones. Why assume that the material world created by gods that reside on a higher plane, or which is only a metaphor for the true higher world, is only uncountably infinitely weaker?

1. We are thinking beings with working brains, which is why we can reason out these things. "I don't think there's a good reason to believe it" is hardly an argument if it, itself, has nothing substantiating it.

2. I don't think a vague "higher plane" is any tier at all. And I'd place the latter at 1-A, yes.

 

[Agnaa]

"It will have to be so maximally vague as to not communicate anything" implies that "Above all possible dimensionalities" doesn't communicate anything intelligible, which is very blatantly false. "Its definition could be easily worked around by adding more axioms" is false, as well. If you transcend the very notion and definition of "dimensional space," you do indeed transcend those extensions as well, since they would fall under that same definition, by... Well, definition.

No.

"Above all dimensionalities" doesn't communicate anything intelligible, because you don't rigorously define "dimensionalities". Finite numbers can be rigorously defined. If you rigorously define a cardinal where dimensionality ends, I could create a new cardinal beyond your definition. Yet, your proposed tiering system would not allow me to do this, and so, it is not.

You don't seem to be saying that "dimensions" have certain properties that accommodate cardinals up to mahlo. You appear to be using "all dimensions" as an obfuscation for "all of mathematics".

By that token, "we can rigorously define infinite numbers that are beyond all finite numbers" doesn't mean you can prove them from finite numbers, which is what your argument requires to be consistent. Even the Axiom of Infinity is, after all, unprovable (For the same reason large cardinal axioms are)

What? I'm not asking for anything to be proven. I do not see the link you're trying to draw here.

What I said does indeed practically follow from what you said. If you say that the only way to compare non-mathematical things with mathematical things at all is to treat the two as equivalent, and that otherwise we can't index them at all, then you're basically saying non-math things have no real tiering outside of what math thing we map them to.

You don't have to treat them as equivalent. Treating "each atom in this universe is another universe" as 3-A is not treating it as equivalent to dimensions, and it is indexing them.

I find the lowball to place the cosmologies at, given their description, and provide it. This happens to treat some constructions (sufficiently justified dimensions and R>F differences) as equivalent, yet not others.

And to jog your memory, we got here because I said "I think they both land here, due to being immutable to effects from lower-tiered things", you're the one who invoked "they're incomparable, therefore one is beyond all mathematics compared to each other". My argument has no roots in what you're alleging.

1. We are thinking beings with working brains, which is why we can reason out these things. "I don't think there's a good reason to believe it" is hardly an argument if it, itself, has nothing substantiating it.

I gave a reason. In fact, we're still arguing down that chain just above.

2. I don't think a vague "higher plane" is any tier at all. And I'd place the latter at 1-A, yes.

I have some related topics I could use this as a jumping pad for, but I think I should probably leave that until we resolve the earlier stuff.

 

[Ultima_Reality]

No.

"Above all dimensionalities" doesn't communicate anything intelligible, because you don't rigorously define "dimensionalities". Finite numbers can be rigorously defined. If you rigorously define a cardinal where dimensionality ends, I could create a new cardinal beyond your definition. Yet, your proposed tiering system would not allow me to do this, and so, it is not.

You don't seem to be saying that "dimensions" have certain properties that accommodate cardinals up to mahlo. You appear to be using "all dimensions" as an obfuscation for "all of mathematics".

"Dimensionality" just means "The quality of having dimensions," which does indeed include spaces of all conceivable dimensions, due to the fact those have the quality of having dimensions. You don't need to define a cardinal where dimensionality ends to justify something as "Above dimensionality," just like you don't need to justify a finite number where all finite numbers end to justify something as "Above finiteness."

It's no obfuscation, by the by. I've no issue with calling it "Above mathematics" or whatever you like, either.

What? I'm not asking for anything to be proven. I do not see the link you're trying to draw here.

It's pretty straightforward. You claim that being "Above all dimensionality" is incoherent due to being unprovable. I respond to that with "If you say this is unprovable, you will have to say infinity in general is unprovable too, for the same reasons."

You don't have to treat them as equivalent. Treating "each atom in this universe is another universe" as 3-A is not treating it as equivalent to dimensions, and it is indexing them.

I find the lowball to place the cosmologies at, given their description, and provide it. This happens to treat some constructions (sufficiently justified dimensions and R>F differences) as equivalent, yet not others.

And to jog your memory, we got here because I said "I think they both land here, due to being immutable to effects from lower-tiered things", you're the one who invoked "they're incomparable, therefore one is beyond all mathematics compared to each other". My argument has no roots in what you're alleging.

Rating such a thing as 3-A is rating it as equivalent to 3-dimensional space, so, it is, yes. Actually, at face value, it is just 3-D space.

And it does indeed have roots in what I'm saying. To jog your memory: I said "These things being equated to each other simply because of superficial similarities is a false equivalence. Therefore they shouldn't be equated" (Which was in fact mean to segue into my reasons for why R>F and BDE being above mathematics in general makes the most sense). You started saying "Actually, if we can't compare them at all, we can't even index them." Which itself presupposed that two things have to be tiered as on a similar level in order to be compared (Which isn't true. Saying X > Y is a comparison, still)

I gave a reason. In fact, we're still arguing down that chain just above.

"Being above dimensionality is unprovable" is hardly a reason to disbelieve my reasoning. In fact, I would say my reasoning just shows that being above dimensionality as a whole is not actually unprovable.

