Earlier in the thread ExcelsisBerny presented an interpretation, or more head-canon really, about "atomic information" which is a term never stated in the light novel, but even without that, its wrongly used here:
Ah I see, so you're still throwing unproductive rhetorical fallacies. I can never understand the point of saying another person is interpreting something through a head canon lens, when backed up by textual references but alright. Also, 'atomic information' doesn't need to be stated when the definition is invoked derivatively by the structure of possible worlds. As we will observe, even from the very pieces of evidence you're using to contest this.
And the part of the light novel she uses to lie about this, is a scan she used that goes against this:
It doesn't:
Maybe opening up all the possibilities was a mistake. Space is finite. Characters are finite. But their combinations are infinite. Opening up a possibility meant breaking down the walls of the worlds within Akuto that might have been. It was the equivalent of giving birth to a new universe within himself. Of course, the tools for this universe weren’t limited to what was inside Akuto. The gods of the outer universe, even they became a part of the story. As a result, the story became chaos. What does it mean when a story turns into chaos? You can find the answer within one of our oldest stories: “The Tower of Babel.”
From what we are told in chapter 4, in the novel. The construction of these possible worlds is conditioned by:
- Finite space (funny)
- Finite characters
Finite space is partly the atomic fact here, because complex syntax/propositions or characters are modeled—with the presupposition of the fact that the space is finite. Which is tentative to the logical space at hand being bounded, especially in the way in which Shin defined Logical Totalitarianism. You can't make the radically leap “space is not finite” as one of the combinations to construct a possible world, because reconstruction of the world requires that space be 'finite', which is what we're told in chapter 4 explicitly:
Maybe opening up all the possibilities was a mistake. Space is finite.
The novel beats in the idea of this 'logical space' as finite, not only once by twice, through clauses that are right next to one another. Because right after that, you're told the characters of which the construction of possible worlds are grounded by—are also as finite as the space is:
But their combinations are infinite. Opening up a possibility meant breaking down the walls of the worlds within Akuto that might have been.
Which is weird, even something as elementary as the enumeration of natural numbers—in formal theories like Peano Arithmetics yield infinite characters.
Because each variable within the entire process of enumeration i.e {x1, x2, x3..... N}, where for each element of the set. It is mapped directly to a unique natural number N, is at least countably infinite. Now this isn't to say countable sets are impossible to construct within any possible world, but the proposition “one can exemplify all elements of a set of natural numbers N, through enumeration” or establish an algorithm that generates all natural numbers and instantiates all of them fails.
At best, the existence of them would be axiomatic, with no further need to possess infinite characters, to assign to each element of a set a unique natural number N. Which obviously means at least one and more propositions fail in this so-called 'space of all possible worlds'. As if the finite space wasn't bad enough already.
Correct. Anything that can be put into writing can happen here. Which means that nothing will happen that can’t be expressed in words.
~ Demon King Daimaō Volume 13 Chapter 3
This statement would fail miserably in even justifying the radical nature of the Logical Space, because it's obviously hyperbolic in nature. It doesn't take much to demonstrate that. Because even by admission of the contests against this CRT. Need to assume that some propositions fail in some possible world, like the proposition “Akuto Sai can construct a possible worlds, where the law of identity fails” as a meta-logical statement within the confines of the verse fails.
And just to be clear, I'm not saying that's even logically possible, because it's obviously not. But it is a statement that can be written, but a statement that fails regardless. It doesn't help that this statement is overridden by the very source material: chapter 4 as cited. In which some statements are fundamentally true irrespective of the character combinations.
Just clinging to “whatever can be written is possible here” is too much of an oversimplification to count as a meaningful talking point. Even explicitly going by the source material itself.
As you can see, there is nothing about atomic information as suggested by ExcelsisBerny. Instead, if you look at the first paragraph, its about linguistics and things outside of just data being used.
And just for clarity, atomic facts have to do with linguistics too. So referring to linguistics is not contra-distinguishing the linguistic facts considered fundamental, before character combinations and atomic facts. Because atomic facts are also linguistic facts, that cannot be broken down to further components—with respect to the combinations or propositions that are metaphysically possible in a Logical Space. Again, the examples of the facts at hand are listed in the source material:
- Space is finite
- Characters are finite
Infinitely combinations, which represent configurations of those atomic facts, are a derivative of the atomic facts above.
