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Everything posted by Ripheus23
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Finally came up with a good idea about why the engineers of the Keyscape would've failed to complete the absolute proof of the codex for the machine.
Here's the idea: an ecograph is the metrograph, not of an infinite series of infinities, but of an agent correlated with the aleph-metrographs. Now, Apollyon (the antiset) has an ecograph, the antigraph. Now Armirex, for example, thought there was enough disjunction between Apollyon and the Form of Evil that they didn't sufficiently share the antigraph between them, but anyway, the fact is that the seal on the Final Power (the Destroyer-city's disinheritance) depended on a gap in the interpretation of the antigraph's interaction with other ecographs. That is, there is a unique simple topological interface between the antigraph and any other ecograph, so that the "destruction" of the victim structure assumes a particular geometric form, and no other.
But the Host of Ripheus made an honest mistake, maybe the most honest in history ("A mistake such as only the Messiah can make," as the Esauists say). They acknowledged, through and through, the priority of the concept of good over evil, and so did not look as closely at their concept of evil as they could have, and assumed what they thought they needed to satisfy the parameters of the Keyscape (which is an isotypic graph or isograph), which proved not enough: the door to the Anomalies, that is. (At least, this is an aspect of the problem, the "error" in the codex.)
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The nightmare of antimodality is Apollyon's "definition" of transmodality from antipossibility...
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Oooh, read about a new paradox today: "K: K is unknown." Another liar-type sentence.
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I realized, if you take, "Do X," and go to, "Why do X?" you can then define a specific do-X operator recursively (in erotetic logical space) as, "Ask why." This operator can then preface itself to infinity, as aleph-zero:
Why ask "why ask 'why ask ... why ask 'why do X?'"
X itself can take the value of the formula of supererogation, which at infinity is at aleph-zero magnitude. I think, though, inputting supererogation-X into the function takes the first infinity to the power of the second, so it gives a specific higher cardinality. It is easier to represent, in this case, starting with beth-zero and succeeding by transcension alone to beth-one, because beth-one is the Continuum even if it is not equal to aleph-one. So at any rate, the why-transet ++ the supererogation-transet = a deontic transet whose degree is beth-one, i.e. is a continuous transet. This fact is specified in the autoset, which is a unique transcendental number. I.e. it is one out of all the uncountably infinite numbers encoded into the Continuum, that is used to map to the beth-one why-set, and it is not the result of any selection function but free will (within the deontic transet in general).
This might not seem helpfully clear, but it should play a role in the explanation of romantic ideality, from the apex-staircase and the heart-operator relation (which is transfinally arithmetical, it turns out), alongside the nexus-heart and so on. (I've even identified "void numbers" that are negative counterparts of ghost numbers...) At least, that's the goal.
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I think this works but I'm not sure.
Take the "unfair sentence," which = "Don't comply with this sentence." It's an imperative so it = "Don't comply with this imperative." Now, letting A for the unfair sentence:
A is not complied with if and only if it is complied with.
But by erotetic quotation, this = A is not complied with if and only if B is complied with, and B = "Comply with this imperative." This would be the imperative analogue of the disquotational exchange in assertoric logic.
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OK haha before I forget, even though this is in the YouTube version of the essay:
The liar loop can be used in a supernifty proof of the exchange theorem (that, "This sentence is false," and, "This sentence is true," are interchangeable):
- A: B is true ("The next sentence is true")
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B: A is false ("The previous sentence is false")
- "B is true," is true if and only if A is false.
- "A is false," is true if and only if B is false.
- But "if and only if" = identity.
- Therefore, "A: A is false," and, "B: B is true."
In other words, the liar loop "turns into" the conjunction of the liar and honest sentences.
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Ixthos brought up the case of ("Yields falsehood when preceded by its quotation" yields falsehood when preceded by its quotation), which I hadn't considered, but now I think the erotetic 'trick' works here too, and in the way my dialogical approach to the liar index works. But idk...
