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Everything posted by Ripheus23
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"Since ZFC provides us with the resources to construct ultrapowers, we can construct inner models using mice."
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"The souls of the lepidoptera finalitas contain prophecies. Think of them like flying fortune cakes..." "Be gentle! Heed the lepidoptera..."
And they said:
"Hither! Purple whispers creep! The noose is loose! Kitten and a kaboose!"
"There are 9.23 grams of marmalade dried to the base of Mrs. Losensky's blue ceramic bucket..."
"I woke up one morning to find that my nose had detached itself from my face and been transformed into a hideous, lavender-scented aardvark..."
"Apollyon likes bloody omelets..."
"There seem to be a few problems with the argument: it is too long and only quotes The Minstrel of Lettuce..."
"The quotient of a positive shirt and a negative shirt is a set of four-legged pants..."
"Good grief, it looks like I missed the coronation of my skeleton's last remarks..."
"What a mighty! I! What!"
"My nephews never believed that I used the abacus for firewood to power my mitten-crinkling machine..."
"Tsk. As if YOU had ever shaken hands with the Form of Handshakes..."
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I realized that there's a difference between proving "x is not a set of anything" and proving "x is a set of nothing," and I needed to prove that the ur-element is not a set of no elements of any set, including itself. I think I worked it out* but anyway, another result of the model was that while zero is an empty subset of other sets (a set with no elements of any other sets), so all other sets are empty subsets of zero (sets of no elements of zero). So this underscores why for all natural numbers n besides 0, the powerset is uniquely 2 to the power of n, whereas 0 to the power of 0, 1 to the power of 0, 2 the power of zero... 1 to the power of 1, 1 to the power of 2, 1 to the power of 3... = 0 ^^2 = 1 ^^ 2 = 1. <So zero is the only number before aleph-zero that has an infinite number of powerset expressions.>
*my idea is that "being a set of no elements of x" means being 0 (in relation to other numbers) and being other numbers (in relation to zero). But the relation is never defined on the ur-element. More, then, we can just define the ur-element such that it it is not a set of no elements of other sets, nor itself. In conjunction with the ur-element's not being a set of anything either, it follows that it is not a set of anything or nothing, which rules out the ur-element being a set.
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minotaur elements
minotaur ordinals
dragon ordinals
unicorn ordinals
Orpheus surreals
Osirus ordinals
Amaterasu cardinals [again]
Ragnarok cardinals
Michael cardinals
Raphael ordinals
Gabriel surreals
Asmodeus surreals
warlock ordinals
sorcerer ordinals
wizard cardinals
sortilege ordinals
demonic cardinals
leviathan transet
"kenotic transet" <said of the ur-element> and "pleromatic set"
happy cardinals
sad ordinals
priestly cardinals
hieratic ordinals
sword cardinals
sword ordinals
nuclear cardinals
nuclear ordinals
nuclear surreals
presbyter cardinals
deacon cardinals
"reformed cardinals" <so large only divine revelation can give knowledge of them>
Ezekiel cardinals
Oberon numbers
Aquinas cardinals
Nicean cardinals
irminsul ordinals
Odysseus ordinals
Aeneas surreals
Milwaukee cardinals ("a kind of joke cardinal")
cheddar ordinal
parmesan cardinal
cola ordinal
hemlock ordinal
Icarus transet
ambrosiac cardinal
cowardly cardinal
cowardly ordinal
helpless surreal
potato surreal
guitar cardinal
piano ordinal [haha]
Deseret cardinal
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Anselm cardinals. A transet in V proposed by the "cult of the universal constructor." Its elements are supposed to be "cardinals so large that only divine power could have brought them into being" or give them a reference. Note that this concept therefore requires that Anselm numbers be transfinally ordered, making the first Anselm number into the meridian of a nexus <where the Anselm section of V is the "greatest" section>.
cult of the universal constructor, the. Believers in a transcreationist model of the Godelian universal constructor. Their leader is Cardinal Mahlo [finally!], who is actually secretly working with the Septarch of Commandment (also known as Deonomy). According to the cult, it is not provable whether empirical reality was created by a divine nature, but it is provable whether mathematical reality was transcreated by a divine nature. <The argument goes: there is a possible mathematical world that was transcreated; therefore there is a possible transcreatrix; if something is a transcreatrix, it is this necessarily; therefore the transcreatrix, if it exists for any possible mathematical world, exists for all of them.>
Godelian universal constructor. An entity whose existence is supported by Godel's ontological argument. Similar to the necessary agent.
necessary agent, the. Posit of naive deontic logic: there is an obligation that exists purely from logical grounds (an obligation to "uphold" the law of non-contradiction), wherefore there is always (necessarily) an agent able to discharge the obligation. In ecograph theory, this posit is actually a principle for the manifestation of different kinds of "necessary" agents.
Deonomy. The Septarch empowered by divine-command theory. He was also the first ecoarch to manipulate the Keyscape in order to the Septatheon. (Note that ecoarchs are already a peculiar kind of "necessary agent.")
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<Why are Anselm cardinals not defined as "none greater than which can be conceived"? First, in context, there is no individual such cardinal. Second, this definition is implicit in the notion of a transfinal ordering, which attaches to the base definition by virtue of saying "divine nature" there, since a divine nature is one that transfinally orders things <or so the theory goes>. Of course, those who accepted the existence of Amida cardinals thought otherwise: these were "so large that only a mathematician gifted with divine power could access them." But these mathematicians with this gift need not be divine "inherently," only called that by reference to the power at issues (which power could well be impersonal, as in the so-called Tian model).>
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*Regarding zero: Z = {Z}, Z ~= element of ~Z, for all X, if X is not Z then X ~= an element of Z. "Zero is an element of itself, is not an element of any other set, and has no other elements besides itself." By contrast, "The ur-element is not an element of itself, is an element of only one set, and is the only element of that set" = 1.
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Haha, I finally managed to come up with a thoroughly set-theoretic foundation for my theory. The main thing is not to start with the empty set as zero. Rather, we define zero as a Quine atom (a = {a}) and 1 as the equivalent of the empty set. Here zero is the empty subset. I checked the powerset listing under this definition and it works (I couldn't get the classical definition to work, I will add).
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