Nothing more to say here, blatant head-canon from OP to try and limit linguistic possibilities.
You mistook your misapprehension of atomic facts, for her defending 'headcanon'. Which is why I said it's not productive to say another person discussing in the thread is defending headcanon, because they disagree with you. It seems in this case, it is less of a 'headcanon' and more of you not understand concretely what she means by atomic information or facts. Just focus on the substance, instead of compensating for the lack of thereof by pure rhetoric. It's really unhealthy for the discussion really.
Additionally, it only makes sense for them to not be limit to permutations/potentialities of what's beneath the Afterlife, since the whole explanation of Possible Worlds is based on modality of language (every theoretical possible world):
Ersatzist modal realism is based on linguistics and there are many types, with many restrictions of their own and many not being maximal. So I'm kinda confused here.
Berny’s response here is circular because she assumes the very conclusion she’s supposed to demonstrate. That the framework of the Law of Identity and its associated structure are only “High 1-A baseline.” She treats “unreachable” as synonymous with “conceptually above but still within a High 1-A system,” without ever proving that this interpretation applying here, or responding to me to my earlier explanations of this issue.
No, her grip is that the High 1-A+ rating thus is unjustified. And even I have been waiting for a concrete justification, because the blog has it that:
- The space that models all possible worlds is not High 1-A+.
- C: To be beyond it is not High 1-A+
Yet the justification for the anti-universe being High 1-A+ includes:
- It being beyond the space of all possible worlds
But the space is not High 1-A+?
- C: Therefore it is beyond an arbitrary layer in High 1-A, which fails to justify its placement at High 1-A+.
Her being a logical law has already been contested. That's not a justification whatsoever, Shin has already explained that. But I can cash it out myself, since he's busy with exams right now: It will be especially nitpicky to have logical laws that prescriptively bind the symmetric relation of Essentia (a) and Esse (b). Of which Thomistic doctrines utilise this relation to confer Divine Simplicity. If being a logical law was a jump to High 1-A+, but logical laws prescriptively bind Tier 0. Then either
- (I) Tier 0 according to the people against the CRT is metaphysically subordinate to High 1-A+
Or
- (II) Tier 0 is High 1-A+
- (III) But Tier 0 is neither, therefore the High 1-A+ justification through logical laws fail.
- Once more, we still have no justification for the High 1-A+ rating in page 2 no less.
That's why she has been calling it a contradiction, the evasive responses to her critiques are the reason why she concluded that TLOI is High 1-A and no more. Just ignoring every other critique to say 'circular reasoning' doesn't cut it, because you have to engage fully with the arguments to begin with, before calling out circular logic from conclusions arbitrarily.
It's page 2 now, are you ready to provide a justification for the High 1-A+ rating?
The issue here is that instead of addressing the false premise that the CRT relies on, most importantly, the incorrect assumption that the Afterlife “contains” the hierarchy it’s part of literally, she shifts the burden of proof by demanding justification for why the accepted blog should still stand, despite her own argument being the one proposing change.
Hi, hello, I'm Nova. What you're citing here as something you're responding to:
"It, again, assumes an authoritative position as the very truthmaker of the position. It just goes circular, doesn't engage meaningfully with the points of contention. So what's the reason for High 1-A+? Blogs have been accepted just to be later denounced? What exactly does the blog being accepted have to do with the potential for inconsistencies within the blog?"
Is me not her, because every argument posited in the blog has been contested. So I don't know why you're treating it as if she was the one 'shifting the burden', but I'll give you the benefit of the doubt and assume it was a mistake. There's no burden shift here, provide the argument for High 1-A+. Period.
This reversal tries to make the defending side (me) prove the negative (that no contradiction exists) while her side never backs up its own claim. Oh and also by dismissing the observation of a false premise as unproductive a red herring gets commited, steering away from the actual logical flaw that invalidates the CRT’s very basis. (And should be dismissed on that alone, IMO.)
~ StorytellingDemonKing
K, moving on, so what's the reason for High 1-A+? Because surely it's not through the statements that have been contradicted no?