 

[Agnaa]

"Dimensionality" just means "The quality of having dimensions," which does indeed include spaces of all dimensions, due to the fact those have the quality of having dimensions. You don't need to define a cardinal where dimensionality ends to justify something as "Above dimensionality," just like you don't need to justify a finite number where all finite numbers end to justify something as "Above finiteness."

It's no obfuscation, by the by. I've no issue with calling it "Above mathematics" or whatever you like, either.


It's pretty straightforward. You claim that being "Above all dimensionality" is incoherent due to being unprovable. I respond to that with "If you say this is unprovable, you will have to say infinity in general is unprovable too, for the same reasons."

You don't need to justify a finite number where all finite numbers end, but you need to justify what the set of finite numbers is, even if in an iterative way. You are not defining the set of all dimensions, you are loosely alluding to it while truly referring to the undefinable idea of "all mathematics".

The finite numbers comparison does not work for this reason.

Rating such a thing as 3-A is rating it as equivalent to 3-dimensional space, so, it is, yes. Actually, at face value, it is just 3-D space.

Oh, I didn't realise you were making such a point. I thought you were contending with equating R>F to a jump of one dimension, not the idea of comparing R>F to dimensions in the first place.

And it does indeed have roots in what I'm saying. To jog your memory: I said "These things being equated to each other simply because of superficial similarities is a false equivalence. Therefore they shouldn't be equated" (Which was in fact mean to segue into my reasons for why R>F and BDE being above mathematics in general makes the most sense). You started saying "Actually, if we can't compare them at all, we can't even index them." Which itself presupposed that two things have to be tiered as on a similar level in order to be compared (Which isn't true. Saying X > Y is a comparison, still)

I don't think they're comparable because they have to be comparable. I think they're comparable because I see that as a reasonable lowball, for reasons established above. So no, my argument does not have roots in requiring an equivalence to math.

Is there a point to this meta-argument? Arguing about what unstated presuppositions I supposedly have doesn't seem very fruitful.

"Being above dimensionality is unprovable" is hardly a reason to disbelieve my reasoning. In fact, I would say my reasoning just shows that being above dimensionality as a whole is not actually unprovable.

No, that's not the reason I gave that I was referring to. The reason I gave is what you quoted in your first response to me:

Because it encompasses the broadly common feature of R>F; of being able to effortlessly mold it [lower-tiered things], and to being immutable to effects from it.

 

[Ultima_Reality]

I don't think they're comparable because they have to be comparable. I think they're comparable because I see that as a reasonable lowball, for reasons established above. So no, my argument does not have roots in requiring an equivalence to math.

Is there a point to this meta-argument? Arguing about what unstated presuppositions I supposedly have doesn't seem very fruitful.

No, that's not the reason I gave that I was referring to. The reason I gave is what you quoted in your first response to me:

Because it encompasses the broadly common feature of R>F; of being able to effortlessly mold it [lower-tiered things], and to being immutable to effects from it.

That "reason" in-and-of-itself has the claim of "It is impossible to prove something is above all dimensionality" as its foundation, so that appears to be the one and only actual justification you have for your opposition, so far. That seems worth noting down.

Oh, I didn't realise you were making such a point. I thought you were contending with equating R>F to a jump of one dimension, not the idea of comparing R>F to dimensions in the first place.

No clue what this means. But it doesn't seem terribly relevant, unless I'm mistaken, so I'll push it aside.

You don't need to justify a finite number where all finite numbers end, but you need to justify what the set of finite numbers is, even if in an iterative way. You are not defining the set of all dimensions, you are loosely alluding to it while truly referring to the undefinable idea of "all mathematics".

The finite numbers comparison does not work for this reason.

"All possible dimensional spaces" is not undefinable. You claim it is undefinable because "You can always trump whatever definition you give just by chucking in new axioms asserting that large cardinals exist." You can't really do that, though, since a space, regardless of how many dimensions it has, nevertheless has the quality of having dimensions. It has dimensionality, by definition. Therefore it falls under the definition "dimensionality." It's that simple.

Truth is: Formalized Set Theory isn't as fundamental as you think it is. It's just a system providing us with tools that we can use to "simulate" or "encode" our informal, day-to-day reasoning. So it is by no means the end-all-be-all and its axioms don't restrict the definition of terms like "dimension," especially since such basic logical notions aren't in the mathematical language of the theory itself, unlike the axioms. They're in a metalanguage, and as such not constricted to a single formulation of set theory.

 

[Agnaa]

That "reason" in-and-of-itself has the claim of "It is impossible to prove something is above all dimensionality" as its foundation, so that appears to be the one and only actual justification you have for your opposition, so far. That seems worth noting down.

No it doesn't. It has "this is the main quality of relevance with R>F examples and of how we currently treat dimensionality" as its foundation.

Really, I have no idea how you think "it's impossible to prove something is above all dimensionality" relates to it that reason at all.

I'm not going "Well, I would put it above all dimensionality, but that's impossible to prove, so I guess I have to make up something. Hmmm, how about uncountable infinity?" I'm going "Well, what's the minimum based on how it functions? Probably something like a point to a line, so uncountable infinity."

"All possible dimensional spaces" is not undefinable. You claim it is undefinable because "You can always trump whatever definition you give just by chucking in new axioms asserting that large cardinals exist." You can't really do that, though, since a space, regardless of how many dimensions it has, nevertheless has the quality of having dimensions. It has dimensionality, by definition. Therefore it falls under the definition "dimensionality." It's that simple.

That's not the only claim related to it I made. My other claim was:

Any attempt to try to define something that is "above all possible dimensionalities" is fruitless, as it will either have to be so maximally vague as to not communicate anything, or its definition could be easily worked around by adding more axioms.

