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From The Codex
You are no longer bound by causal closure. Your will defeats law. Kill a hundred of your children with a long blade, Auryx, and observe the change in the blade. Observe how the universe shrinks from you in terror.

Summary

The Sword Logic is both a philosophy and a metaphysical framework by which one may gain paracausal powers. It is the antithesis to the philosophy of the Light, which is associated with cooperation and sacrifice for the sake of others.

The central tenet of the Sword Logic is that "existence is the struggle to exist," and that any entity - whether a life-form or a fundamental aspect of nature - which cannot protect itself against defeat should rightfully be destroyed by a more powerful entity. In the context of intelligent beings, the Logic promotes as its ultimate goal the establishment of a systematic, self-proving civilizational structure which can survive until the end of time (and possibly beyond), an end-state often referred to as the "Last True Shape". It may be likened to the ideology of Social Darwinism, in which the survival of the fittest is paramount in all aspects of life.

The Sword Logic is what has built the entire Hive civilization and its hierarchy. Each lesser Hive must prove itself to become greater, or risk annihilation. This holds true for every Hive, from the tiny Thrall to the Ascendant Hive god-kings, including Oryx and his sisters. Even the Worm Gods are not exempt, as evidenced by Oryx slaying Akka to gain an audience with the Darkness itself. As a byproduct of the pact made with the Worm Gods, when a Hive grows stronger from the killing of lesser life-forms and those which follow the dictates of the Light and the Darkness, so does its internal worm's lust for killing, meaning that unless it is fed enough the worm will eventually consume its host.

Powers and Stats

Tier: Varies depending on the user

Name: Sword Logic, the Logic of the Sword

Origin: Destiny

Age: Preceding time

Classification: Force

Wielders: Worm gods (Akka), Ascendants (Oryx, Savathun, Xivu Arath)

Attack Potency: Varies depending on the user

Dimensionality: Varies from 4-D to 5-D to 6-D

Travel Speed: Immeasurable

Combat Speed: Immeasurable

Range: Low Complex Macroversal (Exists throughout the entire Ascendant Realm, which is a 6-D multiverse)

Powers and Abilities: Fate Manipulation (Weighs what should exist and dooms [opposition in combat]), Acausality (Types 3, 4 and 5. Sword Logic is paracausal), Physics Manipulation (Passive. Oryx's use of Sword Logic made the physics of Quria's simulated realities fall apart. See Note 1), Spatial Manipulation and Time Manipulation (Passive. Various users cause space and time to curl and screech around them constantly), Magic (Sword Logic is a power of the Darkness, which is described by lesser-minds as magic, and by the gods over it as [ishtar-collective.net/cards/xviii-leviathan-rises#books-of-sorrow witchcraft]), Law Manipulation (Users' wills defeat law)

Weaknesses: Deprives the user of empathy

Explanations

Fate Manipulation Those who cannot keep up the struggle to exist are literally fated to destruction and ruin. This is how the Darkness says the universe balances itself and sets things straight, through combat that weighs and decides a victor,

"Are you so weak? Born as prey, and doomed to die by predator?"

"War is the natural rectification of inequality. The universe’s way of pursuing equilibrium."

See here:

"If a civilization cannot defend itself, it must be annihilated. If a King cannot hold his power, he must be betrayed. The worth of a thing can be determined only by one beautiful arbiter — that thing’s ability to exist, to go on existing, to remake existence to suit its survival.

All that would oppose this arbiter is unholy and false. All the misery and terror of your ancestors springs from the lies of the Sky, who deny this truth."

This is proven later.

"It’s done. Eir and Yul feed on the Leviathan’s carcass. Xivu Arath has made a temple of the Chroma-Admiral’s impaled corpse. Below us, Savathûn’s poisons stain the Ammonite home sea black. Their screams flavor the void."

"And your people, suffering in the Deep, you became more worthy of existence than the Ammonite. You have proven it."

Paracausality: Paracausality is described as "superordinate to mere material physics," this implying superordinate to mere causality. The prefix "para" also means "adjacent to," so this implies a separate form of causality transcendent of regular causality and outside of it, or acausality types 3, 4 and 5.