1. Categorical error
There have been a few misunderstandings when it comes to what I have said, interpreting things I said in ways I didn't.
~ StorytellingDemonKing
Mind you, you cited this as evidence for the possible worlds in the afterlife being unbounded:
Correct. Anything that can be put into writing can happen here. Which means that nothing will happen that can’t be expressed in words.
To which I responded with:
This statement would fail miserably in even justifying the radical nature of the Logical Space, because it's obviously hyperbolic in nature. It doesn't take much to demonstrate that.Because even by admission of the contests against this CRT. Need to assume that some propositions fail in some possible world, like the proposition “Akuto Sai can construct a possible world, where the law of identity fails” as a meta-logical statement within the confines of the verse fails.
And just to be clear, I'm not saying that's even logically possible, because it's obviously not. But it is a statement that can be written, but a statement that fails regardless. It doesn't help that this statement is overridden by the very source material: chapter 4 as cited. In which some statements are fundamentally true irrespective of the character combinations.
Just clinging to “whatever can be written is possible here” is too much of an oversimplification to count as a meaningful talking point. Even explicitly going by the source material itself.
~ Super_Nova
So not sure where the category error is, because you did insinuate that. By clinging to the statement “anything that can be put into writing can happen here”, so the statement is either radically true in all possible worlds or fails for some possible worlds. If it fails for some possible worlds, the afterlife has possible worlds constrained by higher realities.
It just repeats the claim that his starting point was finite, which the novel already acknowledges. (Since he can reality warp and make it infinite anyway due to controlling a logical space.)
~ StorytellingDemonKing
Not really supported by the novel, but whatever:
Maybe opening up all the possibilities was a mistake. Space is finite. Characters are finite. But their combinations are infinite. Opening up a possibility meant breaking down the walls of the worlds within Akuto that might have been.
The two predicates of logical space:
- Space is finite
- Characters are finite
Has the conjunction “But their combinations are infinite”. For Akuto Sai to warp reality to make it infinite, he needs the finite space as that predicate is conjunctive to the construction of combinations that allow for the generation of possible worlds. It's especially damning because the first sentence says “opening up all possibilities was a mistake”. So amidst all possibilities that were opened up, the space with which they were contained is finite and characters were finite.
This sentiment is echoed in chapter 3, where they say:
“If the world we lived on in life was fictional, so is this one. So I was thinking, what’s the difference?” he said. ”And the difference is whether there’s a wall between us and the outside. When we were alive, we lived in a world with a wall. And now, there’s no wall here. No matter what direction you go in three dimensional space, you come back to where you started. You can go forever, but it’s finite.”
For whatever is considered a fictional world [quantifies all possible worlds, as they are all equally fictional worlds to TLOI]. They possess two structural differences:
- It has a wall
- it has no wall
For fictional worlds with no walls, they behave like topologically unbounded spaces. Whereby no matter how long you travel, you'll come back to a point where you began your journey. But
nevertheless, even for fictional worlds without boundaries—the space is finite precisely because you return to where you began your journey. This is just extremely consistent in the novel, for anyone to just arbitrarily assume that Akuto Sai can just rewrite the Logical Space to be infinite.
Not only that, but it is metaphysically impossible even independent of the novel. Because to use Logical Space to construct possible worlds, requires that you use modality constrained to Logical Space. Its structural limits are limits of what you can actualize in the Logical Space. Akuto Sai would need power from what is beyond the Logical Space to change the Logical Space, because the Logical Space cannot be changed by itself. Because it is already the space of all possibilities, including all possible changes that can occur within it.
Not only does it require that you stretch the consistency of the novel, but just stretch the logical consistency of your position itself. That's a harder bar to commit to and a ridiculous hill to die on, instead of just admitting that the Logical Space has atomic constraints. Why is anyone other than you, even obligated to follow this interpretation irrespective of what is described within the novel?
To illustrate why this point doesn't work, let's remember that possible worlds are based on every theoretically possible world that can be put into writing, not being limited to what's inside Akuto (data):
~ StorytellingDemonKing
Good thing I've responded to this argument twice now, I'll be gearing to see how you go around it.