You are now taking the "maximally vague as to not communicate anything" route. By seemingly defining it as "anything people say has dimensions".

I could construct something that literally has greater size than a construct you claim is "above all dimensions" and then declare it as a space, thereby making it composed entirely of dimensions, thereby contradicting its own definition of being above all of those. The issue with this seems to be the definition of "above all dimensions". You're trying to assign a fixed point to the "set of all sets", except even worse, by constructing "the set of anything that can be called a space". This quickly runs into nonsense.

Truth is: Formalized Set Theory isn't as fundamental as you think it is. It's just a system providing us with tools that we can use to "simulate" or "encode" our informal, day-to-day reasoning. So it is by no means the end-all-be-all and its axioms don't restrict the definition of terms like "dimension," especially since such basic logical notions aren't in the mathematical language of the theory itself, unlike the axioms. They're in a metalanguage, and as such not constricted to a single formulation of set theory.

I don't think it is. That's why I talked about adding axioms. I'm not confining my ideas to a standard formulation of ZFC.

 

[Ultima_Reality]

No it doesn't. It has "this is the main quality of relevance with R>F examples and of how we currently treat dimensionality" as its foundation.

Really, I have no idea how you think "it's impossible to prove something is above all dimensionality" relates to it that reason at all.

I'm not going "Well, I would put it above all dimensionality, but that's impossible to prove, so I guess I have to make up something. Hmmm, how about uncountable infinity?" I'm going "Well, what's the minimum based on how it functions? Probably something like a point to a line, so uncountable infinity."

If you unironically think that something above dimensionality can be reasonably placed as equivalent to a difference in dimensionality, then that's even worse, and you have, in fact, come to the point where you are objectively wrong. That's like saying "This thing has no volume or space or dimensions whatsoever, but it's equivalent to the size of that 4 m³ cube over there." You seem to think volume is some magical element that you just "have," when it isn't. It's a description, and if you fit that description, you have volume.

Earlier on, I noticed that a lot of the defenders of the current system (You included, given some of what you've said) often call the equalizations we do a "compromise." That directly contradicts your claim that you flat-out think "A dimensional jump" is a valid way to measure BDE and R>F. Either you claim it's perfectly logical (And thus not really a "compromise") or you accept it's illogical and indeed just something you made up based on textbook false equivalences (Which it is, since two things sharing a property does not make them equal)

You are now taking the "maximally vague as to not communicate anything" route. By seemingly defining it as "anything people say has dimensions".

I could construct something that literally has greater size than a construct you claim is "above all dimensions" and then declare it as a space, thereby making it composed entirely of dimensions, thereby contradicting its own definition of being above all of those. The issue with this seems to be the definition of "above all dimensions". You're trying to assign a fixed point to the "set of all sets", except even worse, by constructing "the set of anything that can be called a space". This quickly runs into nonsense.

Not "anything people say is a space," no, but "Anything that has the property of dimensionality." And that's not vague, just broad, and being broad doesn't make it vague. It's no more vague than "The set of all finite numbers," really, because you can indeed define any given dimensional space.

You also can't construct that "something," no. You can claim it exists, but that claim would be incorrect, because you'd basically be saying "There is a dimensional space above the set of all dimensional spaces," which is obviously paradoxical.
Your argument seems to basically be saying that the only way to be "superior" to anything is through being equivalent to some math number, and that a gap in power that's greater than all such numbers is thus inherently contradictory, since it'd be indirectly claiming the existence of the above. So your entire argument is non-sequiturs based on a faulty premise, that being "Any superiority has to be equivalent to some number or volume."

I don't think it is. That's why I talked about adding axioms. I'm not confining my ideas to a standard formulation of ZFC.

If your argument isn't "You can trump something beyond dimensionality by just adding large cardinal axioms that extend dimensionality!", then that's a bit better, at least.

 

[DontTalkDT]

I generally think Agnaa makes good sense so far. I didn't go much into whether or not we should equalize in my arguments, but I also think that it is in practice a much better system than to tier every system separately due to calling comparisons between them false equivalences.

He clarified what he was proposing on Discord, and I am now on board with it. There was actually a big difference between a true R>F Transcendence and a pseudo R>F. Some random gag of a cosmic character pulling a human out of a board game and pointing to said board game that he came from there is not evidence of 1-A and would simply not be anything beyond a regular transcendence. I was told that in order to qualify for a true R>F, there needs to be a beyond dimensional existence statement that is made literal. And it basically needs to perceive fiction as mere illusions; like how in a R>F setting, any humanoid from the R can hack or reprogram a Infinite-D being as they see fit is an example. And as for verse specifics, Chronicles of Narnia was considered a perfect example of a verse that qualifies. As Wood Between Worlds is a R>F over both "The Real World" and Narnia (Which are parallel universes of each other) and that there is an infinite cardinal amount of stackings of R>F above WBW and Aslan's Country happens to be at the very top of those infinite stacks.

I would still like a clarification from him directly.

For example, that a beyond dimensional existence statement is needed in addition to R>F has not been brought up before. And if such a statement is required, I wonder: Does this just need any (as in, do statements that only apply to the small spacetime of a verse count) or a general one (as in, all dimensions no matter how many)?

The additional "specifically like an illusion"-criteria would need clarification, too. As I pointed out in my last long post I think such statements can be taken to varying degrees of literal and we almost certainly don't wish to take the most literal one (the one where you can add more R>F since an illusion shouldn't stop you from adding something about an author writing the universe). What evidence makes a R>F difference have that specific nature? And would the infinite D example require actual feats or statements in that regard or would that be a consequence of the assumption of it being "like an illusion"?

