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The logic (理 kotowari, localized as the reason) are the absolute fundamentals of the world. It consists of the four elements: fire, earth, water and wind and the Two Origins (二大起源 Ni dai Kigen), light and darkness.
There exists one known mortal being who is outside of the logic: Valkenhayn R. Hellsing, the implied reason behind this is that he was created from sorcery. Another being who existed outside of the logic before its death was the Black Beast; because it existed outside of the fundamentals, it was close to invincible, as not even nuclear weapons could dent its hide. To counter it, weapons had to be created outside of the logic to fight back; Ars Magus, Ars Armagus and the Nox Nyctores were the eventual products. Rachel Alucard also exists outside of the logic, although it is implied that all vampires are.
In the ancient past, humanity created magic in order to combat beings that existed outside of the logic. Sorcery is actually slightly related to the logic, unlike magic, which utilizes only seithr. An example being that a flame created from the practice will still burn a piece of paper like an ordinary flame would; what separates the average flame and the one created via sorcery, however, is that a flame created through sorcery can harm those outside of the logic.