- (a) Considering that not holding that statement to be hyperbolic, when taken seriously—means Akuto Sai can just write “the Law of Identity fails”. If so, will the Law of Identity fail or is the Law of Identity beyond the afterlife? If the law of identity is beyond the afterlife, then statements that can be written fail in the afterlife.
- (b) I anticipate your next response to this, being that “the Law of identity cannot be written in the afterlife”. If so, it means some statements cannot be written in the afterlife, so what's your proof of the statement “Logical Space as the space of all possible worlds, can be what it is not, for it can be rewritten to be infinite. Even when it is atomically regarded as finite”?
What else I didn't respond to, regarding the fallacies, is because it seems irrelevant and just evasive.
Now, if I understand your atomic facts correctly... the issue is that DKD explicitly defines “possible worlds” in its own internal logic. Because of the given definitions and additional context surrounding this series, I would personally argue from it's own definitions, and have been doing so. And, the novel defines this as character finitude with infinite combinations. That is, finite “building blocks” that can yield infinite logically valid stories. (Technically speaking, I'm pretty sure this would be the case for High 1-A+ modal realism anyhow, but staff can correct me if I'm wrong, I guess.)
~ StorytellingDemonKing
Shin already responded to the infinite combinations facet to not be apt, as an argument against Logical Space being bounded, you just repeated what you said earlier in the page—in pretense that you actually responded to Shin. Bounded Logical Spaces can generate infinite combinations, while still being constituted by atomic facts.
Finite components (characters, data, etc.) combine to yield infinite possibilities..
~ StorytellingDemonKing
This doesn't break away from Tractatus Logico-Philosophicus:
2.013 Every thing is, as it were, in a space of possible atomic facts. I can think of this space as empty, but not of the thing without the space.
2.0131 A spatial object must lie in infinite space. (A point in space is an argument place.)
Objects for Wittgenstein exist in an infinite space and:
2.0201 Every statement about complexes can be analysed into a statement about their constituent parts, and into those propositions which completely describe the complexes.
Every statement about complex objects that exist within infinite space, can be analysed into a statement about their parts that constitute them. Including with their nature aggregates in ontology, which have to do with their proximity to one another (i.e spatial relation). Any particle that constitutes any object for example in three-dimensional space, can be broken down infinitely, by its partitions as an aggregate. Because any object is constituted by particles and any particle can be in any possible location for every n in N which reflects its possible states in superposition (i.e superposition). And N can be ∞, so you can make infinitely many combinations/propositions about the position of a particle in infinite space.
Even with a finite amount of atomic facts for the general Logical Space, this overtly oversimplifies Shin's point honestly. And this doesn't account for the fact that Shin wasn't suggesting that the verse functions under Wittgensteinian Logical Space. He was just making an example of the differences between a bounded Logical Space and an unbounded Logical Space essentially. At least that's what I got from what he said, so even if it wasn't a Wittgensteinian Logical Space—it doesn't immediately suggest that it's an unbounded Logical Space. That will be valid of an assumption to make logically.
which also yield infinite spaces and cosmoligies, so to my knowledge, a rejection of Wittgenstein’s determinacy.
Is what the novel says, in what sense? I don't know. The verse is already 1-A+, Logical Space being finite can mean many things, even if we assume geometrically it would be taken to be infinite. The same way a 'finite being' scholastically would just be any Being contingent on an infinite Being (The Absolute).
You can't hide behind the argument
“anything that can be written, can be actualized within it” now. So it appears to me that the statement is hyperbolic, to anyone who reads it and takes it seriously.
I wonder if maybe DKD anticipates this to an extent. I'll try to work with the narrative:
- The Afterlife is a logical closure of all possible propositions/stories (logical space), with infinite layers of fictions above.
- The Anti-Univers” is a negation of that closure and stories (the void within void).
- The Law of Identity being the absolute that grounds even the negation.
- (1) Is not High 1-A+
- (2) One is beyond a structure that's not High 1-A+
- (3) is beyond a structure that's not High 1-A+
Solid High 1-A to me at best, the verse doesn't anticipate anything. Two statements are being used to stretch the context for the verse to be High 1-A+, the second highest tier in the wiki being reached through two statements that can logically can fit for just High 1-A for the Anti-Universe and TLOI, whilst the afterlife remains 1-A+.