I had the impression Ultima indicated before that such properties are in his opinion an automatic consequence of R>F. If that's not the case after all, I think making an explicit list of clear requirements of which additional evidence is needed beyond just R>F (and hence not being automatically implied by it) would be a good idea.

 

[Ultima_Reality]

I generally think Agnaa makes good sense so far. I didn't go much into whether or not we should equalize in my arguments, but I also think that it is in practice a much better system than to tier every system separately due to calling comparisons between them false equivalences.

For clarity's sake: I never said comparisons between two different things are false equivalences. If you say "X is superior to Y," then you're still making a comparison between X and Y. Saying X and Y are equal due to sharing some superficial similarity, however, is indeed a false equivalence. That gets into the topic of "Does X need to be equivalent to some number or volume to be superior to Y at all?", but that's something still being discussed.

---

As for the other stuff: I've already answered all of these questions before and my whole point in this thread is that qualitative superiorities (So, R>F and Type 2 BDE) are 1-A regardless of whether or not infinite dimensions are mentioned in the verse, so I feel no need to repeat myself at length here.

That said, to address DDM now: One thing I have to note is that I don't think "genuine" R>F Transcendences require -verbal- statements of Type 2 BDE to qualify for 1-A under these revamps. However, there does need to be some very good indication that the beings in the higher layers exist above the dimensions of the lower ones.
So, like I mentioned before: An example would be a case where the higher being is, literally, an author of books, and not a cosmic entity simply perceived as an author, which would mean that their layer has its own set of dimensions exclusively contained in it, and thus isn't really related to other layers by dimensional differences at all. In a way where even lower-dimensional things in their world would be above whatever exists in a lower layer.

Are you fine with that? @DarkDragonMedeus

 

[DontTalkDT]

One thing I have to note is that I don't think "genuine" R>F Transcendences require -verbal- statements of Type 2 BDE to qualify for 1-A under these revamps. However, there does need to be some very good indication that the beings in the higher layers exist above the dimensions of the lower ones. So, like I mentioned before: An example would be a case where the higher being is, literally, an author of books, and not a cosmic entity simply perceived as an author, which would mean that their layer has its own set of dimensions exclusively contained in it, and thus isn't really related to other layers by dimensional differences at all. In a way where even lower-dimensional beings in their world would be above whatever exists in a lower layer.

I hope you don't mind me asking about this, given that it ultimately is of relevance to me as well: I take it the last sentence there is an automatic consequence of the before, not a requirement that is separate to prove? I.e. the evidence required in the example is only that the character is protrayed as an author writing a book, yes?

 

[Ultima_Reality]

I hope you don't mind me asking about this, given that it ultimately is of relevance to me as well: I take it the last sentence there is an automatic consequence of the before, not a requirement that is separate to prove? I.e. the evidence required in the example is only that the character is protrayed as an author writing a book, yes?

Oh, let this exchange be a microcosm of all our debates up until this point.

If I say "We must be absolutely sure that it really is X, and not at all a case of Y in disguise. So it must be Z as well," then I mean "We must be absolutely sure that it really is X, and not at all a case of Y in disguise. So it must be Z as well." Showing a semblance of X alone is, in fact, insufficient.

If you want a good preamble of what exactly I mean when I say "It has to be literal," you can go check out the page image here (We don't have a profile for the character anymore, unfortunately, but if we did, he'd certainly fit the bill). I could elaborate further and further if you like, but this would be the ground of such elaborations.

 

[Agnaa]

If you unironically think that something above dimensionality can be reasonably placed as equivalent to a difference in dimensionality, then that's even worse, and you have, in fact, come to the point where you are objectively wrong. That's like saying "This thing has no volume or space or dimensions whatsoever, but it's equivalent to the size of that 4 m³ cube over there." You seem to think volume is some magical element that you just "have," when it isn't. It's a description, and if you fit that description, you have volume.

I don't think that something above dimensionality can be reasonably placed as equivalent to a difference in dimensionality. I just don't think that R>F differences are necessarily above dimensionality. I'm surprised you rushed to the former, instead of the latter.

Earlier on, I noticed that a lot of the defenders of the current system (You included, given some of what you've said) often call the equalizations we do a "compromise." That directly contradicts your claim that you flat-out think "A dimensional jump" is a valid way to measure BDE and R>F. Either you claim it's perfectly logical (And thus not really a "compromise") or you accept it's illogical and indeed just something you made up based on textbook false equivalences (Which it is, since two things sharing a property does not make them equal)

I don't think it's a compromise, I think it's a reasonable low-end between many reasonable ends. One could say that R>F is just a countably infinite power increase, but that seems a bit unreasonably low to me, I don't think the difference is quite that of a normal space to that same space extended infinitely. I don't think your idea is wholly without basis, I just think it's a ludicrous high-end, that's typically unjustified, and so it shouldn't be applied broadly. There's other higher ends I've seen suggested (such as three or four dimensional differences) which are also a bit high for my tastes, when talking about broad use.

Not "anything people say is a space," no, but "Anything that has the property of dimensionality." And that's not vague, just broad, and being broad doesn't make it vague. It's no more vague than "The set of all finite numbers," really, because you can indeed define any given dimensional space.

You also can't construct that "something," no. You can claim it exists, but that claim would be incorrect, because you'd basically be saying "There is a dimensional space above the set of all dimensional spaces," which is obviously paradoxical.

They aren't comparable, actually. I don't believe that there's anyone who has mathematically defined a mahlo-cardinal-dimensional space. And so, what you must be doing, to declare "beyond dimensions" as "beyond all mathematics", is baselessly assuming that there is some metric by which one can arbitrarily use any quantity, no matter the axioms to compose it that may give "quantity" a different meaning, to describe a dimensional space. And so, I can use the quantity of size (or whichever analogue you view as appropriate) in an R>F difference to define a dimensional space, causing a contradiction.

Yes this causes a paradox, but your willingness to assign literally any mathematical construct to a dimensional space without a mechanism shows that that step cannot be the one at fault. And so, I suspect that the faulty step is the one of claiming that there's a "size above the set of all dimensional spaces", using your definition of "dimension".

As I've said, your issue is essentially saying that there is a set of all sets. Except it's mildly obfuscated, it's a "thing of size where size matters" which is larger than "all things of size where size matters".

Your argument seems to basically be saying that the only way to be "superior" to anything is through being equivalent to some math number, and that a gap in power that's greater than all such numbers is thus inherently contradictory, since it'd be indirectly claiming the existence of the above. So your entire argument is non-sequiturs based on a faulty premise, that being "Any superiority has to be equivalent to some number or volume."

How many times do I have to tell you that it isn't?

I don't disagree with the general idea of there being superiorities beyond math. Really my point of disagreement is that if you're willing to extend "dimensions" arbitrarily to any possible set of axioms, that it should be able to extend to "superiorities beyond math" as well; there would still be "superiorities beyond math", they just wouldn't be said to be "beyond all dimensions". That or, that the "superiorities beyond math" are all an equivalent state of omnipotence, with no comparison between them.

 

[DontTalkDT]

Oh, let this exchange be a microcosm of all our debates up until this point.

If I say "We must be absolutely sure that it really is X, and not at all a case of Y in disguise. So it must be Z as well," then I mean "We must be absolutely sure that it really is X, and not at all a case of Y in disguise. So it must be Z as well." Showing a semblance of X alone is, in fact, insufficient.

If you want a good preamble of what exactly I mean when I say "It has to be literal," you can go check out the page image here (We don't have a profile for the character anymore, unfortunately, but if we did, he'd certainly fit the bill). I could elaborate further and further if you like, but this would be the ground of such elaborations.

So is that a yes or no? It really is characteristic that I ask a yes or no question and get no straight answer.

If there is an extra requirement you demand for it being "literal", beyond an author writing reality as fiction, which is fulfilled on the page you bring up, which is it?

 

[Ultima_Reality]

I don't think that something above dimensionality can be reasonably placed as equivalent to a difference in dimensionality. I just don't think that R>F differences are necessarily above dimensionality. I'm surprised you rushed to the former, instead of the latter.

I don't think it's a compromise, I think it's a reasonable low-end between many reasonable ends. One could say that R>F is just a countably infinite power increase, but that seems a bit unreasonably low to me, I don't think the difference is quite that of a normal space to that same space extended infinitely. I don't think your idea is wholly without basis, I just think it's a ludicrous high-end, that's typically unjustified, and so it shouldn't be applied broadly. There's other higher ends I've seen suggested (such as three or four dimensional differences) which are also a bit high for my tastes, when talking about broad use.

Up there you've said that you treat Type 2 Beyond-Dimensional Existence as equivalent to a single dimensional jump for the same reasons you do so with R>F. In my lenses, that's not at all consistent with what you are claiming to me now. Saying my idea is "not wholly without basis, just a very high-end interpretation" doesn't seem very consistent, either, seeing as early on you claimed that it is flat-out incoherent.

How many times do I have to tell you that it isn't?

I don't disagree with the general idea of there being superiorities beyond math. Really my point of disagreement is that if you're willing to extend "dimensions" arbitrarily to any possible set of axioms, that it should be able to extend to "superiorities beyond math" as well; there would still be "superiorities beyond math", they just wouldn't be said to be "beyond all dimensions". That or, that the "superiorities beyond math" are all an equivalent state of omnipotence, with no comparison between them.

They aren't comparable, actually. I don't believe that there's anyone who has mathematically defined a mahlo-cardinal-dimensional space. And so, what you must be doing, to declare "beyond dimensions" as "beyond all mathematics", is baselessly assuming that there is some metric by which one can arbitrarily use any quantity, no matter the axioms to compose it that may give "quantity" a different meaning, to describe a dimensional space. And so, I can use the quantity of size (or whichever analogue you view as appropriate) in an R>F difference to define a dimensional space, causing a contradiction.

Yes this causes a paradox, but your willingness to assign literally any mathematical construct to a dimensional space without a mechanism shows that that step cannot be the one at fault. And so, I suspect that the faulty step is the one of claiming that there's a "size above the set of all dimensional spaces", using your definition of "dimension".

As I've said, your issue is essentially saying that there is a set of all sets. Except it's mildly obfuscated, it's a "thing of size where size matters" which is larger than "all things of size where size matters".

Defining Cartesian Products R^κ where κ is some arbitrarily-large cardinal number isn't very hard at all. Go look up the definition of them on Wikipedia and see if you can find anything preventing you from using it to construct a space with a mahlo cardinal's worth of dimensions. You'll find no such thing.

Adding large cardinal axioms to Set Theory also doesn't change the meaning and definition of "quantity." Nor does it change the intension of "dimension." It changes no meanings and no definitions at all, in fact. So if your point is "Your definition of size is so broad that it'd also have to encompass something that allegedly trancends it, since it's already being declared to encompass all definitions of size by being declared to encompass all dimensionality" (I think it is that, at any rate), it's a mistaken one and honestly even poorer than I thought.