Mostly a spitball here, so I'll wait for your response to this. The difference might be you assuming real logical totalitarianism, while I'm trying to work with, and analyze, a fictional metaphysical analogue in a way that could fit the current standards.
Which has to do with the standards, just as the standards refuse Lewisian Modal Realism not being High 1-A+ because all possible worlds are confined by spatiotemporality. And the same way Wittgensteinian Logical Space is also not High 1-A+ due to structural constraints, that—if you assume it to be High 1-A+—High 1-A+ collapses below 1-A; let alone High 1-A.
I wonder if this case really applies here. Dimensional hierarchies are quantitative, while DKD's overarching story hierarchy(-ies) are qualitative. A model already described by Yoshie where each layer contains infinite possibilities and then infinite layers of fiction above that.
He was making an analogy about the different ways infinity manifests, both through quantity—in this case the amount of combinations. And structural constraints, in which the Logical Space is described as finite in some way; perhaps by measure to higher planes.
Now, as discussed by me before, since Akuto would be creating every single theoretically possible world, a world with 1-A+ hierarchy could very well be made since the wording combination for such a hierarchy is present which then in retrospect makes the larger system Afterlife is a part of High 1-A and above (meta-qualitative), and the baseline for this Afterlife hierarchy would be 1-A+, ergo why Afterlife is High 1-A. (Afterall, as I have said before, the Afterlife isn't integrating the actual hierarchy it's part of. So, the hierarchy that could be made from existing data and words would be within the Afterlife as possible worlds were defined by the LN.)
Refer to the
four arguments I gave against the maximality of this statement:
Correct. Anything that can be put into writing can happen here. Which means that nothing will happen that can’t be expressed in words.
~ Demon King Daimaō Volume 13 Chapter 3
Because this has already been contested, even earlier by Bern. Who, you wrongfully accused of committing a categorical error.
So essentially you want us to assume the statement to be maximal, but nitpick its maximality—by also assuming certain statements can't be postulated in the Afterlife? Including the propositions that may assert that the TLOI and the Anti-Universe being beyond the afterlife? Because significantly
huge and I mean
HUGE leaps in logic are being made, by using the statement as a tool.
Then the convenient spot you want the anti-universe to be in, is the spot where certain propositions that can be written cannot be asserted? In the space where all propositions that can be written are asserted?
It seems to me then, that not all propositions can be asserted. It would be easier set than done if the source material actually directly stated; or discussed infinitely layered hierarchies for 1-A+.
Being confined in some singular proposition in the space, which it doesn't. It just posits an infinitely layered hierarchy arbitrarily, without specifying whether or not it's confined by a few propositions in the afterlife.
Just to be clear, you want the people against the CRT to assume, just with these two statements alone by the way:
Correct. Anything that can be put into writing can happen here. Which means that nothing will happen that can’t be expressed in words.
You hated fiction, while living inside a fiction. You had a fetish for revealing that which was fictional, and kept doing it again and again. You would destroy what seemed to be a closed system, only to activate the system that lay beyond it. A multilayered fiction. An infinite regression. It’s a hell that continues forever. Which makes this... difficult.
That there's not only an infinite regression, through these two statements for 1-A+. But an infinite regress through just these two statements, for 1-A+ and then High 1-A? By just these two statements. Which, by the way, also conveniently the first statement doesn't apply to the Anti-Universe and the Law of Identity. After you told us, going by your arguments—that we should take the statement to be maximal?
All of this, over these two statements and somehow these two statements subsume every single contradiction within them novel? Where exactly does Daimo get off, having High 1-A+ from this minuscule evidence again? I knew the Logical Laws argument was ridiculous enough, but this is just utterly preposterous. This is not how preponderance and the strengthening of an induction works, this is how you build cases for dogma.
Now that I understand where the points of contention come from, I absolutely hard disagree. There's nothing unique about this verse, that should be given this level of benefit of the doubt. Some of the responses I've made here, apply as a response to Qawsedf234. So take it as me disagreeing with that assessment as well.