So, since the definitions of "quantity" and "dimensionality" are the same for any and all dimensions, defining some higher analogue of "size" above these definitions doesn't require that analogue to turn around and contain itself. That's just silly.

 

[Agnaa]

Up there you've said that you treat Type 2 Beyond-Dimensional Existence as equivalent to a single dimensional jump for the same reasons you do so with R>F. In my lenses, that's not at all consistent with what you are claiming to me now. Saying my idea is "not wholly without basis, just a very high-end interpretation" doesn't seem very consistent, either, seeing as early on you claimed that it is flat-out incoherent.

We don't treat Type 2 BDE as being beyond every single dimension.

These characters aren't necessarily superior to spacetime on every level, but just within the scope which they are shown.

If it was a character above spacetime on every level, I wouldn't draw an equivalence in power to an uncountably infinite power increase.

I view the "above all mathematics such that there are no different sizes and every verse scales to exactly the same power" interpretation of it as "just a very high-end interpretation", I'd also view the "above all dimensionality" with a rigorous definition of dimensionality as "just a very high-end interpretation". I view the fusion of both as incoherent.

Fair enough if you view that as inconsistent with what I said 6 weeks ago, I don't remember my thought process at the time, and whether it actually changed or if I'm just expressing myself better now.

EDIT: Looking back, I only said that "transcending dimensionality entirely", when not rigorously defined, was incoherent, and I still hold that view. Although any particular rigorous definition would probably end up just being "a very high-end interpretation".

Defining Cartesian Products R^κ where κ is some arbitrarily-large cardinal number isn't very hard at all. Go look up the definition of them on Wikipedia and see if you can find anything preventing you from using it to construct a space with a mahlo cardinal's worth of dimensions. You'll find no such thing.

Adding large cardinal axioms to Set Theory also doesn't change the meaning and definition of "quantity." Nor does it change the intension of "dimension." It changes no meanings and no definitions at all, in fact. So if your point is "Your definition of size is so broad that it'd also have to encompass something that allegedly trancends it, since it's already being declared to encompass all definitions of size by being declared to encompass all dimensionality" (I think it is that, at any rate), it's a mistaken one and honestly even poorer than I thought.

So, since the definitions of "quantity" and "dimensionality" are the same for any and all dimensions, defining some higher analogue of "size" above these definitions doesn't require that analogue to turn around and contain itself. That's just silly.

While that holds true for "ZFC" and "ZFC with additional large cardinal axioms", I seriously doubt that it holds true over "literally any set of mathematical axioms that could be created".

 

[Agnaa]

So is that a yes or no? It really is characteristic that I ask a yes or no question and get no straight answer.

If there is an extra requirement you demand for it being "literal", beyond an author writing reality as fiction, which is fulfilled on the page you bring up, which is it?

Ultima's answer was very clear.

He said "An example would be an author writing a book."

You asked "Is the only evidence required that the character's portrayed as an author writing a book?"

He responded "I mean what I say. An example that would qualify is this scan, showing a character portrayed as an author writing a book."

Or in short, the answer was "yes".

 

[Ultima_Reality]

While that holds true for "ZFC" and "ZFC with additional large cardinal axioms", I seriously doubt that it holds true over "literally any set of mathematical axioms that could be created".

I don't understand the distinction being made here. Could you clarify? "ZFC and its extensions" and "All mathematics" are virtually indistinguishable to me, so what mean you by the latter, exactly?

 

[DontTalkDT]

Ultima's answer was very clear.

He said "An example would be an author writing a book."

You asked "Is the only evidence required that the character's portrayed as an author writing a book?"

He responded "I mean what I say. An example that would qualify is this scan, showing a character portrayed as an author writing a book."

Or in short, the answer was "yes".

Is that so? I thought when he pointed out how it has to be an especially "literal" interpretation he meant there are additional criteria to be taken into consideration.
But if it's indeed just meant to be an extended form of saying "yes, your interpretation of what I said is right" then that's good.
Making sure that my interpretation of what he says aligns with what he says is the point of the question. Trying to take as few risk with misinterpreting arguments as possible and all that.

 

[Agnaa]

I don't understand the distinction being made here. Could you clarify? "ZFC and its extensions" and "All mathematics" are virtually indistinguishable to me, so what mean you by the latter, exactly?

Because there are ways of engaging with mathematics that don't involve the axioms of ZFC.

One simple enough for me to know and regale only involves two axioms:

1. There is a successor function S(x), which maps one unique input to one unique output.
2. The number 0 is never the output of S(x).

You can add another axiom (the positive integers is the smallest such collection of these), to get the positive integers, as we conventionally understand them. And off of these, addition and multiplication can be built. But without that additional axiom, there can be other closed loops of any finite length which operate in a circle, such that the successor of yota is gamma, and the successor of gamma is yota, with no proper mathematical relation to the rest of the integers.

In such a system distinct from ZFC (iirc, predating it), and as such, lacking R entirely, does it make sense to talk about how much a yota amount of dimensions would be, by trying to shove it into R^n?

And more broadly, I'm certain that "any possible mathematical axiom" would extend to things far weirder than this.

 

[Ultima_Reality]

Because there are ways of engaging with mathematics that don't involve the axioms of ZFC.

One simple enough for me to know and regale only involves two axioms:

1. There is a successor function S(x), which maps one unique input to one unique output.
2. The number 0 is never the output of S(x).

You can add another axiom (the positive integers is the smallest such collection of these), to get the positive integers, as we conventionally understand them. And off of these, addition and multiplication can be built. But without that additional axiom, there can be other closed loops of any finite length which operate in a circle, such that the successor of yota is gamma, and the successor of gamma is yota, with no proper mathematical relation to the rest of the integers.

In such a system distinct from ZFC (iirc, predating it), and as such, lacking R entirely, does it make sense to talk about how much a yota amount of dimensions would be, by trying to shove it into R^n?

And more broadly, I'm certain that "any possible mathematical axiom" would extend to things far weirder than this.

That's not really what I asked for, so let me rephrase: Do you agree that "Being above dimensionality" would place you above all the cardinals described in ZFC and its extensions, as those all share a common notion of dimensionality? With that said, I add: How exactly do you define "All mathematics" in a way where it encompasses the prior definition of "Above dimensionality"?

 

[Agnaa]

That's not really what I asked for, so let me rephrase: Do you agree that "Being above dimensionality" would place you above all the cardinals described in ZFC and its extensions, as those all share a common notion of dimensionality? With that said, I add: How exactly do you define "All mathematics" in a way where it encompasses the prior definition of "Above dimensionality"?

"dimensionality" is an arbitrary term, once we get past real-world use-cases like R^R. You could define it that way, and that would be more reasonable. Although I would still hold some concerns, given the potential addition of literally any possible axioms, and any possible number of them, to ZFC, would you confidently assert that all of them leave "quantity", "dimensions", and R intact?

I think "ZFC and current conventional extensions" would be a more reasonable bar to set, really.

I'm not sure whether your second question still makes sense in light of this answer, so I'll hold off on answering it until you respond again.

 

[Ultima_Reality]

"dimensionality" is an arbitrary term, once we get past real-world use-cases like R^R. You could define it that way, and that would be more reasonable. Although I would still hold some concerns, given the potential addition of literally any possible axioms, and any possible number of them, to ZFC, would you confidently assert that all of them leave "quantity", "dimensions", and R intact?

I do confidently assert that, yes. There is no fundamental difference between a set of 4 points and a mahlo cardinal's worth of points, for example. Neither is there any fundamental difference between a set of 3 dimensions and a set of inaccessibly-many dimensions. Basic logical notions such as these don't change just because you've affirmed the existence of larger numbers, since as I've said they are not in a theory but in a metatheory. Much like, say, Godel's Incompleteness Theorems, which are metatheorems about formal systems, and which thus apply to any of them once certain factors are in place.

 

[Agnaa]

I do confidently assert that, yes. There is no fundamental difference between a set of 4 points and a mahlo cardinal's worth of points, for example. Neither is there any fundamental difference between a set of 3 dimensions and a set of inaccessibly-many dimensions. Basic logical notions such as these don't change just because you've affirmed the existence of larger numbers, since as I've said they are not in a theory but in a metatheory. Much like, say, Godel's Incompleteness Theorems, which are metatheorems about formal systems, and which thus apply to any of them once certain factors are in place.

Perhaps you're right about those specific changes, since they don't involve changing anything fundamental related to dimensions. But any possible extensions of ZFC also includes ones which involve axiomatic redefinitions of sizes, which apply at all levels.

Unless you think that such a change occurring, even through any number of axioms of arbitrary content, would be impossible.

 

[Ultima_Reality]

Perhaps you're right about those specific changes, since they don't involve changing anything fundamental related to dimensions. But any possible extensions of ZFC also includes ones which involve axiomatic redefinitions of sizes, which apply at all levels.

Unless you think that such a change occurring, even through any number of axioms of arbitrary content, would be impossible.

Extensions of ZFC are basically just theories that contain ZFC and also have more tools that allow us to do more stuff than ZFC alone, so everything that's correct in ZFC would be correct in an extension of ZFC as well. Extending the theory doesn't really constitute fundamental changes of its basic notions. And if you do apply such changes, you're just defining something that's... not really ZFC, anymore.

And I'm frankly not terribly convinced that fundamentally alternative systems of that sort factor here (If they can exist), yes. They'd basically hold none of the notions we even use to scale things by that point.

 

[Agnaa]

Extensions of ZFC are basically just theories that contain ZFC and also have more tools that allow us to do more stuff than ZFC alone, so everything that's correct in ZFC would be correct in an extension of ZFC as well. Extending the theory doesn't really constitute fundamental changes of its basic notions. And if you do apply such changes, you're just defining something that's... not really ZFC, anymore.

And I'm frankly not terribly convinced that fundamentally alternative systems of that sort factor here (If they can exist), yes. They'd basically hold none of the notions we even use to scale things by that point.

Then at least, couldn't there be a change, such that at points were ZFC gives an ambiguous answer, there is an altered definition of size that gives a concrete answer in higher regions?

Still, this is really starting to feel like I'm nitpicking. If you did drop your definition of "all dimensions" from "all mathematics" to "ZFC and conventional extensions that don't noticeably change how size functions", that would be sufficient for almost every single verse in existence.

There would still be the theoretical possibility of something reaching 1-A in this new system through mathematics alone, but that would require the story explicitly laying out novel axioms that alter how size functions, and we'd have to verify that they do, so I seriously doubt that would ever come up.

In the imaginary space of how much stronger than tiers below 1-A that would make such characters, it does drop that gap by some amount (i.e. I disagree, and think it would still be relevant to the notions of how we scale things), but that would likely never actually matter on the site.

If you worked with that alteration, I'd still find that to be a needlessly high-end interpretation, but I wouldn't see it as incoherent.

 

[Ultima_Reality]

Then at least, couldn't there be a change, such that at points were ZFC gives an ambiguous answer, there is an altered definition of size that gives a concrete answer in higher regions?

I don't believe so, no. Once you start messing with such primitive notions, you'll get a system that's just inconsistent with ZFC, I reckon.

Still, this is really starting to feel like I'm nitpicking. If you did drop your definition of "all dimensions" from "all mathematics" to "ZFC and conventional extensions that don't noticeably change how size functions", that would be sufficient for almost every single verse in existence.

There would still be the theoretical possibility of something reaching 1-A in this new system through mathematics alone, but that would require the story explicitly laying out novel axioms that alter how size functions, and we'd have to verify that they do, so I seriously doubt that would ever come up.

In the imaginary space of how much stronger than tiers below 1-A that would make such characters, it does drop that gap by some amount (i.e. I disagree, and think it would still be relevant to the notions of how we scale things), but that would likely never actually matter on the site.

I didn't really "drop" anything so much as we found out there were communication issues between the two of us. Mind you: My proposals do include a tier for something like (What you referred to as) "above all mathematics such that there are no different sizes and every verse scales to exactly the same power," but that's what I defined for Tier 0. What we're talking about right now is what I defined for 1-A.

If you worked with that alteration, I'd still find that to be a needlessly high-end interpretation, but I wouldn't see it as incoherent.

We can work on that. First, though, we need to settle whether or not these things are coherent.

 

[Agnaa]

I don't believe so, no. Once you start messing with such primitive notions, you'll get a system that's just inconsistent with ZFC, I reckon.

Does it have to involve messing with the primitive notions? Couldn't it just define new aspects, and define how the old aspects compare to the new, such that within the new aspects, new behaviour emerges?

And to clarify, by "inconsistent with ZFC" do you exclusively mean "sometimes declares truth values that differ from conventional ZFC, for statements other than ones which ZFC finds inconclusive"?

If so, that makes me wonder whether there are any systems which are considered extensions of ZFC, but are "inconsistent" with it by that definition, but I don't know enough about strange axiomatic systems to answer that myself.

I didn't really "drop" anything so much as we found out there were communication issues between the two of us.

I didn't mean to imply you already had. I was using "if you did" in the potential future tense, and "drop" as in "alter the definition to be lower" rather than "abandon the idea of".

We can work on that. First, though, we need to settle whether or not these things are coherent.

If there's more to do on that end, let me know.

 

[Ultima_Reality]

Does it have to involve messing with the primitive notions? Couldn't it just define new aspects, and define how the old aspects compare to the new, such that within the new aspects, new behaviour emerges?

And to clarify, by "inconsistent with ZFC" do you exclusively mean "sometimes declares truth values that differ from conventional ZFC, for statements other than ones which ZFC finds inconclusive"?

If so, that makes me wonder whether there are any systems which are considered extensions of ZFC, but are "inconsistent" with it by that definition, but I don't know enough about strange axiomatic systems to answer that myself.

With regards to notions such as "dimension" and whatnot, I wouldn't say that's possible, since they're not really present in the language of the theory itself, but in the metalanguage instead, as I said. Under those lenses, statements about dimensionality as an intensional notion, to begin with, are not something ZFC can refer to.

I didn't mean to imply you already had. I was using "if you did" in the potential future tense, and "drop" as in "alter the definition to be lower" rather than "abandon the idea of".

Well, to be clear: I didn't alter anything, really. It looks like the better part of this discussion indeed was just a miscommunication issue between us. I'm glad it was just that.

If there's more to do on that end, let me know.

Well, let's start with a question: Given the above conversation, would you say that "Above dimensionality" (In the sense or surpassing the very notion and meaning of having dimensions) places you above the cardinals described in ZFC and all its "conventional" extensions? (Those extensions being ones involving additions of large cardinals). The current Tiering System has a rather strange insistence on limiting even statements such as that to only what physically exists in a verse's cosmology, and that's largely where my disagreement lies.

 

[Agnaa]

With regards to notions such as "dimension" and whatnot, I wouldn't say that's possible, since they're not really present in the language of the theory itself, but in the metalanguage instead, as I said. Under those lenses, statements about dimensionality as an intensional notion, to begin with, are not something ZFC can refer to.

That's not a well-defined notion of dimensionality, if it's not within the theory and not something external to it that you can point to and which we can investigate the limits of. Which would then loop us back to my earlier post about how something so general that it can apply to any arbitrary extensions of axioms, should also be able to apply to R>F differences.

You responded to that by beginning discussion about Cartesian Products, but here I'm gesturing at "would it ever be possible to add axioms to ZFC such that you cannot take the Cartesian Product of certain newly-introduced ordinals".

Well, let's start with a question: Given the above conversation, would you say that "Above dimensionality" (In the sense or surpassing the very notion and meaning of having dimensions) places you above the cardinals described in ZFC and all its "conventional" extensions? (Those extensions being ones involving additions of large cardinals). The current Tiering System has a rather strange insistence on limiting even statements such as that to only what physically exists in a verse's cosmology, and that's largely where my disagreement lies.

It depends on which definition of "dimensionality" you use, since that's a very loose and arbitrary term.

Without further in-verse context, I'd just cap it at standard ones used within real-world theories, R^R. And I believe that's where our Tiering System currently limits it; didn't we, in the past year, have a thread about this topic where we came to that conclusion? That you needed some sufficient amount of statements, but at some points, you could generalise to Low 1-A/1-A without infinite dimensions?